0.16 Repeating as a Fraction Worksheet
Introduction
Repeating decimals can be converted into fractions, and in this worksheet, we will focus on the decimal 0.16 repeating. This decimal has an infinite number of 16s, making it a repeating decimal. Let's explore how to convert it into a fraction.
Converting 0.16 Repeating to a Fraction
To convert 0.16 repeating to a fraction, we can use the following steps:
Step 1: Let x = 0.1616...
Let x equal the repeating decimal 0.1616...
Step 2: Multiply x by 100
Multiply both sides of the equation by 100 to get rid of the decimal point.
100x = 16.1616...
Step 3: Subtract x from both sides
Subtract x from both sides of the equation to eliminate the repeating decimal.
99x = 16
Step 4: Simplify the fraction
Divide both sides of the equation by 99 to simplify the fraction.
x = 16/99
The Answer
So, the fraction equivalent of 0.16 repeating is 16/99.
Practice Exercises
Convert the following decimals into fractions:
1. 0.25 repeating
2. 0.33 repeating
3. 0.45 repeating
Answer Key
1. 1/4
2. 1/3
3. 9/20
Conclusion
Converting repeating decimals into fractions is an important skill in mathematics. By following the steps outlined in this worksheet, you can convert any repeating decimal into a fraction. Remember to practice regularly to become proficient in this skill.
Note
Make sure to simplify your fractions to their lowest terms. Happy practicing!
