Question

1. explain how to round answers to the correct number of significant figures when adding or subtracting.
2. explain how to round answer to the correct number of significant figures when multiplying or dividing.

calculations: be sure to round your answers to the correct number of sig figs and record the correct units.

1. 81.32 m / 6.50 s =
2. 2.099 cm + 0.05681 cm =
3. 102 mm - 1.6 mm =
4. 87.3 g - 1.655 g =
5. 3.1000 m - 1.99 m =
6. 1.34 km x 0.075 km =
7. 0.3287 mm x 45.2 mm =
8. 789.2 m x 2.55 m =
9. 45.45 g / 2.4 ml =
10. 2.22 g + 8.8 g =

Explanation:

Step1: Rule for addition - subtraction

When adding or subtracting, round to the least - precise decimal place among the values being added or subtracted.

Step2: Rule for multiplication - division

When multiplying or dividing, round to the least number of significant figures among the values being multiplied or divided.

Step3: Solve 13)

$81.32\ m\div6.50\ s=\frac{81.32}{6.50}\ m/s\approx12.5\ m/s$ (3 significant figures as 6.50 has 3 significant figures).

Step4: Solve 14)

$2.099\ cm + 0.05681\ cm=2.15581\ cm\approx2.156\ cm$ (rounded to 4 decimal places as 2.099 is least precise to 3 decimal places).

Step5: Solve 15)

$102\ mm-1.6\ mm = 100.4\ mm\approx100\ mm$ (rounded to the ones place as 102 is least precise to the ones place).

Step6: Solve 16)

$87.3\ g-1.655\ g=85.645\ g\approx85.6\ g$ (rounded to 1 decimal place as 87.3 is least precise to 1 decimal place).

Step7: Solve 17)

$3.1000\ m - 1.99\ m=1.11\ m$ (rounded to 2 decimal places as 1.99 is least precise to 2 decimal places).

Step8: Solve 18)

$1.34\ km\times0.075\ km = 0.1005\ km^{2}\approx0.10\ km^{2}$ (2 significant figures as 0.075 has 2 significant figures).

Step9: Solve 19)

$0.3287\ mm\times45.2\ mm=14.86724\ mm^{2}\approx14.9\ mm^{2}$ (3 significant figures as 45.2 has 3 significant figures).

Step10: Solve 20)

$789.2\ m\times2.55\ m = 2012.46\ m^{2}\approx2010\ m^{2}$ (3 significant figures as 2.55 has 3 significant figures).

Step11: Solve 21)

$45.45\ g\div2.4\ mL=\frac{45.45}{2.4}\ g/mL\approx19\ g/mL$ (2 significant figures as 2.4 has 2 significant figures).

Step12: Solve 22)

$2.22\ g+8.8\ g = 11.02\ g\approx11.0\ g$ (rounded to 1 decimal place as 8.8 is least precise to 1 decimal place).

Answer:

1. $12.5\ m/s$
2. $2.156\ cm$
3. $100\ mm$
4. $85.6\ g$
5. $1.11\ m$
6. $0.10\ km^{2}$
7. $14.9\ mm^{2}$
8. $2010\ m^{2}$
9. $19\ g/mL$
10. $11.0\ g$