1.45454545455 as a Fraction

Professor Greenline Explaining Math Concepts

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.

1.45454545455 as a Fraction for US Students

What is 1.45454545455 as a Fraction?

Answer

The answer for 1.45454545455 as a fraction will be 16/11.

Explanation

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.

Important Glossaries for 1.45454545455 as a Fraction

Fraction: A numerical quantity that is not a whole number, representing a part of a whole.
Decimal: A number that uses base ten and includes a decimal point to separate the whole part from the fractional part.
Repeating Decimal: A decimal in which a sequence of digits repeats 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.