Concept explainers
Carry out the following operations as if they were calculations of experimental results, and express each answer in the correct units with the correct number of significant figures:
- (a) 7.310 km ÷ 5.70 km
- (b) (3.26 × 10−3 mg) × (7.88 × 10−5 mg)
- (c) (4.02 × 106 dm) + (7.74 × 107 dm)
- (d) (7.8 m − 0.34 m)/(1.15 s + 0.82 s)
(a)
Interpretation:
The given mathematical operation has to be done in right way and the answer should be written in correct unit with the correct number of significant figures.
Concept introduction:
Significant figures are all the digits in a measurement that are known with certainty.
Rules for significant digits
- Digits from 1 to 9 are always significant
- Zeros between two other significant digits are always significant.
- One or more additional zeroes to the right of both the decimal place and other significant digits are significant.
- Zeroes used solely for spacing the decimal point are not significant.
Rules for rounding off numbers
If the digits to the immediate right of the last significant figure are less than five do not change.
Example:
If the digit to the immediate right of the last significant figures is greater than five, round up the last significant figures.
Example:
Explanation of Solution
Given,
All the given terms are in same unit so conversions of units are not required. This division operation can be done as follows,
The three in
The answer with correct unit with the correct number of significant figures is
(b)
Interpretation:
The given mathematical operation has to be done in right way and the answer should be written in correct unit with the correct number of significant figures.
Concept introduction:
Significant figures are all the digits in a measurement that are known with certainty.
Rules for significant digits
- Digits from 1 to 9 are always significant
- Zeros between two other significant digits are always significant
- One or more additional zeroes to the right of both the decimal place and other significant digits are significant.
- Zeroes used solely for spacing the decimal point are not significant.
Rules for rounding off numbers
If the digits to the immediate right of the last significant figure are less than five do not change.
Example:
If the digit to the immediate right of the last significant figures is greater than five, round up the last significant figures.
Example:
Explanation of Solution
Given,
All the given terms are in same unit so conversions of units are not required. This subtraction operation can be done as follows,
Writing both numbers in decimal notation,
The answer with correct unit with the correct number of significant figures is
The bolded digits in
(c)
Interpretation:
The given mathematical operation has to be done in right way and the answer should be written in correct unit with the correct number of significant figures.
Concept introduction:
Significant figures are all the digits in a measurement that are known with certainty.
Rules for significant digits
- Digits from 1 to 9 are always significant
- Zeros between two other significant digits are always significant.
- One or more additional zeroes to the right of both the decimal place and other significant digits are significant.
- Zeroes used solely for spacing the decimal point are not significant.
Rules for rounding off numbers
If the digits to the immediate right of the last significant figure are less than five do not change.
Example:
If the digit to the immediate right of the last significant figures is greater than five, round up the last significant figures.
Example:
Explanation of Solution
Given,
All the given terms are in same unit so conversions of units are not required. This addition operation can be done as follows,
Writing both number with exponents which is equal to
The answer with correct unit with the correct number of significant figures is
(d)
Interpretation:
The given mathematical operation has to be done in right way and the answer should be written in correct unit with the correct number of significant figures.
Concept introduction:
Significant figures are all the digits in a measurement that are known with certainty.
Rules for significant digits
- Digits from 1 to 9 are always significant
- Zeros between two other significant digits are always significant.
- One or more additional zeroes to the right of both the decimal place and other significant digits are significant.
- Zeroes used solely for spacing the decimal point are not significant.
Rules for rounding off numbers
If the digits to the immediate right of the last significant figure are less than five do not change.
Example:
If the digit to the immediate right of the last significant figures is greater than five, round up the last significant figures.
Example:
Explanation of Solution
Given,
This subtraction, addition and division operation can be done as follows,
The answer with correct unit with the correct number of significant figures is
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