What is .375 as a fraction in its simplest form?
To convert a decimal number to a fraction divide the numbers after the decimal place by 10 to the power of the quantity of numbers after the decimal place.
For example, the number 0.375 has the number 375 after the decimal point and as there are 3 numbers after the decimal point 10 to the power of 3 gives 1,000: a one with 3 zeroes after it.
Therefore, your decimal in fraction form would initially look like this:
| 375 |
| 1000 |
This is the decimal 0.375 in its initial fractional form, but can you reduce both numbers of the denominator and the numerator in that fraction to smaller numbers?
How To Reduce A Fraction
Reducing a fraction means the numerator and the denominator numbers of a fraction become smaller by dividing both numbers by the same common factor . Therefore, the decimal value value of the fraction will stay the same , but the fraction will be different.
To determine whether you can reduce a fraction to smaller numbers you need to find a common factor.
If you can find the highest common factor for both numbers then you only need to reduce once . If you find anything but the highest common factor then you will need to do multiple reductions .
Here’s how reducing our fraction above would look if you chose the highest common factor approach, or if you chose another approach.
Step 1: Find All Factors Of Both Numbers
What are the factors of 375 and 1,000?
List them out first:
375 {1, 3, 5, 15, 25, 75, 125, 375}
1000 {1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000}
As you can see from the two sets of numbers representing all the factors of each number, the highest common factor between both is 125.
Step 2A: Using Highest Common Factor
To reduce the original fraction using the highest common factor simply divide both numbers by the highest common factor:
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Therefore, by dividing each number in the fraction by 125 we can reduce the original fractional form to its simplest form in one go.
Step 2B: Using Smaller Common Factors
But sometimes it may be difficult to find the highest common factor, especially as the numbers get larger, so another approach is to find smaller common factors and to keep dividing by these lesser amounts until there are no common factors shared between both numbers.
Using the approach may look a little something like this:
A) Both numbers share a common factor of 5, so divide both numbers by 5:
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B) Both numbers still share a common factor of 5, so divide the two new numbers by 5 again:
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C) Both numbers still share a common factor of 5, so divide the two new numbers by 5 yet again:
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As there are no common factors between 3 and 8 the reduction process using this approach has finished.
Step 3: Check Your Fraction
A final step you can do to see if you have the correct answer is to perform the division on the reduced fraction to see if it produces the same decimal.
Using the short-form version of division, structure your numbers like so:
| 8 | 3 |
Then start the division process: how many times does 8 go into 3?
It doesn’t, therefore place 0 directly above the 3, insert a decimal point after the three, and carry the remainder portion, being 3, up against the first zero after the decimal:
| 0 | . | ||
| 8 | 3 | . | 3 0 |
Repeat the division process again: how many times does 8 go into 30?
It goes 3 times with 6 remaining. Place the 3 above the division line and place the remainder over against the next zero after the first zero:
| 0 | . | 3 | ||
| 8 | 3 | . | 3 0 | 6 0 |
Repeat the division process again: how many times does 8 go into 60?
It goes 7 times with 4 remaining. Therefore, place the 7 above the division line and carry the remainder over against the next zero after the second zero:
| 0 | . | 3 | 7 | ||
| 8 | 3 | . | 3 0 | 6 0 | 4 0 |
Repeating the division process again: how many times does 8 go into 40?
It goes exactly 5 times. Therefore, place this number above the division line and since there is nothing left to carry you have arrived at your answer and this is the same decimal number you started with. Therefore, the reduced fraction of 3 over 8 is the simplified fraction of the decimal 0.375.
| 0 | . | 3 | 7 | 5 | |
| 8 | 3 | . | 3 0 | 6 0 | 4 0 |
Summary
The decimal number .375 can be expressed as a fraction of 3 eighths (3 over 8).
To perform the conversion of a decimal number to a fraction simply divide the numbers after the fraction by the quantity of numbers raised to the power of 10. Then with your initial fraction try to reduce both numbers by a common factor to achieve the simplest fraction form of the decimal number.
Next, you might want to see how you go with a similar problem of representing .625 as a fraction .