### Video Transcript

Convert four ninetieths to a decimal.

We recall that the line in a fraction means divide. This means we need to divide four by 90. In this question, we’ll do this in two steps. We’ll divide four by nine and then the answer by 10. We might recall that the fraction one-ninth is equal to 0.1 recurring. A recurring decimal exists when a decimal number repeats forever. This is denoted by a bar or dot above the repeating digits.

Multiplying the fraction and decimal by four tells us that four-ninths is equal to 0.4 recurring. This means that four divided by nine is also 0.4 recurring. If we didn’t recall this fact, we could divide four by nine using the short division bus stop method.

We need to add a decimal point and some zeros after it as four is not divisible by nine. Carrying the four to the tenths column, we need to divide 40 by nine. This is equal to four reminder four as nine multiplied by four is 36. We can continue this process so that four divided by nine is equal to 0.4444 and so on. This can be written as 0.4 recurring.

We need to divide this number by 10. This involves moving all of our digits one place to the right. 0.4 recurring divided by 10 is equal to 0.04 recurring. It is important to note that we only put the bar or dot on the four as this is the only number that is repeating. Had we written the bar above the zero and the four, this would be equal to 0.040404 and so on. The fraction four ninetieths is equal to the recurring decimal 0.04 recurring.