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# TutorMe Blog

## What Is Decimal Expansion? Your Quick and Easy Guide

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Andrew Lee
March 23, 2021 Decimal expansion may sound complicated, but it only means turning a fraction or a whole number into its decimal representation. This is helpful if you are working with a calculator or want to perform operations on numbers in a decimal format.

Here, we'll show you how to use decimal expansion and the difference between finite and infinite decimal expansion.

But first, a quick review: The decimal place marks different units such as tenths, hundredths, thousandths, and so on.

And a quick note: Irrational numbers, such as Euler's number, pi, or the golden ratio, cannot be expressed as a quotient of a numerator and denominator (a fraction).

## Finite Decimal Expansion vs. Infinite Decimal Expansion

There are two types of decimal expansion: finite decimal expansion and infinite decimal expansion (sometimes called periodic decimal expansion).

A finite decimal expansion has a clear end. Take the fraction 1/2. Its decimal expansion is 0.5, which is non-repeating. The terminating decimal is the 5 in the tenths place digit.

An infinite decimal expansion does not have a clear end — it goes on in an infinite sequence. An easy example is 1/3. Its decimal expansion is 0.3333, or , in which the bar represents that the digit repeats forever.

Another example of an infinite decimal expansion is 1/11, which expands to 0.0909 or , (meaning the .09 repeats forever). The period, or the group of digits that repeat, is 09. The number of digits in the decimal expansion goes on infinitely.

## When To Use Decimal Expansion

Remember that finding a number’s decimal expansion is just a fancy way of putting it into decimal form. Keep track of the decimals, and put a bar over the digits that repeat on forever.

Sometimes, you will need to convert between fractions and decimals. Other times, you just need to recognize when a number has a repeating decimal expansion or a terminating decimal expansion.

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