Question

In a decimal number, a bar over one or more consecutive digits means that the pattern of digits under the bar repeats without end. What fraction is equal to 7.583?

Answer 1

`(7583)/(1000)`

Explanation:

Yes, the bar over the digits means the digit pattern repeats.

To convert the decimal into a fraction, we simply count the number of digits after the decimal point.

In this particular case, we have three digits after the decimal point.

We convert the digits after the decimal point into a fraction by simply dividing it by a multiple of 10, which is decided by the number of digits after the decimal point.

I will make it simpler for you, let's say there are two digits after the decimal point; we remove the point and divide the digits by 100.

Eg: 1.5477, there are four digits after the decimal point hence the number will be divided by 10000. (four-zeroes)

To further simplify, we say that the number of zeroes are determined by the number of digits after the decimal point.

Hence, to remove the decimal point we have divided the entire number by 1000. It then becomes a fraction:
`(7583)/(1000)`, which in this case cannot be reduced any further.