Problem 5 · 1998 AJHSME
Medium
Fractions, Decimals & Percents
compare-decimals
Which of the following numbers is largest?
Show answer
Answer: B — 9.1234Μ (B).
Show hints
Hint 1 of 2
Don't read the overline bars as 'long' β read them as 'what comes next.' Every choice opens 9.1234β¦, so line them up and find the first place where one digit beats the others.
Still stuck? Show hint 2 →
Hint 2 of 2
To compare decimals, scan left to right and stop at the first column where they differ β the bigger digit there wins, no matter how many digits trail behind.
Show solution
Approach: line them up and find the first column that differs
- Write the bars out a few places: A 9.12344, B 9.12344Μ = 9.123444β¦, C 9.1234343β¦, D 9.1234234β¦, E 9.1234123β¦. All share 9.1234, so look at the 5th decimal place: it's 4 for A and B, but only 3, 2, 1 for C, D, E. The winner is A or B.
- A and B agree through 9.12344. At the next place A has nothing (it stopped) β that's a 0 β while B keeps going with another 4. So B pulls ahead: B is largest.
- Trap to remember: more digits does NOT mean bigger. A short number can beat a long one (0.9 > 0.12345). Compare position by position, left to right, and the first place that differs decides it.
Mark:
· log in to save