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Carry out the following operations as if they

Chapter 1, Problem 36P

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QUESTION:

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) \(7.310\mathrm{\ km}\div5.70\mathrm{\ km}\)

(b) \(\left(3.26 \times 10^{-3} \ \mathrm{mg}\right)-\left(7.88 \times 10^{-5} \ \mathrm{mg}\right)\)

(c) \(\left(4.02 \times 10^{6} \ \mathrm{dm}\right)+\left(7.74 \times 10^{7} \ \mathrm{dm}\right)\)

(d) \((7.8m-0.34\ m)/(1.15s+0.82\ s)\)

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QUESTION:

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) \(7.310\mathrm{\ km}\div5.70\mathrm{\ km}\)

(b) \(\left(3.26 \times 10^{-3} \ \mathrm{mg}\right)-\left(7.88 \times 10^{-5} \ \mathrm{mg}\right)\)

(c) \(\left(4.02 \times 10^{6} \ \mathrm{dm}\right)+\left(7.74 \times 10^{7} \ \mathrm{dm}\right)\)

(d) \((7.8m-0.34\ m)/(1.15s+0.82\ s)\)

ANSWER:

Step 1 of 2

Here, we are asked to perform the calculations and express each answer in the correct units with the correct number of significant figures:

Significant figures refer to the number of single digits from 0 to 9, in the coefficient of an expression in a scientific notation.

The rules for rounding of significant numbers are:

(1) For Multiplication and Division: Among the given numbers, the number with least significant figures determine the number of significant figures in the answer.  

(2) For Addition and Subtraction: Here, we look only at the numbers that are to the right of the decimal point. The number of significant figures in the answer is determined by rounding the answer to the least number of the decimal part of any number.

 

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