Question

Change the following decimals to fractions give your answers in their simplest form a) 0.3 b) 0.46 c) 0.075

Answer 1

`0.3 = (3)/(10)\\\\ 0.46 = (23)/(50) \\\\0.075 = (3)/(40)`

Explanation:

To convert decimals to fractions, you look at the place of the last digit of the fraction (i.e. the digit that the farthest right from the decimal)

For 0.3, 3 is in the tenths place, so we end up with the fraction
`(3)/(10)`

For 0.46, 6 is in the hundreths place, so before simplifying we have
`(46)/(100)`

The GCF of 46 and 100 is 2 so we divide the fraction by
`(2)/(2)` to get
`(46)/(100)` ÷
`(2)/(2)` =
`(23)/(50)`

For 0.075, the 5 is in the thousandths place, so before simplifying we have
`(75)/(1000)`

The GCF of 75 and 1000 is 25 so we decide the fraction by
`(25)/(25)` to get
`(75)/(1000)` ÷
`(25)/(25)` =
`(3)/(40)`