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Chapter 1: Problem 25

Express the answers to these in scientific notation: (a) \(145.75+\left(2.3 \times 10^{-1}\right)\) (b) \(79,500 \div\left(2.5 \times 10^{2}\right)\) (c) \(\left(7.0 \times 10^{-3}\right)-\left(8.0 \times 10^{-4}\right)\) (d) \(\left(1.0 \times 10^{4}\right) \times\left(9.9 \times 10^{6}\right)\)

Short Answer

Expert verified
(a) \(145.98\), (b) \(3.18 \times 10^{2}\), (c) \(6.2 \times 10^{-3}\), (d) \(9.9 \times 10^{10}\)

Step by step solution

01

Problem (a)

Firstly, \(2.3 \times 10^{-1}\) must be converted to standard form, which equals 0.23. So, the problem becomes \(145.75+0.23\). When adding these numbers, you get \(145.98\).
02

Problem (b)

Firstly, \(2.5 \times 10^{2}\) must be converted to standard form, which equals 250. So, the problem becomes \(79500 \div 250\). Dividing these numbers gives 318. Because this number is larger than 10, it should be expressed in scientific notation, resulting in \(3.18 \times 10^{2}\).
03

Problem (c)

Since these two numbers are already presented in scientific notation, and they have the same order of magnitude, they can be subtracted directly: \(7.0 - 0.8 = 6.2\). After the subtraction, you get \(6.2 \times 10^{-3}\).
04

Problem (d)

When multiplying numbers in scientific notation, we simply need to multiply the decimal parts and add the exponents. In this case, \(1.0 \times 9.9 = 9.9\) and \(10^{4} \times 10^{6} = 10^{10}\). Therefore, the answer is \(9.9 \times 10^{10}\).

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Most popular questions from this chapter

A student is given a crucible and asked to prove whether it is made of pure platinum. She first weighs the crucible in air and then weighs it suspended in water (density \(\left.=0.9986 \mathrm{~g} / \mathrm{cm}^{3}\right)\). The readings are \(860.2 \mathrm{~g}\) and \(820.2 \mathrm{~g}\), respectively. Given that the density of platinum is \(21.45 \mathrm{~g} / \mathrm{cm}^{3},\) what should her conclusion be based on these measurements? (Hint: An object suspended in a fluid is buoyed up by the mass of the fluid displaced by the object. Neglect the buoyancy of air.)

Write the equations for converting degrees Celsius to degrees Fahrenheit and degrees Fahrenheit to degrees Celsius.

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A resting adult requires about \(240 \mathrm{~mL}\) of pure oxygen/min and breathes about 12 times every minute. If inhaled air contains 20 percent oxygen by volume and exhaled air 16 percent, what is the volume of air per breath? (Assume that the volume of inhaled air is equal to that of exhaled air.)
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