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Chapter 2: Problem 173

Write each number in scientific notation, taking all trailing zeros to be nonsignificant: (a) 502,000 (b) \(0.000038402\) (c) \(436,000,000\) (d) 8470 (e) \(0.00591\) (f) \(0.658\)

Short Answer

Expert verified
The numbers in scientific notation are: (a) \(5.02 \times 10^5\) (b) \(3.8402 \times 10^{-5}\) (c) \(4.36 \times 10^8\) (d) \(8.47 \times 10^3\) (e) \(5.91 \times 10^{-3}\) (f) \(6.58 \times 10^{-1}\)

Step by step solution

01

(a) Convert 502,000 to scientific notation.

First, identify the number between 1 and 10 that we will multiply by a power of 10. In this case, it's 5.02. Next, determine the power of 10 by counting the number of decimal places we move to get from 502,000 to 5.02. Since we moved the decimal place 5 times to the left, our power of 10 would be 10^5. Therefore, the scientific notation for 502,000 is \(5.02 \times 10^5\).
02

(b) Convert 0.000038402 to scientific notation.

The number between 1 and 10 that we will multiply by a power of 10 is 3.8402. To get from 0.000038402 to 3.8402, we need to move the decimal place 5 times to the right. This makes our power of 10 to be 10^-5. So, the scientific notation for 0.000038402 is \(3.8402 \times 10^{-5}\).
03

(c) Convert 436,000,000 to scientific notation.

For this number, the number between 1 and 10 that we will multiply by a power of 10 is 4.36. We move the decimal place 8 times to the left to get from 436,000,000 to 4.36, making the power of 10 as 10^8. The scientific notation for 436,000,000 is \(4.36 \times 10^8\).
04

(d) Convert 8470 to scientific notation.

The number between 1 and 10 is 8.47. To get from 8470 to 8.47, we need to move the decimal place 3 times to the left. This gives us a power of 10^3. The scientific notation for 8470 is \(8.47 \times 10^3\).
05

(e) Convert 0.00591 to scientific notation.

For this number, the number between 1 and 10 that we will multiply by a power of 10 is 5.91. We move the decimal place 3 times to the right to get from 0.00591 to 5.91, making the power of 10 as 10^-3. The scientific notation for 0.00591 is \(5.91 \times 10^{-3}\).
06

(f) Convert 0.658 to scientific notation.

In this case, the number between 1 and 10 is 6.58. We only need to move the decimal place 1 time to the right to get from 0.658 to 6.58, so our power of 10 is 10^-1. The scientific notation for 0.658 is \(6.58 \times 10^{-1}\).

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