Chapter MH, Problem 4PP

Solution

a)

Interpretation : The number of significant figures in the measurement is to be determined.

Concept Introduction : The known digits plus the last, estimated digit make up the significant figures in a measurement.

The number of significant figures is infinite.

The known digits plus the last, estimated digit make up the significant figures in a measurement.

Because calculated results frequently depend on the number of significant figures in the values used in the calculation, measurements must always be reported to the right number of significant figures.

There is a set of rules to detect the digits in a significant measured value. The rules are as follows:

1. It is assumed that every nonzero digit in a given measurement is significant.
2. Zeros that come in between nonzero numbers are significant.
3. A zero following a decimal point and to the right of it are both always significant.
4. Zeros that are to the left of an understandable decimal point at the rightmost end of measurement are not significant.
5. In some cases, a number may have an infinite number of significant figures.

The given measurement is $35\text{g}$ .

The measurement is the exact count. According to rule 5, the significant figure is infinite.

b)

Interpretation : The number of significant figures in the measurement is to be determined.

Concept Introduction : The known digits plus the last, estimated digit make up the significant figures in a measurement.

The number of significant figures is $3$ .

The known digits plus the last, estimated digit make up the significant figures in a measurement.

Because calculated results frequently depend on the number of significant figures in the values used in the calculation, measurements must always be reported to the right number of significant figures.

There is a set of rules to detect the digits in a measured value that is significant. The rules are as follows:

1. It is assumed that every nonzero digit in a given measurement is significant.
2. Zeros that come in between nonzero numbers are significant.
3. A zero following a decimal point and to the right of it are both always significant.
4. Zeros that are to the left of an understandable decimal point at the rightmost end of measurement are not significant.
5. In some cases, a number may have an infinite number of significant figures.

The given measurement is $3.57\text{m}$ .

According to rule 1, the significant figure is $3$ .

c)

Interpretation : The number of significant figures in the measurement is to be determined.

Concept Introduction : The known digits plus the last, estimated digit make up the significant figures in a measurement.

The number of significant figures is $4$ .

The known digits plus the last, estimated digit make up the significant figures in a measurement.

Because calculated results frequently depend on the number of significant figures in the values used in the calculation, measurements must always be reported to the right number of significant figures.

There is a set of rules to detect the digits in a significant measured value. The rules are as follows:

1. It is assumed that every nonzero digit in a given measurement is significant.
2. Zeros that come in between nonzero numbers are significant.
3. A zero following a decimal point and to the right of it are both always significant.
4. Zeros that are to the left of an understandable decimal point at the rightmost end of measurement are not significant.
5. In some cases, a number may have an infinite number of significant figures.

The given measurement is $3.507\text{km}$ .

According to rules 1 and 2, the significant figure is $4$ .

d)

Interpretation : The number of significant figures in the measurement is to be determined.

Concept Introduction : The known digits plus the last, estimated digit make up the significant figures in a measurement.

The number of significant figures is $2$ .

The known digits plus the last, estimated digit make up the significant figures in a measurement.

Because calculated results frequently depend on the number of significant figures in the values used in the calculation, measurements must always be reported to the right number of significant figures.

There is a set of rules to detect the digits in a significant measured value. The rules are as follows:

1. It is assumed that every nonzero digit in a given measurement is significant.
2. Zeros that come in between nonzero numbers are significant.
3. A zero following a decimal point and to the right of it are both always significant.
4. Zeros that are to the left of an understandable decimal point at the rightmost end of measurement are not significant.
5. In some cases, a number may have an infinite number of significant figures.

The given measurement is $0.035\text{kg}$ .

According to rule 4, the significant figure is $2$ .

e)

Interpretation : The number of significant figures in the measurement is to be determined.

Concept Introduction : The known digits plus the last, estimated digit make up the significant figures in a measurement.

The number of significant figures is $3$ .

The known digits plus the last, estimated digit make up the significant figures in a measurement.

Because calculated results frequently depend on the number of significant figures in the values used in the calculation, measurements must always be reported to the right number of significant figures.

There is a set of rules to detect the digits in a significant measured value. The rules are as follows:

1. It is assumed that every nonzero digit in a given measurement is significant.
2. Zeros that come in between nonzero numbers are significant.
3. A zero following a decimal point and to the right of it are both always significant.
4. Zeros that are to the left of an understandable decimal point at the rightmost end of measurement are not significant.
5. In some cases, a number may have an infinite number of significant figures.

