Comparing and Ordering Decimals: Homework

Plot it, line up the points, compare place by place, and watch for the decimal that only looks bigger.

Part A — Plot and Compare / 12

For 1 and 2, put a dot on the number line for each decimal, then write which is greater using > or <. For 3 to 12, write <, > or =.

1.
Plot 3.4 and 3.7. Which is greater?
Answer
2.
Plot 0.58 and 0.505. (0.505 sits halfway between two marks.) Which is greater?
Answer
3.
6.07 ___ 6.7Answer
4.
12.40 ___ 12.4Answer
5.
3.14 ___ 3.141Answer
6.
0.70 ___ 0.07Answer
7.
8.2 ___ 8.20Answer
8.
15.009 ___ 15.09Answer
9.
0.48 ___ 0.408Answer
10.
2.500 ___ 2.5Answer
11.
9.99 ___ 10.1Answer
12.
0.3 ___ 0.29Answer

Each of these has a trap. Annex zeros so the numbers are the same length before you decide.

These are real times, in seconds. In a race the SMALLER time wins, so read each question carefully.

Think it through, then write your answer and one sentence about how you knew.

1.
The numbers 512, 384, 270 and 196 are in order from greatest to least. Put a decimal point in each one, without moving any digits or changing the order of the numbers, so they read from least to greatest.Answer
2.
Put a zero into 4.5 in three different places: 04.5, 4.50 and 4.05. Which ones change the value, and why?Answer

Write your own, then trade with someone or solve it yourself.

1.
Write four decimals that all start with 7. and put them in order from least to greatest. Make at least one of them a trap: a longer decimal that is actually smaller.Answer

Total / 26

Graded by

Notes

Part A — the comparison.

Part B — the answer.

>
=
2.03 < 2.033 < 2.3 < 2.303
0.66 > 0.606 > 0.6 > 0.066
Any decimal between them, such as 1.395 or 1.391. (1.4 is 1.40, so anything from 1.391 to 1.399 works.)

Part C — the answers.

a. 9.63 < 9.75 < 9.79 (Bolt, Blake, Gatlin) b. No. 9.8 is 9.80, which is more than 9.79, so it is slower. c. 0.12 seconds
a. Yes. Each time is less than the one above it. b. 0.16 seconds, by Bolt's record in 2009 c. No. 9.6 is 9.60, and 9.60 is more than 9.58, so his time is slower.

Part D — one correct answer, and what a good explanation says.

One way: 0.512 < 3.84 < 27.0 < 196. Other answers work if each number is less than the next.
Only 4.05 changes. A zero at the front or the end leaves 4.5 the same, but a zero after the point pushes the 5 into the hundredths place, so 4.05 is smaller.

Part E — what a good problem looks like.

Answers vary. A good one mixes lengths, such as 7.09 < 7.1 < 7.15 < 7.2, where 7.09 has more digits than 7.1 but is smaller.