now what about converting a decimal into a fraction how can we do that notice that we have one digit to the right of the decimal it's in the tenths place what you want to do is put it over one and multiply the top and the bottom by ten if there's two digits use one hundred four three years of thousand now 0.3 times ten is basically equal to three you just got to move the decimal point and one unit to the right 1 times 10 is 10 so 0.3 is the same as 3 over 10 that's how you can convert it into a fraction let's try another example point 3 6 go ahead and convert that into a fraction so notice that we have two digits to the right of the decimal point so in this case we're gonna multiply the top and the bottom by a hundred 0.36 times 100 is 36 and 1 times 100 is 100 and now let's reduce it both numbers are divisible by 4 36 divided by 4 is equal to 9 a hundred divided by 4 is 25 so 0.36 is 9 over 25 as a fraction now what about 3.75 let's try that so we're gonna do the same thing we're going to multiply it by a hundred over 100 and this will give us 375 over 100 now both numbers are divisible by 5 any time a number ends in 5 or 0 it's divisible by 5 so let's divide each by 5 375 divided by 5 is 75 and 100 divided by 5 is 20 so now notice that we can divide it by 5 again 20 divided by 5 is 4 75 divided by 5 is 15 so the final answer is 15 divided by 4 that's equal to 3 point 7 5 and let's try one more example let's convert point 2 8 4 into a fraction so because we have 3 numbers to the right of the decimal point we're going to multiply by a thousand over a thousand point two eight four times a thousand is two hundred and eighty four and one times a thousand is simply a thousand now both numbers are even so we can divide by two half of 2 is 1 half of 8 is 4 half of 4 is 2 half of a thousand is 500 so we still have even numbers we can divide it again by 2 half of 14 is 7 half of 2 is 1 so half of one 42 is 70 one half of 500 250 and at this point we can't reduce it any further 71 is not divisible by two or three and so that's the answer it's 71 over 250