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Chapter 1: Problem 37

Round each of the following numbers to four significant figures, and express the result in standard exponential notation: (c) \(0.008543210,\) (d) 0.000257870 , (a) \(102.53070,(\mathbf{b}) 656,980,\) (e) -0.0357202 .

Short Answer

Expert verified
When rounded to four significant figures and expressed in standard exponential notation, the numbers are as follows: (a) \(1.0253 \times 10^2\) (b) \(6.570 \times 10^5\) (c) \(8.543 \times 10^{-3}\) (d) \(2.579 \times 10^{-4}\) (e) \(-3.572 \times 10^{-2}\)

Step by step solution

01

(a) Rounding 102.53070 to four significant figures

To round the number 102.53070 to four significant figures, we start counting from the first non-zero digit, which is 1. The fourth digit after 1 is 5. Therefore, we need to round the number to the nearest hundredth. We end up with 102.53.
02

(a) Expressing 102.53070 in standard exponential notation

Now, we express 102.53 in standard exponential notation: \(1.0253 \times 10^2\).
03

(b) Rounding 656,980 to four significant figures

To round the number 656,980 to four significant figures, we start counting from the first non-zero digit, which is 6. The fourth digit after 6 is 9. Therefore, we need to round the number to the nearest hundred. We end up with 657,000.
04

(b) Expressing 656,980 in standard exponential notation

Now, we express 657,000 in standard exponential notation: \(6.570 \times 10^5\).
05

(c) Rounding 0.008543210 to four significant figures

To round the number 0.008543210 to four significant figures, we start counting from the first non-zero digit, which is 8. The fourth digit after 8 is 3. Therefore, we need to round the number to the nearest ten-thousandth. We end up with 0.008543.
06

(c) Expressing 0.008543210 in standard exponential notation

Now, we express 0.008543 in standard exponential notation: \(8.543 \times 10^{-3}\).
07

(d) Rounding 0.000257870 to four significant figures

To round the number 0.000257870 to four significant figures, we start counting from the first non-zero digit, which is 2. The fourth digit after 2 is 8. Therefore, we need to round the number to the nearest hundred-millionth. We end up with 0.0002579.
08

(d) Expressing 0.000257870 in standard exponential notation

Now, we express 0.0002579 in standard exponential notation: \(2.579 \times 10^{-4}\).
09

(e) Rounding -0.0357202 to four significant figures

To round the number -0.0357202 to four significant figures, we start counting from the first non-zero digit, which is 3. The fourth digit after 3 is 2. Therefore, we need to round the number to the nearest ten-thousandth. We end up with -0.03572.
10

(e) Expressing -0.0357202 in standard exponential notation

Now, we express -0.03572 in standard exponential notation: \(-3.572 \times 10^{-2}\).

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