Video: Converting a Rational Number to a Decimal Using Long Division

Convert 1/3 into its decimal form.

01:36

Video Transcript

Convert one-third into its decimal form.

One-third is a commonly used fraction. And we often learn its decimal equivalents off by heart. If we don’t know the answer however, we recall that the line in a fraction means divide. So we need to divide one by three. We can do this using the short division bus stop method. We knew that three does not divide into one. So it is worth adding a decimal point and some zeros after this. We could add any number of zeros after the decimal point.

As mentioned, three does not divide into one. So we carry the one to the tenths column. After putting the decimal point on the answer line, we see that 10 divided by three is equal to three remainder one. This time, we carry the one to the hundredths column. Once again, we have 10 divided by three, which is three remainder one. This pattern would continue indefinitely. This is known as a recurring decimal as the decimal numbers repeat forever.

As the three is the only number that repeats, we only need to write this once. And we put a bar or a dot above it. The fraction one-third written in decimal form is 0.3 recurring.

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