The given measurement is $0.246\text{L}$ .

According to rule 4, the significant figure is $3$ .

f)

Interpretation : The number of significant figures in the measurement is to be determined.

Concept Introduction : The known digits plus the last, estimated digit make up the significant figures in a measurement.

The number of significant figures is $1$ .

The known digits plus the last, estimated digit make up the significant figures in a measurement.

Because calculated results frequently depend on the number of significant figures in the values used in the calculation, measurements must always be reported to the right number of significant figures.

There is a set of rules to detect the digits in a significant measured value. The rules are as follows:

1. It is assumed that every nonzero digit in a given measurement is significant.
2. Zeros that come in between nonzero numbers are significant.
3. A zero following a decimal point and to the right of it are both always significant.
4. Zeros that are to the left of an understandable decimal point at the rightmost end of measurement are not significant.
5. In some cases, a number may have an infinite number of significant figures.

The given measurement is $0.004{\text{m}}^3$ .

According to rule 4, the significant figure is $1$ .

g)

Interpretation : The number of significant figures in the measurement is to be determined.

Concept Introduction : The known digits plus the last, estimated digit make up the significant figures in a measurement.

The number of significant figures is $5$ .

The known digits plus the last, estimated digit make up the significant figures in a measurement.

Because calculated results frequently depend on the number of significant figures in the values used in the calculation, measurements must always be reported to the right number of significant figures.

There is a set of rules to detect the digits in a significant measured value. The rules are as follows:

1. It is assumed that every nonzero digit in a given measurement is significant.
2. Zeros that come in between nonzero numbers are significant.
3. A zero following a decimal point and to the right of it are both always significant.
4. Zeros that are to the left of an understandable decimal point at the rightmost end of measurement are not significant.
5. In some cases, a number may have an infinite number of significant figures.

The given measurement is $24.068\text{kPa}$ .

According to rules 1 and 2, the significant figure is $5$ .

h)

Interpretation : The number of significant figures in the measurement is to be determined.

Concept Introduction : The known digits plus the last, estimated digit make up the significant figures in a measurement.

The number of significant figures is infinite.

The known digits plus the last, estimated digit make up the significant figures in a measurement.

Because calculated results frequently depend on the number of significant figures in the values used in the calculation, measurements must always be reported to the right number of significant figures.

There is a set of rules to detect the digits in a significant measured value. The rules are as follows:

1. It is assumed that every nonzero digit in a given measurement is significant.
2. Zeros that come in between nonzero numbers are significant.
3. A zero following a decimal point and to the right of it are both always significant.
4. Zeros that are to the left of an understandable decimal point at the rightmost end of measurement are not significant.
5. In some cases, a number may have an infinite number of significant figures.

The given measurement is $268\text{K}$ .

The measurement is an exact value. According to rule 5, the significant figure is infinite.

i)

Interpretation : The number of significant figures in the measurement is to be determined.

Concept Introduction : The known digits plus the last, estimated digit make up the significant figures in a measurement.

The number of significant figures is $7$ .

The known digits plus the last, estimated digit make up the significant figures in a measurement.

Because calculated results frequently depend on the number of significant figures in the values used in the calculation, measurements must always be reported to the right number of significant figures.

There is a set of rules to detect the digits in a significant measured value. The rules are as follows:

1. It is assumed that every nonzero digit in a given measurement is significant.
2. Zeros that come in between nonzero numbers are significant.
3. A zero following a decimal point and to the right of it are both always significant.
4. Zeros that are to the left of an understandable decimal point at the rightmost end of measurement are not significant.
5. In some cases, a number may have an infinite number of significant figures.

The given measurement is $20.04080\text{g}$ .

According to rules 1 and 2, the significant figure is $7$ .

j)

Interpretation : The number of significant figures in the measurement is to be determined.

Concept Introduction : The known digits plus the last, estimated digit make up the significant figures in a measurement.

The number of significant figures is infinite.

The known digits plus the last, estimated digit make up the significant figures in a measurement.

Because calculated results frequently depend on the number of significant figures in the values used in the calculation, measurements must always be reported to the right number of significant figures.

