What is .125 as a fraction and what is it in simplified form?
To convert a decimal into a fraction simply divide the numbers after the fraction by the number of numbers after the decimal raised to the power of 10. With the number .125 there are 3 numbers after the decimal place therefore the denominator is 10 to the power of 3 which is 1000.
The initial fraction when converting a decimal to a fraction using this technique sees its representation as follows:
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However, while this is a fraction , it’s not the simplest fraction . Meaning the numbers for both the numerator and denominator could be reduced to smaller numbers and the result would still be the same being 0.125.
How Do You Reduce A Fraction
You reduce a fraction by finding a common factor shared between both the numerator and denominator and dividing both numbers by the common factor.
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In the example with the initial fraction representing 0.125 you can reduce both numbers by 5.
By doing this the reduced fraction would look something like this:
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As you can see from the above process the original fraction has been reduced by a common factor of five which produces a new fraction with a different numerator and denominator.
However, you should see with the new numerator and denominator that both of these numbers can be divided by a common factor of 5 again.
Performing this operation on the new fraction would produce the following:
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As you can see the process of a successful reduction on a fraction produces a new fraction. There can’t be any remainder portion from applying the common factor to both numbers.
Once again with the new fraction after the second reduction you can apply reduction by once again reducing both numbers by 5. This would produce our final simplified fraction of 0.125:
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As you can no longer reduce either number any further you have arrived at the simplest representation in fraction form of 0.125.
Reducing Fractions In One Go
While you can reduce fractions multiple times you could do the same process in one go provided you find the highest common factor between both numbers.
Finding the highest common factor (HCF) will reduce error in reduction as it only happens once.
To find the HCF between 125 and 1000 list all the common factors shared between both numbers and once you have your list choose the highest number from this list.
Here’s a list of the common factors between 125 and 1000:
{ 1, 5, 25, 125 }Therefore, the HCF is 125 and applying it to the initial fraction would look something like this:
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The result will be exactly the same as if you were doing it the longer multiple factor way!
Summary
The decimal .125 as a fraction is one eighth in its simplest form. To convert a decimal to a fraction divide the number after the decimal place by the number of numbers raised to the 10th power and then reduce this fraction by any common factors.
Therefore, your initial fraction when converting 0.125 to a fraction will be 125 over 1000, and when you reduce this fraction by dividing both numbers by the highest common factor of 125 it will reduce the fraction to 1 over 8.
Next, you might want to try and see how you go finding out what .375 as a fraction would be, or .625 as a fraction .