Decimals & Percents · Understand percents · 5.4

Benchmark percents.

A few percents come up constantly: 50% = 1/2 = 0.5, 25% = 1/4 = 0.25, 10% = 1/10 = 0.1, 75% = 3/4 = 0.75. Knowing these by heart makes percent work fast.

01 / THE IDEA

See it work.

One picture, three forms

Out of one hundred.

25 of the 100 squares are shaded.

decimal0.25
percent25%
fraction1/4

Watch the method

Benchmark percents

0.25 = 25% = 1/4.

1 / 2
0.250.25
1

Multiply by 100

Percent means “out of 100”, so ×100 — shift the point two places right.

0.25×1000.25 \times 100
2

Add the % sign

The result is the percent.

=25%= 25\%
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a percent, e.g. 25%.

streak 0
best 0
… =
— / WHY IT WORKS

The idea underneath.

Know the common ones

The benchmark percents and their decimal/fraction forms are worth memorising for speed.

Why it works

25% is a quarter; 50% is a half.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Write 0.6 as a percent.

1

Multiply by 100

Percent means “out of 100”, so ×100 — shift the point two places right. 0.6 × 100

2

Add the % sign

The result is the percent. = 60%

EX 2medium

Write 0.8 as a percent.

1

Multiply by 100

Percent means “out of 100”, so ×100 — shift the point two places right. 0.8 × 100

2

Add the % sign

The result is the percent. = 80%

EX 3hard

Write 0.125 as a percent.

1

Multiply by 100

Percent means “out of 100”, so ×100 — shift the point two places right. 0.125 × 100

2

Add the % sign

The result is the percent. = 12.5%

04 / COMMON TRAPS

Where students slip.

Trap

Re-deriving 25% = 0.25 every time.

Fix

Memorise the benchmarks.

Trap

Mixing 0.1 and 0.01.

Fix

10% = 0.1, 1% = 0.01.

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

Write 0.6 as a percent.

Need a hint?
  • Recall the common equivalents.
  • Use the grid to confirm.
C2

Write 0.6 as a percent.

Need a hint?
  • Recall the common equivalents.
  • Use the grid to confirm.
C3

Write 0.25 as a percent.

Need a hint?
  • Recall the common equivalents.
  • Use the grid to confirm.
C4

Write 0.5 as a percent.

Need a hint?
  • Recall the common equivalents.
  • Use the grid to confirm.
Apply

Apply (4)

A1

Write 0.1 as a percent.

Need a hint?
  • Recall the common equivalents.
  • Use the grid to confirm.
A2

Write 0.5 as a percent.

Need a hint?
  • Recall the common equivalents.
  • Use the grid to confirm.
A3

Write 0.8 as a percent.

Need a hint?
  • Recall the common equivalents.
  • Use the grid to confirm.
A4

Write 0.4 as a percent.

Need a hint?
  • Recall the common equivalents.
  • Use the grid to confirm.
Extension

Extension (4)

E1

Write 0.2 as a percent.

Need a hint?
  • Recall the common equivalents.
  • Use the grid to confirm.
E2

Write 0.5 as a percent.

Need a hint?
  • Recall the common equivalents.
  • Use the grid to confirm.
E3

Write 0.5 as a percent.

Need a hint?
  • Recall the common equivalents.
  • Use the grid to confirm.
E4

Write 0.05 as a percent.

Need a hint?
  • Recall the common equivalents.
  • Use the grid to confirm.