What Is .3 Repeating As a Fraction?

If you’re wondering what .3 repeating as a fraction is, you’re not alone. Many people are confused by this concept, but it’s actually quite simple. In this article, we’ll explain what .3 repeating as a fraction means and how to calculate it.

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.3 Repeating as a Fraction

.3 repeating as a fraction is equal to 1/3. To find this, we can use long division.

What Does .3 Repeating Mean?

In mathematics, a repeating decimal is a decimal whose digits are recurring. For example, the number 0.3 (read “three tenths”) has the digit 3 repeating indefinitely. In contrast, the number 0.0333.. (read “three thousandths”) has the digit 3 appearing only once after the decimal point and repeats infinitely because it is one-third of one. The number 1.2346 ( read “one and two thousandths, three hundred forty-six ten-thousandths”) has no recurring decimal part and thus does not repeat indefinitely.

How to Convert .3 Repeating to a Fraction

The number 0.3 recurring is equal to 1/3, or one third. To convert 0.3 recurring to a fraction, divide 1 by 3 and write the answer as a mixed number:

1 ÷ 3 = 0 + 1/3 = 1/3

Converting .3 Repeating to a Decimal

To convert .3 repeating to a decimal, simply divide 3 by 10. The answer is 0.3.