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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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Most popular questions from this chapter

How many significant figures are in each of these measurements? (a) \(7.68 \mathrm{g}\) (b) \(0.420 \mathrm{kg}\) (c) \(0.073 \mathrm{m}\) (d) \(7.68 \times 10^{5} \mathrm{g}\) (e) \(4.20 \times 10^{3} \mathrm{kg}\) (f) \(7.3 \times 10^{-2} \mathrm{m}\) (g) \(2.300 \times 10^{4} \mathrm{s}\)
You are given these approximate measurements: (a) the radius of Earth is $6 \times 10^{6} \mathrm{m},\( (b) the length of a human body is \)6 \mathrm{ft},(\mathrm{c})\( a cell's diameter is \)10^{-6} \mathrm{m},$ (d) the width of the hemoglobin molecule is \(3 \times 10^{-9} \mathrm{m},\) and (e) the distance between two atoms (carbon and nitrogen) is $3 \times 10^{-10} \mathrm{m} .$ Write these measurements in the simplest possible metric prefix forms (in either nm, Mm, \(\mu \mathrm{m}\), or whatever works best).
Density is the ratio of mass to volume. Mercury has a density of $1.36 \times 10^{4} \mathrm{kg} / \mathrm{m}^{3} .$ What is the density of mercury in units of \(\mathrm{g} / \mathrm{cm}^{3} ?\)
A scanning electron micrograph of xylem vessels in a corn root shows the vessels magnified by a factor of \(600 .\) In the micrograph the xylem vessel is \(3.0 \mathrm{cm}\) in diameter. (a) What is the diameter of the vessel itself? (b) By what factor has the cross-sectional area of the vessel been increased in the micrograph?
An average-sized capillary in the human body has a cross-sectional area of about \(150 \mu \mathrm{m}^{2} .\) What is this area in square millimeters \(\left(\mathrm{mm}^{2}\right) ?\)
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