Decimals & Percents · Understand decimals · 1.2

On the number line.

Decimals sit on the number line between the whole numbers. Splitting each unit into ten equal parts gives the tenths; splitting again gives hundredths. Further right is greater.

01 / THE IDEA

See it work.

Watch the method

Decimals on the number line

0.6 is right of 0.45, so 0.6 > 0.45.

1 / 1
0.6  □  0.450.6 \;\square\; 0.45
1

Line up the place values

Compare digits from the left, place by place.

0.6  >  0.450.6 \;>\; 0.45
— / WHY IT WORKS

The idea underneath.

Decimals as positions

Between 0 and 1, ten tenths; between tenths, ten hundredths. The position shows the size.

Why it works

0.6 is past the halfway mark; 0.45 is just before it.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Compare: 6.17 ▢ 2.84

1

Line up the place values

Compare digits from the left, place by place. 6.17 > 2.84

EX 2medium

Compare: 7.59 ▢ 2.17

1

Line up the place values

Compare digits from the left, place by place. 7.59 > 2.17

EX 3hard

Compare: 1.97 ▢ 3.27

1

Line up the place values

Compare digits from the left, place by place. 1.97 < 3.27

04 / COMMON TRAPS

Where students slip.

Trap

Thinking 0.45 > 0.6 (more digits).

Fix

Line them up: 0.60 vs 0.45 → 0.6 is bigger.

Trap

Misplacing tenths and hundredths.

Fix

Each unit splits into ten tenths.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Compare: 6.83 ▢ 2.41

Need a hint?
  • Compare tenths first.
  • Add a zero so both have the same places.
C2

Compare: 0.75 ▢ 8.73

Need a hint?
  • Compare tenths first.
  • Add a zero so both have the same places.
C3

Compare: 8.28 ▢ 9.52

Need a hint?
  • Compare tenths first.
  • Add a zero so both have the same places.
C4

Compare: 0.41 ▢ 0.56

Need a hint?
  • Compare tenths first.
  • Add a zero so both have the same places.
Apply

Apply (4)

A1

Compare: 8.65 ▢ 8.03

Need a hint?
  • Compare tenths first.
  • Add a zero so both have the same places.
A2

Compare: 6.47 ▢ 9.46

Need a hint?
  • Compare tenths first.
  • Add a zero so both have the same places.
A3

Compare: 1.71 ▢ 9.37

Need a hint?
  • Compare tenths first.
  • Add a zero so both have the same places.
A4

Compare: 6.97 ▢ 7.66

Need a hint?
  • Compare tenths first.
  • Add a zero so both have the same places.
Extension

Extension (4)

E1

Compare: 9.94 ▢ 4.78

Need a hint?
  • Compare tenths first.
  • Add a zero so both have the same places.
E2

Compare: 5.88 ▢ 8.45

Need a hint?
  • Compare tenths first.
  • Add a zero so both have the same places.
E3

Compare: 7.89 ▢ 6.04

Need a hint?
  • Compare tenths first.
  • Add a zero so both have the same places.
E4

Compare: 0.12 ▢ 9.78

Need a hint?
  • Compare tenths first.
  • Add a zero so both have the same places.