Problem 2 · 1987 AJHSME
Easy
Fractions, Decimals & Percents
scale-to-power-of-ten
2 ⁄ 25 =
Show answer
Answer: B — .08.
Show hints
Hint 1 of 2
Decimals are just fractions whose denominator is 10, 100, 1000… Can you nudge the 25 into one of those?
Still stuck? Show hint 2 →
Hint 2 of 2
25 × 4 = 100, and a denominator of 100 means you can read the answer straight off as hundredths.
Show solution
Approach: scale the denominator to a power of 10
- A denominator of 25 isn't a power of ten, but 25 × 4 = 100 is. Multiply top and bottom by 4: 2⁄25 = 8⁄100.
- 8⁄100 is just 8 hundredths = 0.08.
- Why this transfers: any fraction whose denominator divides a power of 10 (denominators built only from 2s and 5s) becomes an exact decimal this way — 7⁄20 → 35⁄100 = 0.35, 3⁄8 → 375⁄1000 = 0.375.
Another way — long division:
- Divide 2 ÷ 25 directly: 25 goes into 20 zero times, into 200 eight times exactly.
- Result 0.08 — same answer, but scaling to 100 skips the work.
Mark:
· log in to save