fractions
Repeating Decimals to Fractions
January 17, 2026
5 min read
PanMaths Team
The Algebraic Method
Convert 0.333... (0.3 repeating) to a fraction:
1
Let x = the repeating decimal
x = 0.333...2
Multiply by 10 (or 100 for 2-digit repeat)
10x = 3.333...3
Subtract the original equation
10x - x = 3.333... - 0.333...4
Simplify
9x = 3, so x = 3/9 = 1/3💡Pattern Shortcut
For single-digit repeats: divide by 9 (0.333... = 3/9 = 1/3). For two-digit repeats: divide by 99 (0.272727... = 27/99 = 3/11). For three-digit repeats: divide by 999!
More Examples
0.666...2/310x - x = 6
0.272727...27/99 = 3/11100x - x = 27
0.142857...1/71000000x - x = 142857
Common Repeating Decimals
0.333... = 1/30.666... = 2/30.111... = 1/90.166... = 1/60.142857... = 1/70.0909... = 1/11Classroom & Homeschool Print Packs
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