There is a set of rules to detect the digits in a significant measured value. The rules are as follows:

1. It is assumed that every nonzero digit in a given measurement is significant.
2. Zeros that come in between nonzero numbers are significant.
3. A zero following a decimal point and to the right of it are both always significant.
4. Zeros that are to the left of an understandable decimal point at the rightmost end of measurement are not significant.
5. In some cases, a number may have an infinite number of significant figures.

The given measurement is $20\text{dozen}$ .

The measurement is an exact count. According to rule 5, the significant figure is infinite.

k)

Interpretation : The number of significant figures in the measurement is to be determined.

Concept Introduction : The known digits plus the last, estimated digit make up the significant figures in a measurement.

The number of significant figures is infinite.

The known digits plus the last, estimated digit make up the significant figures in a measurement.

Because calculated results frequently depend on the number of significant figures in the values used in the calculation, measurements must always be reported to the right number of significant figures.

There is a set of rules to detect the digits in a significant measured value. The rules are as follows:

1. It is assumed that every nonzero digit in a given measurement is significant.
2. Zeros that come in between nonzero numbers are significant.
3. A zero following a decimal point and to the right of it are both always significant.
4. Zeros that are to the left of an understandable decimal point at the rightmost end of measurement are not significant.
5. In some cases, a number may have an infinite number of significant figures.

The given measurement is $730000\text{kg}$ .

The measurement is an exact count. According to rule 5, the significant figure is infinite.

l)

Interpretation : The number of significant figures in the measurement is to be determined.

Concept Introduction : The known digits plus the last, estimated digit make up the significant figures in a measurement.

The number of significant figures is $4$ .

The known digits plus the last, estimated digit make up the significant figures in a measurement.

Because calculated results frequently depend on the number of significant figures in the values used in the calculation, measurements must always be reported to the right number of significant figures.

There is a set of rules to detect the digits in a significant measured value. The rules are as follows:

1. It is assumed that every nonzero digit in a given measurement is significant.
2. Zeros that come in between nonzero numbers are significant.
3. A zero following a decimal point and to the right of it are both always significant.
4. Zeros that are to the left of an understandable decimal point at the rightmost end of measurement are not significant.
5. In some cases, a number may have an infinite number of significant figures.

The given measurement is $6.751\text{g}$ .

According to rule 1, the significant figure is $4$ .

m)

Interpretation : The number of significant figures in the measurement is to be determined.

Concept Introduction : The known digits plus the last, estimated digit make up the significant figures in a measurement.

The number of significant figures is $3$ .

The known digits plus the last, estimated digit make up the significant figures in a measurement.

Because calculated results frequently depend on the number of significant figures in the values used in the calculation, measurements must always be reported to the right number of significant figures.

There is a set of rules to detect the digits in a significant measured value. The rules are as follows:

1. It is assumed that every nonzero digit in a given measurement is significant.
2. Zeros that come in between nonzero numbers are significant.
3. A zero following a decimal point and to the right of it are both always significant.
4. Zeros that are to the left of an understandable decimal point at the rightmost end of measurement are not significant.
5. In some cases, a number may have an infinite number of significant figures.

The given measurement is $0.157\text{kg}$ .

According to rules 1 and 4, the significant figure is $3$ .

n)

Interpretation : The number of significant figures in the measurement is to be determined.

Concept Introduction : The known digits plus the last, estimated digit make up the significant figures in a measurement.

The number of significant figures is $3$ .

The known digits plus the last, estimated digit make up the significant figures in a measurement.

Because calculated results frequently depend on the number of significant figures in the values used in the calculation, measurements must always be reported to the right number of significant figures.

There is a set of rules to detect the digits in a significant measured value. The rules are as follows:

1. It is assumed that every nonzero digit in a given measurement is significant.
2. Zeros that come in between nonzero numbers are significant.
3. A zero following a decimal point and to the right of it are both always significant.
4. Zeros that are to the left of an understandable decimal point at the rightmost end of measurement are not significant.
5. In some cases, a number may have an infinite number of significant figures.

The given measurement is $28.0\text{ml}$ .

According to rules 1 and 3, the significant figure is $3$ .

o)

Interpretation : The number of significant figures in the measurement is to be determined.

Concept Introduction : The known digits plus the last, estimated digit make up the significant figures in a measurement.

The number of significant figures is infinite.

The known digits plus the last, estimated digit make up the significant figures in a measurement.

Because calculated results frequently depend on the number of significant figures in the values used in the calculation, measurements must always be reported to the right number of significant figures.

