Convert 1/8 to a decimal. Round to the nearest hundredth.
a. 0.18
b. 0.13
c. 0.018
d. 0.12
The correct Answer and Explanation is :
To convert a fraction like ( \frac{1}{8} ) into a decimal, you divide the numerator (1) by the denominator (8).
[
1 \div 8 = 0.125
]
Now, let’s round this decimal to the nearest hundredth. The hundredths place is the second digit to the right of the decimal point (in this case, it’s the 2 in 0.125). To round, we look at the digit in the thousandths place (which is the 5). Since this digit is 5 or higher, we round the hundredths place up by 1. So, 0.125 rounds to 0.13.
Therefore, the correct answer is:
b. 0.13
Explanation of the Process:
- Understanding fractions: A fraction like ( \frac{1}{8} ) means “1 part out of 8 equal parts.” To convert it into a decimal, we divide the numerator by the denominator.
- Division: When you divide 1 by 8, you get 0.125. This means that ( \frac{1}{8} ) is exactly 0.125 in decimal form.
- Rounding rules: To round a decimal to the nearest hundredth, you look at the third digit after the decimal point (the thousandths place). If that digit is 5 or higher, you round the hundredths place up by 1. If it’s less than 5, you leave the hundredths place unchanged. In this case, since the third digit (5) is 5 or higher, we round the decimal up from 0.125 to 0.13.
- Final result: After rounding, ( \frac{1}{8} ) is approximately 0.13, making option b the correct answer.