How to turn a decimal into a fraction, repeating ones too.
How to turn 0.375 into 3/8, and a repeating decimal such as 0.1666… into 1/6, step by step, plus the nearest fraction of an inch to a decimal.
By Suraj Kumar4 min read
A decimal that ends is a fraction over a power of ten. One that repeats takes one more trick, which always works.
A decimal that ends.
0.375 has three digits after the point, so it is 375/1000. Divide the top and bottom by 125, the largest number that goes into both, and it is 3/8.
A decimal that repeats.
Call 0.1666… x. Multiply by 100 to move one repeat past the point, 100x = 16.666…, and by 10 for the digit that does not repeat, 10x = 1.666… Take one from the other and the repeating sixes cancel: 90x = 15, so x = 15/90 = 1/6. On the page, write 0.1(6) or 0.1666… and these steps are shown.
The nearest simple fraction, and inches.
For a long decimal such as 3.14159, the page lists simpler fractions near it, found by continued fractions: 22/7, then 333/106, then 355/113. For the part after the point it also gives the nearest half, quarter and so on down to a sixty-fourth, as on a tape measure, with how far off each is.
Further reading
Topics: decimal to fraction · repeating decimal to fraction · convert decimal to fraction · 0.333 as a fraction · recurring decimal · decimal to inches
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