Chapter MH, Problem 5PP

Solution

(a)

Interpretation : The given measurement is to be rounded off to three significant figures.

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

The answer in three significant figures is $2.75\text{g}$ .

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

There is a set of rules to detect the digits in a significant measured value.

Round the number to three significant figures in the measurement.

If the 4^th digit number is greater than or equal to 5, then the 3^rd digit is added up by the number 1 while leaving the remaining digit after the 4^th digit is simply dropped. If the 4^th digit number is lesser than 5, then the values till the 3^rd digit are alone taken up.

The given question is $2.7518\text{g}$ .

The significant figure is given as:

  $2.7518\text{g}\text{=}2.75\text{g}$

(b)

Interpretation : The given measurement is to be rounded off to two significant figures.

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

The answer in two significant figures is $8.6\text{m}$ .

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

There is a set of rules to detect the digits in a significant measured value.

Round the number to two significant figures in the measurement.

If the 3^rd digit number is greater than or equal to 5, then the 2^nd digit is added up by the number 1 while leaving the remaining digit after the 3^rd digit is simply dropped. If the 3^rd digit number is lesser than 5, then the values till the 2^nd digit are alone taken up.

The given question is $8.6439\text{m}$ .

The significant figure is given as:

  $8.6439\text{m}\text{=}8.6\text{m}$

(c)

Interpretation : The given measurement is to be rounded off to two significant figures.

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

The answer in two significant figures is $14\text{g}$ .

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

There is a set of rules to detect the digits in a significant measured value.

Round the number to three significant figures in the measurement.

If the 3^rd digit number is greater than or equal to 5, then the 2^nd digit is added up by the number 1 while leaving the remaining digit after the 3^rd digit is simply dropped. If the 3^rd digit number is lesser than 5, then the values till the 2^nd digit are alone taken up.

The given question is $13.841\text{g}$ .

The significant figure is given as:

  $13.841\text{g}\text{=}14\text{g}$

(d)

Interpretation : The given measurement is to be rounded off to five significant figures.

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

The answer in five significant figures is $186.50\text{m}$ .

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

There is a set of rules to detect the digits in a significant measured value.

Round the number to five significant figures in the measurement.

If the 6^th digit number is greater than or equal to 5, then the 5^th digit is added up by the number 1 while leaving the remaining digit after the 6^th digit is simply dropped. If the 6^th digit number is lesser than 5, then the values till the 5^th digit are alone taken up.

The given question is $186.499\text{m}$ .

The significant figure is given as:

  $186.499\text{m}\text{=}186.50\text{m}$

(e)

Interpretation : The given measurement is to be rounded off to four significant figures.

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

The answer in four significant figures is $634900$ .

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

There is a set of rules to detect the digits in a significant measured value.

Round the number to three significant figures in the measurement.

If the 5^th digit number is greater than or equal to 5, then the 4^th digit is added up by the number 1 while leaving the remaining digit after the 5^th digit is simply dropped. If the 5^th digit number is lesser than 5, then the values till the 4^th digit are alone taken up.

The given question is $634892.34$ .

The significant figure is given as:

  $634892.34=634900$

(f)

Interpretation : The given measurement is to be rounded off to two significant figures.

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

The answer in two significant figures is $360000\text{g}$ .

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

There is a set of rules to detect the digits in a significant measured value.

Round the number to three significant figures in the measurement.

If the 3^rd digit number is greater than or equal to 5, then the 2^nd digit is added up by the number 1 while leaving the remaining digit after the 3^rd digit is simply dropped. If the 3^rd digit number is lesser than 5, then the values till the 2^nd digit are alone taken up.

The given question is $355500\text{g}$ .

The significant figure is given as:

  $355500\text{g}\text{=}360000\text{g}$