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Why does one fraction turn into a decimal that ends neatly, while another can continue with digits forever? The answer has to do with the numbers in the fraction—and 5/16 is a great example to explore.
The decimal for 5/16 is 0.3125.
But how do we get this number, and how can we be sure it is correct? Let's work it out step by step.
How Do You Convert 5/16 to a Decimal?
Imagine splitting something into 16 equal parts and taking 5 of them. The fraction 5/16 represents those five parts out of the total 16.
To express this fraction as a decimal, divide the numerator (the top number) by the denominator (the bottom number).
Fraction to Decimal
5 ÷ 16 = 0.3125
Here is how the division works:
The digits after the decimal point are 3, 1, 2, and 5. That gives us 0.3125.
But there is something interesting about this result: the division ends exactly. Why doesn't it continue with more digits?
Why Does 5/16 Have a Decimal That Ends?
A decimal that stops after a finite number of digits is called a terminating decimal. For example, 0.5 and 0.25 are terminating decimals, while 0.333... continues indefinitely.
The reason 5/16 terminates becomes clearer when you look at its denominator.
Rewrite the fraction
5/16 = (5 × 625)/(16 × 625)
= 3125/10,000 = 0.3125
Since 16 = 2 × 2 × 2 × 2, we can rewrite the fraction with a denominator of 10,000:
Now the decimal is easy to see: 3,125 ten-thousandths equals 0.3125.
This is a useful trick to remember.
A fraction in its simplest form has a terminating decimal when its denominator contains only the prime factors 2 and/or 5. Since the denominator here is 16, the decimal ends.
How Can You Check That 0.3125 Is Correct?
You don't have to repeat the long division to check your answer. Instead, reverse the calculation.
Multiply the decimal by the original denominator:
Verification
0.3125 × 16 = 5
You get the original numerator, 5, so the conversion checks out.
Try the same check whenever you convert a fraction to a decimal: multiply your decimal answer by the denominator. If the result matches the numerator, you have verified the calculation.
What Is 5/16 of an Inch in Decimal Form?
The same conversion is useful when measuring length. Five-sixteenths of an inch equals exactly 0.3125 inches.
Exact Measurement
0.3125 inches
However, you may sometimes see this measurement written as 0.31 inches. Is that a different measurement?
Not exactly. It is the same measurement rounded to two decimal places.
| Form | Value |
|---|---|
| Fraction | 5/16 inch |
| Exact decimal | 0.3125 inches |
| Rounded to the nearest hundredth | 0.31 inches |
| Percentage of one inch | 31.25% |
The distinction matters when precision is important. For a calculation that requires the exact value, use 0.3125. If a measurement needs to be rounded to the nearest hundredth of an inch, use 0.31 inches.
Explore more math topics related to division, fractions, decimals, measurements, and everyday math.
Quick Challenge
Can You Convert Another Fraction?
Now that you know how 5/16 becomes a decimal, try this one before checking the answer.
YOUR NEXT FRACTION
What is 3/16 as a decimal?
Divide 3 by 16:
3 ÷ 16 = 0.1875
Notice that the denominator is still 16, so the decimal also ends after four places. The numerator changes the result, but the same conversion method works.
Frequently Asked Questions
Remember
Converting a fraction to a decimal is not just about memorizing an answer. Divide the numerator by the denominator, check the result, and look for patterns that help you solve the next fraction more easily.
