What is the fraction for 0.18?

Answer 1

I like to do this as follows:

1.) I put the number in question at the top of a fraction (I think it's called "numerator" in English) and a "1" at the bottom ("denominator"), as everything stays the same if you divide it by one. It looks like this:

0.18 --> 0.18/1

2.) Then add a few zeros to the "1" so that both numbers have an equal number of digits. Now you can remove the decimal point from the first number.
This is ok: The fraction line means that this whole thing is the "ratio" or "relationship" of the upper bit in comparison to the lower bit. And 18 compared to a hundred is the same as 0.18 compared to one. Also you can now take away the leading zero:

0.18/1 --> 018/100 --> 18/100

3.) Now comes the hard bit (but also the bit where you can be creative. Who said that Maths is dull?): find a number that can fill out both 18 and 100 completely without leaving any space. Then you need to divide both numbers through that number so the become smaller. This is called "cancelling". It makes the fraction smaller and nicer.

So can you think of a number? How about "1"? Well it would fill both 18 and 100 completely without leaving any space, but it wouldn't get us anywhere. Remember that everything stays the same if you divide it by "1". So how about the next higher number: "2"

good, 2 fits exactly 9 times into 18 (2+2+2+2+2+2+2+2+2) and exactly 50 times into 100. So now we insert these numbers in our fraction:

9/50

And now? Normally we would now do the same thing again and again and again: find a number that fills both the numerator and the denominator completely without leaving a rest, then divide both by that number and put the results in our fraction.

How about you try it for yourself :-)

... Hah, tricked you. There are no more numbers that you can use for that. That means, we're finished: the fraction for 0.18 is: 9/50 !!

Try it with a few other numbers: 0.35, 0.12, 0.155.....

If you keep practicing (just make up two or three numbers every day and find their fraction) you will one day just have to look at a decimal number the fraction will come to you automatically.

P.S. If you come across a decimal number that has a different number than a zero on the left of the point, then just exchange it for a zero and put it away, somewhere where you can't lose it. Then find the fraction finally and put the number back in front. For example:

7.16 --> 0.16 --> 0.16/1 --> 016/100 --> 16/100 --> 8/50 --> 4/25 --> 7 4/25

By the way, the answers for the examples are

0.35 --> 7/20
0.12 --> 3/25
0.155 --> 31/155

But surely you know that already, hm? :-)