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Chapter 1: Problem 47

Round each of the following numbers to four significant figures and express the result in standard exponential notation: (a) \(102.53070,\) (b) \(656.980,\) (c) 0.008543210 ,(d) \(0.000257870 (\mathbf{e})-0.0357202\)

Short Answer

Expert verified
Rounded to four significant figures and expressed in standard exponential notation, the numbers are: (a) \(1.025\times10^2\), (b) \(6.57\times10^2\), (c) \(8.543\times10^{-3}\), (d) \(2.58\times10^{-4}\), and (e) \(-3.572\times10^{-2}\).

Step by step solution

01

Rounding to 4 significant figures (a)

First, we identify the first four significant figures in the number: 102.53070. The first four significant figures are 1, 0, 2, and 5. Then, we look at the digit after the 5, which is a 3. Since this is less than 5, we round down and the number becomes 102.5.
02

Standard exponential notation (a)

Now, we convert 102.5 to standard exponential notation: \(1.025\times10^2\).
03

Rounding to 4 significant figures (b)

First, we identify the first four significant figures in the number: 656.980. The first four significant figures are 6, 5, 6, and 9. Then, we look at the digit after the 9, which is an 8. Since this is greater than 5, we round up and the number becomes 657.0.
04

Standard exponential notation (b)

Now, we convert 657.0 to standard exponential notation: \(6.57\times10^2\).
05

Rounding to 4 significant figures (c)

First, we identify the first four significant figures in the number: 0.008543210. The first four significant figures are 8, 5, 4, and 3. Then, we look at the digit after the 3, which is a 2. Since it's less than 5, we round down and the number becomes 0.008543.
06

Standard exponential notation (c)

Now, we convert 0.008543 to standard exponential notation: \(8.543\times10^{-3}\).
07

Rounding to 4 significant figures (d)

First, we identify the first four significant figures in the number: 0.000257870. The first four significant figures are 2, 5, 7, and 8. Then, we look at the digit after the 8, which is a 7. Since it's greater than 5, we round up and the number becomes 0.000258.
08

Standard exponential notation (d)

Now, we convert 0.000258 to standard exponential notation: \(2.58\times10^{-4}\).
09

Rounding to 4 significant figures (e)

First, we identify the first four significant figures in the number: -0.0357202. The first four significant figures are 3, 5, 7, and 2. Then, we look at the digit after the 2, which is a 0. Since it's less than 5, we round down and the number becomes -0.03572.
10

Standard exponential notation (e)

Now, we convert -0.03572 to standard exponential notation: \(-3.572\times10^{-2}\).

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