Example 1 · level 1
Write 0.44444… (the 4 repeats) in the form p/q (lowest terms).
Show solution
- Let x = 0.4444…
- 10x = 4.4444…
- 10x − x = 4 → 9x = 4 → x = 4/9.
Answer: 4/9
CLASS 9 MATHS · NUMBER SYSTEMS
Convert recurring decimals to p/q form
Let x be the decimal, multiply by 10, 100 … to line up the repeating part, subtract, and solve for x.
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Worked examples
Example 2 · level 2
Write 0.31313131… (the block 31 repeats) in the form p/q (lowest terms).
Show solution
- Let x = 0.313131…
- 100x = 31.313131…
- 100x − x = 31 → 99x = 31 → x = 31/99.
Answer: 31/99
Example 3 · level 3
Write 0.277777… (only the 7 repeats) in the form p/q (lowest terms).
Show solution
- Let x = 0.27777…
- 10x = 2.7777… and 100x = 27.777…
- 100x − 10x = 27 − 2 = 25 → 90x = 25 → x = 5/18.
Answer: 5/18