Fraction to Decimal Conversion Tricks & Percent Shortcuts

Converting fractions like $1/7$, $1/8$, or $5/9$ into decimals mentally makes standardized test taking and real-world math effortless.

2. The Magic Cycle of Sevenths (1/7 = 0.142857...)

5. Proof & Algorithm for Converting Repeating Decimals to Fractions

To convert a repeating decimal like $0.142857142857dots$ or $0.272727dots$ into an exact fraction:

6. Converting Fractions to Percentages Instantly

To convert any fraction to a percentage in your head, break it down into benchmark units (1/2 = 50%, 1/4 = 25%, 1/10 = 10%, 1/100 = 1%):

7. Terminating vs. Repeating Decimals Rule

A reduced fraction p/q converts to a terminating decimal if and only if the prime factorization of denominator q contains NO prime factors other than 2 and 5.

8. The 99 and 999 Rule for Complex Repeating Decimals

Any repeating decimal with a repeating block of length $k$ can be written immediately over a denominator of $k$ nines:

9. Mental Percent Multiplication: The Split & Combine Method

To find 15% of $240$, split 15% into $10% + 5%$: $10% ext{ of } 240 = 24$, $5% ext{ of } 240 = 12 implies 24 + 12 = 36$!