### Video Transcript

Calculate 0.13 divided by three-fifths, rounding your answer to the nearest hundredth.

In order to answer this problem, we need to turn both of our terms into either decimals or fractions. As we need to round to the nearest hundredth, it’s insensible to turn them both into decimals. We need to convert three-fifths into a decimal. Three-fifths is equivalent to or the same as six 10ths. We can multiply the numerator and denominator by two. Three multiplied by two is equal to six and five multiplied by two equals 10.

The line in a fraction means divide and six divided by 10 is equal to 0.6. When dividing by 10, we move all the digits one place to the right. Our calculation, therefore, becomes 0.13 divided by 0.6. Once again, this can be written as a fraction: 0.13 over 0.6. As it is easier to divide by a whole number than a decimal, we can multiply the numerator and denominator by 10. This means that 0.13 divided by 0.6 is the same as 1.3 divided by six.

To calculate 0.13 divided by three-fifths, we need to divide 1.3 by six. We can do this using the bus stop method. As six does not divide exactly into 13, it’s worth remembering that we can put any number of zeros after the decimal point. We cannot divide one by six. So we need to carry the one to the tenths column. Remember to keep the decimal point in the same place in the answer. 13 divided by six is equal to two remainder one as two multiplied by six is 12. 10 divided by six is equal to one remainder four. 40 divided by six is equal to six remainder four as six multiplied by six is 36. This pattern will then continue indefinitely. 1.3 divided by six is equal to 0.2166 and so on or 0.216 recurring.

We need to round our answer to the nearest hundredth, which is the same as rounding to two decimal places. As the number after this point is a six, we need to round up. Therefore, 0.2166 and so on to the nearest hundredth is 0.22.

0.13 divided by three-fifths is equal to 0.22 to the nearest hundredth.