What is 0.10110 as a fraction?

Numbers can be represented in a variety of ways including percentages, decimals, and fractions. The ability to convert any number from one format to another is an important math skill to have. These skills are typically thought in fifth grade math and require an understanding of place values and Greatest Common Factor (GCF).

In this article, we teach those skills step by step while demonstrating how to convert decimal 0.10110 into a fraction.

Answer: 0.10110 as a fraction equals 10110/100000 or 1011/10000

Here is the solution for converting 0.10110 to a fraction:

Step 1:

First, we write 0.10110 as  
0.10110/1

Step 2:

Next, we multiply both the numerator and denominator by 10 for each digit after the decimal point. Remember the numerator is the top part of the fraction and the denominator is the bottom part!
0.10110/1
  =  
0.10110 x 100000/1 x 100000
  =  
10110/100000


Step 3:

Next, we find the Greatest Common Factor (GCF) for 10110 and 100000. A factor is a number that divides into another number without any remainder.

The factors of 10110 are: 1  2  3  5  6  10  15  30  337  674  1011  1685  2022  3370  5055  10110 
The factors of 100000 are: 1  2  4  5  8  10  16  20  25  32  40  50  80  100  125  160  200  250  400  500  625  800  1000  1250  2000  2500  3125  4000  5000  6250  10000  12500  20000  25000  50000  100000 
So for 10110 and 100000 that gives us a GCF value of: 10

Step 4:

For the last step we reduce the fraction. This just means writing the fraction in the simplest way. To do this we divide both the numerator and denominator by the GCF value we determined in step 3.
10110/100000
  =  
10110 ÷ 10/100000 ÷ 10
  =  
1011/10000


Good work! We have just walked through the steps on how to represent 0.10110 as a fraction.

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