What is .625 as a fraction in its simplest form and how do you work it out?
To convert a decimal to a fraction simply divide the number after the decimal place (the dot) by the number of numbers raised to the 10th power. This will give you the decimal in its initial fraction form. Then just reduce both numbers by the highest common factor to produce the decimal in its simplest fractional form.
For example, the decimal number 0.625 has 625 as its number after the decimal place and has 3 numbers after the decimal place and 10 to the power of 3 is 1,000. Therefore, placing both numbers into fractional form would produce the following:
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This is 0.625 as a fraction. At least, initially.
How To Reduce A Fraction
Reducing a fraction means representing the fraction using smaller numbers. For this to occur both the number on top (the numerator) and the number on the bottom (the denominator) must both be divided by the same number and produce whole numbers (no remainders) as results.
Reducing a fraction can involve one step: if you can find the highest common factor shared between both numbers, or can involve many steps if you reduce by factors smaller than the highest common factor.
Each approach works fine, with obviously the reduction by the highest common factor being the best as only one reduction is needed. However, finding the highest common factor between two numbers can be tedious – especially when the numbers are large!
Reduce Fraction With Highest Common Factor
To reduce a fraction using the highest common factor you need to find the highest common factor first.
The easiest way is to list all the factors for each number so that no factors are missed.
Here are the factors of 625 and 1,000:
625 { 1, 5, 25, 125, 625 }
1000 { 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 125, 200, 250, 500, 1000}As you can see from the list of factors above for both numbers, the following factors are shared between both:
{ 1, 5, 25, 125 }Which is the highest? It’s 125 .
Therefore, to reduce our initial fraction to its simplest form using the highest common factor you simply divide both numbers by 125, as follows:
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Therefore, the decimal 0.625 as a fraction is 5 eighths.
Reduce Fraction Using Smallest Factors
An easier way to reduce a fraction is to reduce using smaller factors. This approach can feel easier as all you need to do is find a common factor greater than 1 and once you do to perform the division on both numbers. You continue to repeat this process until the only common factor shared between both numbers is the number 1.
The only issue with this problem is that if many steps are involved, it can increase the likelihood of making a mistake. So be careful when using this approach!
Anyway, here’s how this would look when performing this operation on the original fraction above.
The first common factor shared by both 625 and 1000 is 5, therefore, reduce each number by 5:
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The new set of numbers share the factor of 5, therefore, reducing each by 5 again produces a new fraction:
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Again, looking at the new fraction there is a shared factor for 25 and 40 and this is the number 5 again, therefore reducing both by 5 produces another new fraction:
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Looking at both numbers you can see that we have a prime number (5) as one of the numbers, therefore, the reducing process would cease.
Notice how the answer is the same as the process with reducing using the highest common factor?
Check Decimal To Fraction Conversion
To check if a decimal to fraction conversion is correct, you can get your fraction and convert it back to a decimal by using the techniques of division.
As the answer arrived involves small numbers you could check your answer by using short division .
To perform short division write the numbers from the fraction in the following manner:
| denominator | numerator |
Which, from the answer achieved of 5 eighths with this post would mean the short division would be filled in with the following numbers:
| 8 | 5 |
Then to start the division process the question is asked: how many times does 8 go into 5?
It doesn’t, therefore 0 is placed above the number 5, the decimal place could similarly be placed above (as it’s the only decimal in the operation) and the remainder of 5 is passed across to the first zero after the decimal place, like so:
| 0 | . | ||
| 8 | 5 | . | 5 0 |
Then the process continues by asking: how many times does 8 go into 50?
It goes 6 times with 2 remaining, therefore, the 6 goes above the division line (above the first zero) and the remainder of 2 goes across to the next zero, like so:
| 0 | . | 6 | ||
| 8 | 5 | . | 5 0 | 2 0 |
I like to cross out the division I’ve done to make it easier for me to focus on the numbers I need to work on next, which is: how many times does 8 go into 20?
It goes twice with four remaining, therefore, 2 goes above the second zero and 4 moves across against the next zero, like so:
| 0 | . | 6 | 2 | ||
| 8 | 5 | . | 5 0 | 2 0 | 4 0 |
Once again the process repeats until I have to remainders from the division process (or if I notice the same number repeating itself): how many times does 8 go into 40?
It goes 5 times with no remainder, therefore, we have finished our short division exercise.
| 0 | . | 6 | 2 | 5 | |
| 8 | 5 | . | 5 0 | 2 0 | 4 0 |
And as you can see the answer from the short division activity produces the same number as the original starting number of 0.625. Therefore, you can be assured you’ve correctly identified the fraction representing .625.
Summary
The decimal .625 can be represented as the fraction 5 eighths.
To arrive at this answer divide the decimal portion by the number of numbers after the decimal place which will initially produce a fraction of 625 over 1000. When you reduce these numbers by the highest common factor of both by 125 you get a new simplified fraction of 5 over 8.
You might want to try your own hand at finding what .375 as a fraction is next.