Compare decimals when their lengths differ

start. Which is greater, 0.8 or 0.75?

Answer: 0.8 is greater. Eight tenths is eighty hundredths, and eighty hundredths is greater than seventy-five hundredths.

Teacher response: Listen for this idea: 75 is greater than 8, so 0.75 must be greater than 0.8. Follow up: The two digit strings are counting different units. Rename both quantities in hundredths or compare the tenths first.

example. Which is greater, 0.8 or 0.75?

1. Check that both decimals describe the same whole and the same measurement unit.
2. Compare ones first, then tenths. Both numbers have zero ones; 0.8 has eight tenths, while 0.75 has seven tenths and five hundredths.
3. Rename 0.8 as 0.80 if a common unit helps. Compare 80 hundredths and 75 hundredths.
4. Record 0.8 > 0.75 and explain the first place that settled the comparison. If the tenths are equal, compare hundredths next.

Worked example: 0.8 is greater. Eight tenths is eighty hundredths, and eighty hundredths is greater than seventy-five hundredths.

p1. Compare 0.6 and 0.58. Enter <, = or >.

Answer: >

Teacher response: 60 hundredths is greater than 58 hundredths.

p2. Compare 0.32 and 0.39. Enter <, = or >.

Answer: <

Teacher response: The tenths match; two hundredths is less than nine hundredths.

p3. Compare 0.4 and 0.40. Enter <, = or >.

Answer: =

Teacher response: Four tenths is forty hundredths.

e1. Compare 0.09 and 0.1. Enter <, = or >.

Answer: <

Teacher response: One tenth is ten hundredths, just above nine hundredths.

transfer. Can you decide whether 0.9 or 0.86 is greater without rewriting either number?

Answer: Yes. Compare tenths: nine tenths is greater than eight tenths plus six hundredths, which is still below nine tenths.

next. If the learner compares 86 with 9, return to equal wholes and hundredths. If secure, ask for a number lying between two decimals.