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Chapter 2: Problem 10

Explain, in your own words, how to write \(4.1 \times 10^{-3}\) without an exponent.

Short Answer

Expert verified
To write \(4.1 \times 10^{-3}\) without an exponent, first understand that the negative exponent means to divide instead of multiplying, so \(10^{-3}\) equals \(\frac{1}{1000}\). Next, multiply the decimal number \(4.1\) by the fraction, resulting in \(\frac{4.1}{1000}\). Finally, divide the numerator by the denominator to convert the fraction to a decimal, which gives you \(0.0041\).

Step by step solution

01

Understanding the negative exponent

A negative exponent means that we need to divide instead of multiply. The expression \(10^{-3}\) is the same as taking 1 and dividing it by \(10^3\): \[10^{-3} = \frac{1}{10^3}\] \[10^{-3} = \frac{1}{1000}\]
02

Multiplying by the decimal number

Now, we will multiply the given decimal number \(4.1\) by the fraction we found in Step 1, which is \(\frac{1}{1000}\): \[4.1 \times \frac{1}{1000}\]
03

Performing the multiplication

To multiply a decimal by a fraction, we simply multiply the decimal by the numerator of the fraction and then divide it by the denominator: \[4.1 \times \frac{1}{1000} = \frac{4.1 \times 1}{1000}\] \[4.1 \times \frac{1}{1000} = \frac{4.1}{1000}\]
04

Converting the fraction to a decimal

To convert the fraction \(\frac{4.1}{1000}\) into a decimal number, we simply divide the numerator by the denominator: \[4.1 \div 1000 = 0.0041\] Therefore, \(4.1 \times 10^{-3}\) without an exponent is: \(0.0041\).

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