Have you ever come across a decimal number such as 2.33333 that keeps repeating? This decimal number is known as a repeating decimal, and it can be written as a fraction. A repeating decimal is a number that has an infinitely repeating sequence of digits after the decimal point. This means that the number just keeps going in a pattern of the same sequence of numbers. For example, 2.33333 is a repeating decimal that can be expressed as an equivalent fraction.

## Writing 2.33333 as a Fraction

When converting a repeating decimal to a fraction, it is important to understand how to represent the repeating decimal in a fractional form. To write 2.33333 as a fraction, the decimal must be represented using a fractional form. Essentially, the decimal is multiplied by a certain power of 10 to make it a fraction. The power of 10 used to make the fraction must be equal to the number of digits in the repeating decimal. In this case, the decimal has 5 repeating digits, so the power of 10 used is 1/100000.

Once the repeating decimal is expressed in fractional form, the numerator and denominator can be simplified. In this example, the fraction is expressed as 233333/100000. To simplify this fraction, both the numerator and the denominator can be divided by 3, resulting in 77777/33333. This fraction is simplified to 2/3333 which is the equivalent fraction for 2.33333 repeating.

## How to Simplify a Repeating Decimal as a Fraction

Simplifying a repeating decimal as a fraction may seem like a difficult task, but with some practice, it can be done easily. To simplify a repeating decimal as a fraction, the decimal must first be expressed in a fractional form. This involves multiplying the decimal by a power of 10 equal to the number of digits in the repeating sequence. Then, the numerator and denominator can be divided by the same number until the fraction is simplified as much as possible.

## Uses of Repeating Decimals in Math and Real Life

In addition to understanding how to write a repeating decimal as a fraction, it is important to understand the uses of repeating decimals in both math and real life. In math, repeating decimals are used to represent irrational numbers, which are numbers that cannot be expressed as a fraction. In real life, repeating decimals are used to measure quantities that cannot be easily expressed in whole numbers. For example, money is often expressed in decimal form because it cannot be easily expressed in whole numbers.

A repeating decimal such as 2.33333 can be written as an equivalent fraction. To do this, the decimal must first be expressed in a fractional form by multiplying it by a power of 10 equal to the number of digits in the repeating sequence. Then, the numerator and denominator can be divided by the same number until the fraction is simplified. Understanding repeating decimals and how to write them as fractions is important for both math and real life applications.