Question

Write your answer to the following problems with the appropriate number of significant figures. (a) \(6.85 \times 10^{-5} \mathrm{m}+2.7 \times 10^{-7} \mathrm{m}\) (b) \(702.35 \mathrm{km}+1897.648 \mathrm{km}\) (c) \(5.0 \mathrm{m} \times 4.3 \mathrm{m}\) (d) \((0.04 / \pi) \mathrm{cm}\) (e) \((0.040 / \pi) \mathrm{m}\)

Short answer

a) 6.85 x 10^-5 m + 2.7 x 10^-7 m b) 702.35 km + 1897.648 km c) 5.0 m x 4.3 m d) (0.04 / π) cm e) (0.040 / π) m Answer: a) 6.85 x 10^-5 m b) 2601.00 km c) 22 m^2 d) 0.013 cm e) 0.0127 m

Step-by-step solution

Align numbers

In this step, align the given numbers so that the exponents are the same. This can be achieved by rewriting 2.7 x 10^-7 as 0.000027 x 10^-5. 6.85 x 10^-5 m + 0.00027 x 10^-5 m

Add numbers with common exponent

Add the significant digits, keeping the base 10 exponent the same: (6.85 + 0.00027) x 10^-5 m = 6.85027 x 10^-5 m

Apply significant figure rules

Round the result to the least number of decimal places in the given numbers (two decimal places in this case): 6.85 x 10^-5 m #b) 702.35 km + 1897.648 km#

Add numbers

Simply add the two given numbers: 702.35 + 1897.648 = 2600.998 km

Apply significant figure rules

Round the result to the least number of decimal places in the given numbers (two decimal places in this case): 2600.998 km → 2601.00 km #c) 5.0 m x 4.3 m#

Multiply numbers

Multiply the given numbers: 5.0 x 4.3 = 21.5 m^2

Apply significant figure rules

Round the result to the least number of significant figures in the given numbers (two significant figures in this case): 21.5 m^2 → 22 m^2 #d) (0.04 / π) cm#

Divide number by π

Divide the given number by π: (0.04 / π) cm ≈ 0.012732 cm

Apply significant figure rules

Round the result to the least number of significant figures in the given numbers (two significant figures in this case): 0.012732 cm → 0.013 cm #e) (0.040 / π) m#

Divide number by π

Divide the given number by π: (0.040 / π) m ≈ 0.0127324 m

Apply significant figure rules

Round the result to the least number of significant figures in the given numbers (three significant figures in this case): 0.0127324 m → 0.0127 m