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Chapter 1: Problem 13

Perform these operations with the appropriate number of significant figures. (a) \(3.783 \times 10^{6} \mathrm{kg}+1.25 \times 10^{8} \mathrm{kg}\) (b) $\left(3.783 \times 10^{6} \mathrm{m}\right) \div\left(3.0 \times 10^{-2} \mathrm{s}\right)$

Short Answer

Expert verified
a) \(3.783 \times 10^{6} \mathrm{kg} + 1.25 \times 10^{8} \mathrm{kg}\) b) \(\left(3.783 \times 10^{6} \mathrm{m}\right) \div\left(3.0 \times 10^{-2} \mathrm{s}\right)\) Answer: a) \(1.29 \times 10^{8}\ \mathrm{kg}\) b) \(1.3 \times 10^8\ \mathrm{m/s}\)

Step by step solution

01

Determine the least number of decimal places

The least number of decimal places is 2, from the number \(1.25 \times 10^{8}\).
02

Round all numbers to the least decimal place

The numbers are \(3.78 \times 10^{6} \mathrm{kg}\) and \(1.25 \times 10^{8} \mathrm{kg}\) (no need to round since it already has 2 decimal places).
03

Perform the addition and round the result

Add the two numbers, and round the result to 2 decimal places: \((3.78 \times 10^{6})+(1.25 \times 10^{8}) = 1.2878 \times 10^8 = 1.29 \times 10^{8}\ \mathrm{kg}\) (rounded to 2 decimal places). a) Answer: \(1.29 \times 10^{8}\ \mathrm{kg}\) b) $\left(3.783 \times 10^{6} \mathrm{m}\right) \div\left(3.0 \times 10^{-2} \mathrm{s}\right)$
04

Determine the least number of significant figures

The least number of significant figures is 2, from the number \(3.0 \times 10^{-2}\).
05

Perform the operation

Divide \(\left(3.783 \times 10^{6}\right)\) by \(\left(3.0 \times 10^{-2}\right) = 1.261 \times 10^8\)
06

Round the result to the same number of significant figures

Round to 2 significant figures: \(1.3 \times 10^8\ \mathrm{m/s}\). b) Answer: \(1.3 \times 10^8\ \mathrm{m/s}\).

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