121 LearnersLast updated on May 26th, 2025
0.17777 as a Fraction
Numbers can be categorized into different types. A fraction is one of its kinds. It is always represented in the form of p/q, where p is the numerator and q is the denominator. Fractions represent a whole and a fractional part. Decimals represent the fractional part of numbers. For example, 1/2, the numbers in decimal are expressed with a decimal point (.), For example, 0.17777, we are going to learn how to convert this repeating decimal to a fraction.
What is 0.17777 as a Fraction?
Answer
The answer for 0.17777 as a fraction will be 16/90.
Explanation
Converting a repeating decimal to a fraction involves a few more steps but can still be done systematically. Here's how you can convert 0.17777 to a fraction.
Step 1: Let x equal the repeating decimal: x = 0.17777...
Step 2: Multiply both sides of the equation by 100 to shift the decimal point two places to the right: 100x = 17.777...
Step 3: Subtract the original equation from this new equation to eliminate the repeating part: 100x - x = 17.777... - 0.17777... 99x = 17.6
Step 4: Solve for x by dividing both sides by 99: x = 17.6/99
Step 5: Since 17.6 is not a whole number, multiply numerator and denominator by 10 to eliminate the decimal: x = 176/990
Step 6: Simplify the fraction by finding the GCD of 176 and 990, which is 11: x = 16/90
Thus, 0.17777 can be written as a fraction 16/90.
Important Glossaries for 0.17777 as a Fraction
- Fraction: A numerical quantity that is not a whole number, representing a part of a whole.
- Decimal: A number that uses the base ten and includes a decimal point to separate the whole part from the fractional part.
- Repeating Decimal: A decimal in which one or more digits repeat infinitely.
- Numerator: The top part of a fraction, indicating how many parts of the whole are being considered.
- Denominator: The bottom part of a fraction, showing how many parts make up a whole.
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