Before we start talking about decimal to fraction conversion, let’s say something about decimals.
Well, decimal numbers, or as we shorter call them decimals, are a special form of fractions. As classic fractions, they are the way to represent "not-whole" numbers.
In decimals we operate with a system based on 10s. They are much easier than regular fractions. And they have a different way of noting.
Percents, on the other hand, are even more specific fractions. They are fractions with the denominator = 100.
OK, let’s see and convert decimal to fraction in the following less-than-one example, with just one decimal place.
So, no whole numbers, just 8 10ths. Afterwards we can reduce of course.
Now let’s see a greater-than-one example again with 1 decimal place.
2.3 = 2
2×10 + 3
A point (dot) is a separation point between whole numbers part on the left and the
fractions part (10ths, 100ths, 1000ths etc) on the right hand side.
This example, 2 wholes and 3/10, is represented by 2.3.
We notice that there are no 10ths stated anywhere. That’s because they are already implied.
Here’s a shorter (recommended) version for this conversion:
Only 1 decimal place (digit) – means we’re dealing with 10ths, so 1 zero in the denominator (apart from mandatory 1),
and then you just lift the whole number (number 4 in this case) up to the numerator.
Now with 2 decimal places:
Again, very similar, we have 2 decimal places – that means we’ll have 2 zeros in our denominator.
At the end – we lift up the whole number and join it with decimal/fraction part.
It doesn’t matter how big the number is – you always follow the same pattern.
Let’s demonstrate it one more time, now a 2 digit number with 3 decimal places:
After this fast conversion, we simplify if applicable.
Conclusion for Decimal to Fraction Conversion page:
First we deal with fraction part, and then with a whole numbers part
How many decimal places – that many zeros in the denominator
After the fraction part – we lift the whole number part (if any) up to the numerator
Due to 10 based numbers as denominators – we can only simplify by 10s and its factors, i.e. 5 and 2