Question

Write 1.78 as a mixed number in simplest form. 1.78

Answer 1

To write a decimal number as a mixed number we first need to separate its integer part to the decimal one, this is done below:

`1.7878\ldots=1+0.7878\ldots`

Now we need to represent the decimal part as a fraction. To convert a repeating decimal we need to first identify its period, this is the part the repeats in this case it is "78", we then count the number of digits there are in the period, in this case there are two digits, for each digit in the period we divide by one 9, in this case we need to divide by "99". With this in mind let's convert the decimal to a fraction:

`1.7878\ldots=1+(78)/(99)`

Now we have to simplify the fraction, we do that by dividing both the numerator and denominator by 3.

`1.7878\ldots=1+(26)/(33)`

We can then represent it as a mixed fraction:

`1.7878\ldots=1(26)/(33)`