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Chapter 2: Problem 182

Write each number in standard notation: (a) \(1.79 \times 10^{-2}\) (b) \(8.76 \times 10^{-9}\) (c) \(4.88 \times 10^{10}\) (d) \(7.52 \times 10^{1}\) (e) \(8.37 \times 10^{\circ}\) (f) \(4.184 \times 10^{4}\)

Short Answer

Expert verified
(a) 0.0179 (b) 0.000\,000\,008\,76 (c) 48\,800\,000\,000 (d) 75.2 (e) 8.37 (f) 41\,840

Step by step solution

01

(a) Convert \(1.79 \times 10^{-2}\) to standard notation

To convert a number with a negative exponent to standard notation, divide the coefficient by 10 raised to the power of the absolute value of the exponent. In this case, we divide \(1.79\) by \(10^{2}\). Thus, the number in standard notation is: $$1.79 \times 10^{-2} = \frac{1.79}{10^2} = 0.0179$$
02

(b) Convert \(8.76 \times 10^{-9}\) to standard notation

Similar to step (a), we divide \(8.76\) by \(10^{9}\): $$8.76 \times 10^{-9} = \frac{8.76}{10^9} = 0.000\,000\,008\,76$$
03

(c) Convert \(4.88 \times 10^{10}\) to standard notation

This time the exponent is positive, so we multiply the coefficient by 10 raised to the power of the exponent. Multiply \(4.88\) by \(10^{10}\): $$4.88 \times 10^{10} = 48\,800\,000\,000$$
04

(d) Convert \(7.52 \times 10^{1}\) to standard notation

Multiply the coefficient (\(7.52\)) by 10 raised to the power of the exponent (1): $$7.52 \times 10^{1} = 75.2$$
05

(e) Convert \(8.37 \times 10^{0}\) to standard notation

Any non-zero number raised to the power of 0 is equal to 1. Therefore, multiply \(8.37\) by \(1\): $$8.37 \times 10^0 = 8.37$$
06

(f) Convert \(4.184 \times 10^{4}\) to standard notation

Multiply the coefficient (\(4.184\)) by 10 raised to the power of the exponent (4): $$4.184 \times 10^{4} = 41\,840$$ All numbers are now in standard notation: (a) 0.0179 (b) 0.000\,000\,008\,76 (c) 48\,800\,000\,000 (d) 75.2 (e) 8.37 (f) 41\,840

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Most popular questions from this chapter

What mass of each substance occupies a volume of \(50.0 \mathrm{~mL} ?\) (Densities are shown in parentheses.) (a) Lead \((11.4 \mathrm{~g} / \mathrm{mL})\) (b) Ethanol \((0.785 \mathrm{~g} / \mathrm{mL})\) (c) Oxygen gas \(\left(1.4 \times 10^{-3} \mathrm{~g} / \mathrm{mL}\right)\) (d) Hydrogen gas \(\left(8.4 \times 10^{-5} \mathrm{~g} / \mathrm{mL}\right)\) (e) Mercury (13.6 g/mL) (f) Gold \((19.3 \mathrm{~g} / \mathrm{mL})\)

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