Question

significant figures in calculations
when we add or subtract numbers, we should round the result to the same number of
________ as the number with the least number of ________ places (i.e., the least certain
value in terms of addition and subtraction).

when we multiply or divide numbers, we should round the result to the same number of
________ as the number with the least number of ________ figures (the least certain value
in terms of multiplication and division).

calculations
worksheet:

1. 2.01 m + 0.97 m = __________
2. 100.23 g - 99.99 g = __________
3. 10.1 cm * 2.0 cm = __________
4. 20.00 l / 3.0 l = __________
5. 9.999 s + 0.002 s = __________
6. 5.50 m - 2.2 m = __________

Explanation:

Step1: Recall addition rule

For addition and subtraction, round to the same number of decimal places as the number with the least number of decimal places.

Step2: Recall multiplication - division rule

For multiplication and division, round to the same number of significant figures as the number with the least number of significant figures.

Step3: Solve 1

$2.01\ m+0.97\ m = 2.98\ m$ (both numbers have 2 decimal - places, no rounding needed).

Step4: Solve 2

$100.23\ g - 99.99\ g=0.24\ g$ (both numbers have 2 decimal - places, no rounding needed).

Step5: Solve 3

$10.1\ cm\times2.0\ cm = 20.2\ cm^{2}$. 10.1 has 3 significant figures and 2.0 has 2 significant figures. Rounding 20.2 to 2 significant figures gives $20\ cm^{2}$.

Step6: Solve 4

$20.00\ L\div3.0\ L=\frac{20.00}{3.0}\approx6.67$. 3.0 has 2 significant figures, rounding 6.67 to 2 significant figures gives $6.7\ L$.

Step7: Solve 5

$9.999\ s + 0.002\ s=10.001\ s$. 0.002 has 3 decimal - places, rounding 10.001 to 3 decimal - places gives $10.001\ s$.

Step8: Solve 6

$5.50\ m - 2.2\ m$. 2.2 has 1 decimal - place. $5.50 - 2.2 = 3.3\ m$.

Answer:

1. $2.98\ m$
2. $0.24\ g$
3. $20\ cm^{2}$
4. $6.7\ L$
5. $10.001\ s$
6. $3.3\ m$