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Chapter 6: Problem 38

Write fraction notation. $$ 0.125 $$

Short Answer

Expert verified
0.125 as a fraction is \( \frac{1}{8} \).

Step by step solution

01

Understand the decimal

Identify the place value of each digit in the decimal 0.125. Here, the digit 1 is in the tenths place, the digit 2 is in the hundredths place, and the digit 5 is in the thousandths place.
02

Write the decimal as a fraction

Convert 0.125 into a fraction by using the place value identified. Since the digit 5 is in the thousandths place, the equivalent fraction is \( \frac{125}{1000} \).
03

Simplify the fraction

Simplify the fraction \( \frac{125}{1000} \). Divide both the numerator (125) and the denominator (1000) by their greatest common divisor (GCD), which is 125. \[ \frac{125 \text{ 梅 125}}{1000 \text{ 梅 125}} = \frac{1}{8} \].

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Key Concepts

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

decimal to fraction
When you see a decimal like 0.125, you can convert it into a fraction. Start by understanding each digit's place value. The place value helps us know how many parts of a whole we are looking at. In the decimal 0.125, the digit '1' is in the tenths place, '2' is in the hundredths place, and '5' is in the thousandths place. To turn this decimal into a fraction, take the last digit's place value as the denominator. Thus, 0.125 becomes \( \frac{125}{1000} \).
Now you have a fraction, but it might need some simplifying if it's not in its simplest form.
simplifying fractions
After converting a decimal to a fraction, your next task is to simplify the fraction. A simplified fraction has the smallest possible numerator and denominator. In our example, we got \( \frac{125}{1000} \). To simplify it, find the greatest common divisor (GCD) of the numerator and the denominator. The GCD is the largest number that can evenly divide both. For 125 and 1000, the GCD is 125.
Divide both the numerator and the denominator by the GCD:
\( \frac{125 \, \text{梅} \, 125}{1000 \, \text{梅} \, 125} = \frac{1}{8} \)
This gives you the simplified fraction, which in this case is \( \frac{1}{8} \).
place value
Place value is fundamental when converting decimals to fractions. It tells you the value of each digit based on its position.
The digits in decimal places have different values:
  • The first digit to the right of the decimal point is in the tenths place
  • The second digit is in the hundredths place
  • The third digit is in the thousandths place
For the decimal 0.125, '1' is in the tenths place, '2' is in the hundredths place, and '5' is in the thousandths place.
This is why we create the fraction \( \frac{125}{1000} \) when writing the decimal number as a fraction.

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Most popular questions from this chapter

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