Lesson 11

Comparing & Ordering Decimals

Use place value to decide which decimal is larger — and put them in order

Comparing decimals

Decimals on a number line 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.25 0.5 0.75 0.9

Comparing decimals works just like comparing whole numbers — start from the left and go digit by digit.

Step-by-step

  1. Line up the decimal points
  2. Compare digit by digit, left to right
  3. The first different digit tells you which is larger

Example: Which is larger, 3.45 or 3.54?

Ones.TenthsHundredths
3.45
3.54

Same ones (3). Tenths: 4 vs 5 — 5 is larger, so 3.54 > 3.45.

Line up

Write both numbers with the decimal points aligned: 3.45 and 3.54.

Compare ones

Both have 3 in the ones place — they're equal so far.

Compare tenths

3.45 vs 3.54. The tenths are different: 4 vs 5.

Decide

5 > 4, so 3.54 > 3.45. We don't even need to check hundredths!
1 / 4
0.3 < 0.7
0.30
0.70

Common mistake: “more digits = bigger”

0.9 vs 0.85 — which is bigger?

Some students think 0.85 is bigger because it has more digits. Wrong!

Add a zero: 0.9 = 0.90. Now compare: 90 hundredths vs 85 hundredths. 0.9 > 0.85.

Tip: You can always add trailing zeros after the decimal point without changing the value. 0.5 = 0.50 = 0.500

Ordering decimals

To order a set of decimals:

  1. Make all numbers have the same number of decimal places (add zeros)
  2. Compare and arrange from smallest to largest (or largest to smallest)

Example: Order 0.6, 0.45, 0.8, 0.55

Rewrite: 0.60, 0.45, 0.80, 0.55

Order: 0.45 < 0.55 < 0.60 < 0.80

Practice

Which is larger: 2.7 or 2.65?

Put these in order from smallest to largest: 0.3, 0.09, 0.31

Which symbol goes in the blank? 4.05 ___ 4.5

Which decimal is closest to 1?

What number is exactly halfway between 0.2 and 0.3?

Which list is in order from largest to smallest?

Challenge

Quick-Fire Round

Score: 0 / 6 Problem 1 of 6