Question

hello

how do we convert a number into fraction for example :

1.75 = 7/4

0.111... = 1/9

.001=1/1000

how to solve that? please i need help!
Thanks

Answer 1

You can convert a fraction into a decimal by dividing the top number (numerator) by the bottom number (denominator). Here's an example:

1/2 = 1 ÷ 2 = 0.5 (= 50%)

Try it with the others.

Here are some good math websites to help with fractions, decimals, and many other math topics:

http://www.aaamath.com/

http://www.mathisfun.com/ >> http://www.mathsisfun.com/numbers/index.html

http://mathforum.org/dr.math/ >> http://mathforum.org/library/drmath/drmath.elem.html

And here's a good website to use when you want to check your work:
http://www51.wolframalpha.com/

Answer 2

It looks like you already know how. In the first case, just convert the decimal to a mixed number by writing out the fraction part as tenths or hundredths, etc, and reduce the fraction to lowest terms.

In the last case, do the same thing.

The second case, a repeating decimal, is a bit trickier. You have to multiply the number by a power of 10 that causes the repeating decimal to shift and realign with the same numbers above and below. The do a subtraction that leaves you with just integers. For example:

x = 0.142857142857...
1,000,000x = 142857.142857...
999,999x = 142857
x = 142857/999,999 = 1/7

Answer 3

Here is a short-cut algorithm to convert a repeating decimal to a fraction

e.g. 0.12345345345...

numerator:
skipping the decimal, write down all the digits to the end of the first repeat, from that, subtract all the digits that don't repeat
i.e. 12345-12 = 12333
for the denominator:
write down a 9 for each repeating digit, followed by a 0 for each non-repeating digit
i.e. 99900

so .12345345345... = 12333/99900
4111/33300

or for dwrls example of .142857142857..
= (142857 - 0)/999999 = 1/7

for .11111 = (1-0)9
= 1/9