Comparing decimals — answers

for a grown-up1 question

This is the marking copy and it carries every answer. Her sheet is the other file — same numbering, same margin codes, so you can mark straight down the page.

  1. S24-A72 marks

    Arrange the following from the greatest to the smallest: 9/20, 0.54, 4.05, 1/2

    (A) 9/20, 0.54, 1/2, 4.05   (B) 1/2, 9/20, 0.54, 4.05   (C) 4.05, 0.54, 9/20, 1/2   (D) 4.05, 0.54, 1/2, 9/20

    answer (D) — 4.05, 0.54, 1/2, 9/20

    method Turn everything into decimals so they can be compared directly: 9/20 = 45/100 = 0.45, and 1/2 = 0.5. Now the list is 0.45, 0.54, 4.05, 0.5. Greatest to smallest: 4.05, then 0.54, then 0.5 (= 1/2), then 0.45 (= 9/20).

    watch Comparing 0.54 and 0.5 by counting digits and deciding 0.54 is "longer so bigger" — true here, but it fails for 0.5 versus 0.45. Line up the tenths first, every time.