There is a set of rules to detect the digits in a significant measured value. The rules are as follows:

1. It is assumed that every nonzero digit in a given measurement is significant.
2. Zeros that come in between nonzero numbers are significant.
3. A zero following a decimal point and to the right of it are both always significant.
4. Zeros that are to the left of an understandable decimal point at the rightmost end of measurement are not significant.
5. In some cases, a number may have an infinite number of significant figures.

The given measurement is $2500\text{m}$ .

The measurement is an exact count. According to rule 5, the significant figure is infinite.

p)

Interpretation : The number of significant figures in the measurement is to be determined.

Concept Introduction : The known digits plus the last, estimated digit make up the significant figures in a measurement.

The number of significant figures is $2$ .

The known digits plus the last, estimated digit make up the significant figures in a measurement.

Because calculated results frequently depend on the number of significant figures in the values used in the calculation, measurements must always be reported to the right number of significant figures.

There is a set of rules to detect the digits in a significant measured value. The rules are as follows:

1. It is assumed that every nonzero digit in a given measurement is significant.
2. Zeros that come in between nonzero numbers are significant.
3. A zero following a decimal point and to the right of it are both always significant.
4. Zeros that are to the left of an understandable decimal point at the rightmost end of measurement are not significant.
5. In some cases, a number may have an infinite number of significant figures.

The given measurement is $0.070\text{mol}$ .

According to rules 3 and 4, the significant figure is $2$ .

q)

Interpretation : The number of significant figures in the measurement is to be determined.

Concept Introduction : The known digits plus the last, estimated digit make up the significant figures in a measurement.

The number of significant figures is $4$ .

The known digits plus the last, estimated digit make up the significant figures in a measurement.

Because calculated results frequently depend on the number of significant figures in the values used in the calculation, measurements must always be reported to the right number of significant figures.

There is a set of rules to detect the digits in a significant measured value. The rules are as follows:

1. It is assumed that every nonzero digit in a given measurement is significant.
2. Zeros that come in between nonzero numbers are significant.
3. A zero following a decimal point and to the right of it are both always significant.
4. Zeros that are to the left of an understandable decimal point at the rightmost end of measurement are not significant.
5. In some cases, a number may have an infinite number of significant figures.

The given measurement is $30.07\text{nm}$ .

According to rules 1 and 2, the significant figure is $4$ .

r)

Interpretation : The number of significant figures in the measurement is to be determined.

Concept Introduction : The known digits plus the last, estimated digit make up the significant figures in a measurement.

The number of significant figures is $3$ .

The known digits plus the last, estimated digit make up the significant figures in a measurement.

Because calculated results frequently depend on the number of significant figures in the values used in the calculation, measurements must always be reported to the right number of significant figures.

There is a set of rules to detect the digits in a significant measured value. The rules are as follows:

1. It is assumed that every nonzero digit in a given measurement is significant.
2. Zeros that come in between nonzero numbers are significant.
3. A zero following a decimal point and to the right of it are both always significant.
4. Zeros that are to the left of an understandable decimal point at the rightmost end of measurement are not significant.
5. In some cases, a number may have an infinite number of significant figures.

The given measurement is $0.106\text{cm}$ .

According to rules 1 and 4, the significant figure is $3$ .

s)

Interpretation : The number of significant figures in the measurement is to be determined.

Concept Introduction : The known digits plus the last, estimated digit make up the significant figures in a measurement.

The number of significant figures is $2$ .

The known digits plus the last, estimated digit make up the significant figures in a measurement.

Because calculated results frequently depend on the number of significant figures in the values used in the calculation, measurements must always be reported to the right number of significant figures.

There is a set of rules to detect the digits in a significant measured value. The rules are as follows:

1. It is assumed that every nonzero digit in a given measurement is significant.
2. Zeros that come in between nonzero numbers are significant.
3. A zero following a decimal point and to the right of it are both always significant.
4. Zeros that are to the left of an understandable decimal point at the rightmost end of measurement are not significant.
5. In some cases, a number may have an infinite number of significant figures.

The given measurement is $0.0076\text{g}$ .

According to rules 1 and 4, the significant figure is $2$ .

t)

Interpretation : The number of significant figures in the measurement is to be determined.

Concept Introduction : The known digits plus the last, estimated digit make up the significant figures in a measurement.

The number of significant figures is $3$ .

