Question

1. solve the following problems using the correct number of significant figures each time.

a. 10.8 g - 8.264 g
=1.936 to 1.9 (3 sig figs)
b. 4.75 m - 0.4168 m
0.017136m^2 to 0.017m^2 (2 sig figs)
c. 139 cm × 2.3 cm
319.7 cm^2 to
d. 12.78 g / 11.3 ml
e. 1.6 km + 1.62 m + 1,200 cm

Explanation:

Step1: Perform subtraction for a

$10.8 - 8.264=1.936$. The number 10.8 has 3 significant - figures. Rounding 1.936 to 3 significant - figures gives 1.9.

Step2: Perform subtraction for b

$4.75−0.4168 = 4.3332$. The number 4.75 has 3 significant - figures. Rounding 4.3332 to 3 significant - figures gives 4.33. (There is an error in the original for part b as it seems to be an incorrect operation or wrong result shown).

Step3: Perform multiplication for c

$139\times2.3 = 319.7$. The number 2.3 has 2 significant - figures. Rounding 319.7 to 2 significant - figures gives $3.2\times10^{2}\text{ cm}^2$.

Step4: Perform division for d

$\frac{12.78}{11.3}\approx1.131$. The number 11.3 has 3 significant - figures. Rounding 1.131 to 3 significant - figures gives 1.13 g/mL.

Step5: Convert units and perform addition for e

First, convert all lengths to the same unit (meters). $1.6\text{ km}=1600\text{ m}$, $1200\text{ cm} = 12\text{ m}$. Then $1600 + 1.62+12=1613.62\text{ m}$. The number 1.6 km has 2 significant - figures. Rounding 1613.62 to 2 significant - figures gives $1.6\times10^{3}\text{ m}$.

Answer:

a. 1.9 g
b. 4.33 m
c. $3.2\times10^{2}\text{ cm}^2$
d. 1.13 g/mL
e. $1.6\times10^{3}\text{ m}$