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Chapter 7: Problem 30

Convert each number into scientific notation. $$872 \times 10^{5}$$

Short Answer

Expert verified
8.72 \times 10^{7}

Step by step solution

01

Identify the given number

The number provided is \(872 \times 10^{5}\).
02

Convert the number to a form with one non-zero digit before the decimal

To convert 872 to scientific notation, move the decimal point 2 places to the left, which gives us 8.72.
03

Adjust the exponent

Since we moved the decimal 2 places to the left, we need to add 2 to the exponent of 10. So the exponent becomes 5 + 2.
04

Write the final answer

Combine the adjusted number and exponent, yielding the result: \(8.72 \times 10^{7}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Converting Numbers
Converting numbers into scientific notation is a key skill in mathematics and science. Scientific notation simplifies the process of working with very large or very small numbers by condensing them into an understandable format. To convert a number, like the given example \(872 \times 10^{5}\), into scientific notation, you need to make sure it follows the form of \(a \times 10^{n}\). Here, 'a' is a number greater than or equal to 1 but less than 10, and 'n' is an integer. This makes it easier to read and calculate with extremely large or small numbers, often needing less space and simplifying calculations.
Decimal Point
The decimal point plays a crucial role in converting numbers into scientific notation. Let鈥檚 dive deeper using the conversion of \(872 \times 10^{5}\). First, identify the position of the decimal in the given number. For 872, the decimal is at the end since 872 is an integer (872.0). To represent it in scientific notation, we move the decimal point until there is only one non-zero digit to its left. Moving the decimal 2 places to the left gives us 8.72. This value (8.72) is now in a suitable form of \(a \times 10^{n}\). The number of moves tells us how to adjust the exponent.
Adjusting Exponents
Adjusting the exponents is the next and final step in the conversion process. Following our example, initially, the exponent was 5, as shown in \(872 \times 10^{5}\). Since we moved the decimal point 2 places to the left to convert 872 into 8.72, we need to adjust the exponent accordingly. Moving the decimal to the left increases the exponent, so we add these moves to the initial exponent. Therefore, we compute: 5 + 2 = 7. The final step combines our adjusted number (8.72) with the corrected exponent, producing \(8.72 \times 10^{7}\) as our answer in scientific notation.

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Most popular questions from this chapter

Estimate the answer without actually carrying out the computation and make the most appropriate choice. If you multiply \(1.45 \times 10^{-6}\) by \(2.03 \times 10^{4},\) the result is closest to (a) 10 (b) 100 (c) 1 (d) 0.1 (e) 0.01

A collection of 40 coins consists of dimes and quarters. If the total value of the coins is \(\$ 6.70,\) how many of each are there?

The width of a rectangle is 5 less than 3 times its length. Using \(L\) as the variable, express the perimeter and area of the rectangle in terms of \(L\).

A long pole is standing slightly offshore. If one quarter of the pole is in the sand, \(8 \mathrm{ft}\) is in the water, and two thirds of the pole is in the air, how long is the pole?

Do your computation using scientific notation. $$\frac{80}{0.0002}$$
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