Last updated on May 26th, 2025
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. A fraction represents 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 instance, 1.45454545455. We are going to learn how to convert a repeating decimal to a fraction.
The answer for 1.45454545455 as a fraction will be 16/11.
Converting a repeating decimal to a fraction can be achieved through a series of steps. You can follow the steps mentioned below to find the answer.
Step 1: Let x = 1.45454545455. Since the repeating part "45" has 2 digits, multiply x by 100 to move the decimal point two places to the right: 100x = 145.45454545455.
Step 2: Subtract the original x from this equation to eliminate the repeating part: 100x - x = 145.45454545455 - 1.45454545455 99x = 144.
Step 3: Solve for x by dividing both sides by 99: x = 144/99.
Step 4: Simplify the fraction by finding the greatest common divisor (GCD) of 144 and 99, which is 9. Divide both the numerator and the denominator by 9: 144/99 = 16/11.
Thus, 1.45454545455 can be written as a fraction 16/11.