The known digits plus the last, estimated digit make up the significant figures in a measurement.

Because calculated results frequently depend on the number of significant figures in the values used in the calculation, measurements must always be reported to the right number of significant figures.

There is a set of rules to detect the digits in a significant measured value. The rules are as follows:

1. It is assumed that every nonzero digit in a given measurement is significant.
2. Zeros that come in between nonzero numbers are significant.
3. A zero following a decimal point and to the right of it are both always significant.
4. Zeros that are to the left of an understandable decimal point at the rightmost end of measurement are not significant.
5. In some cases, a number may have an infinite number of significant figures.

The given measurement is $0.0230{\text{cm}}^3$ .

According to rules 1 and 4, the significant figure is $3$ .

u)

Interpretation : The number of significant figures in the measurement is to be determined.

Concept Introduction : The known digits plus the last, estimated digit make up the significant figures in a measurement.

The number of significant figures is $5$ .

The known digits plus the last, estimated digit make up the significant figures in a measurement.

Because calculated results frequently depend on the number of significant figures in the values used in the calculation, measurements must always be reported to the right number of significant figures.

There is a set of rules to detect the digits in a significant measured value. The rules are as follows:

1. It is assumed that every nonzero digit in a given measurement is significant.
2. Zeros that come in between nonzero numbers are significant.
3. A zero following a decimal point and to the right of it are both always significant.
4. Zeros that are to the left of an understandable decimal point at the rightmost end of measurement are not significant.
5. In some cases, a number may have an infinite number of significant figures.

The given measurement is $26.509\text{cm}$ .

According to rules 1 and 2, the significant figure is $5$ .

v)

Interpretation : The number of significant figures in the measurement is to be determined.

Concept Introduction : The known digits plus the last, estimated digit make up the significant figures in a measurement.

The number of significant figures is $4$ .

The known digits plus the last, estimated digit make up the significant figures in a measurement.

Because calculated results frequently depend on the number of significant figures in the values used in the calculation, measurements must always be reported to the right number of significant figures.

There is a set of rules to detect the digits in a significant measured value. The rules are as follows:

1. It is assumed that every nonzero digit in a given measurement is significant.
2. Zeros that come in between nonzero numbers are significant.
3. A zero following a decimal point and to the right of it are both always significant.
4. Zeros that are to the left of an understandable decimal point at the rightmost end of measurement are not significant.
5. In some cases, a number may have an infinite number of significant figures.

The given measurement is $54.52{\text{cm}}^3$ .

According to rule 1, the significant figure is $4$ .

w)

Interpretation : The number of significant figures in the measurement is to be determined.

Concept Introduction : The known digits plus the last, estimated digit make up the significant figures in a measurement.

The number of significant figures is $3$ .

The known digits plus the last, estimated digit make up the significant figures in a measurement.

Because calculated results frequently depend on the number of significant figures in the values used in the calculation, measurements must always be reported to the right number of significant figures.

There is a set of rules to detect the digits in a significant measured value. The rules are as follows:

1. It is assumed that every nonzero digit in a given measurement is significant.
2. Zeros that come in between nonzero numbers are significant.
3. A zero following a decimal point and to the right of it are both always significant.
4. Zeros that are to the left of an understandable decimal point at the rightmost end of measurement are not significant.
5. In some cases, a number may have an infinite number of significant figures.

The given measurement is $2.40\times {10}^6\text{kg}$ .

According to rules 1 and 3, the significant figure is $3$ .

x)

Interpretation : The number of significant figures in the measurement is to be determined.

Concept Introduction : The known digits plus the last, estimated digit make up the significant figures in a measurement.

The number of significant figures is $3$ .

The known digits plus the last, estimated digit make up the significant figures in a measurement.

Because calculated results frequently depend on the number of significant figures in the values used in the calculation, measurements must always be reported to the right number of significant figures.

There is a set of rules to detect the digits in a significant measured value. The rules are as follows:

1. It is assumed that every nonzero digit in a given measurement is significant.
2. Zeros that come in between nonzero numbers are significant.
3. A zero following a decimal point and to the right of it are both always significant.
4. Zeros that are to the left of an understandable decimal point at the rightmost end of measurement are not significant.
5. In some cases, a number may have an infinite number of significant figures.

The given measurement is $4.07\times {10}^{16}\text{m}$ .

According to rules 1 and 2, the significant figure is $3$ .