55.55…% = 5/9 in 2 Seconds: Percentage ↔ Fraction Trick for CLAT Quant

QUANT SHORTCUT | 19 OCTOBER 2026

Convert 55.55…% into a fraction. The slow way is to write 5555/10000 and start cancelling, and that is not even the right number, because 55.55…% keeps going (55.5555…%). Amit Sir’s shortcut gives the exact answer, 5/9, in about two seconds. This lesson explains why the trick works, extends it to the whole 1/9 and 1/11 family, and lists the fraction–percentage equivalents every CLAT Quantitative Techniques candidate should know by heart.

The two-second trick

Look at the two-digit block that repeats on both sides of the decimal point.

• The block is in the table of 11 (11, 22, 33 … 99): write 9 in the denominator. The numerator is how many 11s make the block. Example: 55.55…% → 55 = 11 × 5 → 5/9.
• The block is in the table of 9 (09, 18, 27 … 90): write 11 in the denominator. The numerator is how many 9s make the block. Example: 63.63…% → 63 = 9 × 7 → 7/11.

Why it works

Any repeating block ab.abab…% equals ab/99. Since 99 = 9 × 11, a block that is a multiple of 11 cancels to a denominator of 9, and a block that is a multiple of 9 cancels to a denominator of 11. So the trick is simply 1/9 = 11.11…% and 1/11 = 9.09…%, multiplied up: 5/9 = 5 × 11.11…% = 55.55…%, and 7/11 = 7 × 9.09…% = 63.63…%.

Worked examples

1. 44.44…%: 44 = 11 × 4, so the fraction is 4/9.
2. 27.27…%: 27 = 9 × 3, so the fraction is 3/11.
3. 81.81…%: 81 = 9 × 9, so the fraction is 9/11.
4. 88.88…%: 88 = 11 × 8, so the fraction is 8/9.
5. Using it in a sum. 55.55…% of 360 = 5/9 × 360 = 200.
6. Reverse. 7/8 = 7 × 12.5% = 87.5%, and 3/8 = 3 × 12.5% = 37.5%.

Homework from the video: try Amit Sir’s two homework sums yourself, comment your answers under the reel, and check them in the next reel at 12 noon.

Fraction–percentage equivalents (1/2 to 1/20)

Learn the unit fractions below until you can recall them instantly; every other fraction is a multiple of one of them (for example 5/8 = 5 × 12.5% = 62.5%).

Common traps

First, check that the block really repeats. 55.55% written as a plain terminating number is 1111/2000, not 5/9; the trick is for the recurring value. Second, read the whole two-digit block: 72.72…% has the block 72 = 9 × 8, so it is 8/11, not 8/9. Third, 1/7 does not repeat in two digits (14.285714…%), so treat it as 14 2/7%. Finally, when an answer option is a fraction, convert the percentage first and compare fractions; it is faster than turning every option into a decimal.

Sources

Standard quantitative aptitude methods for converting recurring decimals and percentages to fractions, as taught in CLAT Quantitative Techniques preparation. Every value on this page was checked by exact fraction arithmetic.