Decimals & Percents · Understand decimals · 1.5

Decimals & fractions.

A decimal is a fraction with a denominator of 10, 100, or 1000. Read the place value, write it over that power of ten, then simplify. 0.75 = 75/100 = 3/4.

01 / THE IDEA

See it work.

One picture, three forms

Out of one hundred.

75 of the 100 squares are shaded.

decimal0.75
percent75%
fraction3/4

Watch the method

Decimals ↔ fractions

0.75 = 75/100 = 3/4.

1 / 2
0.750.75
1

Read the place value

2 decimal place(s) → over 100.

0.75=751000.75 = \frac{75}{100}
2

Simplify

Reduce to lowest terms.

=34= \frac{3}{4}
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type simplest form, e.g. 3/4.

streak 0
best 0
… =
— / WHY IT WORKS

The idea underneath.

Place value to fraction

Two decimal places → hundredths → over 100. Then reduce to lowest terms.

Why it works

0.75 is 75 hundredths = 3/4.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Write 0.1 as a fraction in lowest terms.

1

Read the place value

1 decimal place(s) → over 10. 0.1 = 1/10

2

Simplify

Reduce to lowest terms. = 1/10

EX 2medium

Write 0.75 as a fraction in lowest terms.

1

Read the place value

2 decimal place(s) → over 100. 0.75 = 75/100

2

Simplify

Reduce to lowest terms. = 3/4

EX 3hard

Write 0.4 as a fraction in lowest terms.

1

Read the place value

1 decimal place(s) → over 10. 0.4 = 4/10

2

Simplify

Reduce to lowest terms. = 2/5

04 / COMMON TRAPS

Where students slip.

Trap

Forgetting to simplify.

Fix

75/100 reduces to 3/4.

Trap

Using the wrong power of ten.

Fix

Count the decimal places: two → /100.

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 fraction in lowest terms.

Need a hint?
  • Count the decimal places for the denominator.
  • Put the digits over it, then reduce.
C2

Write 0.8 as a fraction in lowest terms.

Need a hint?
  • Count the decimal places for the denominator.
  • Put the digits over it, then reduce.
C3

Write 0.4 as a fraction in lowest terms.

Need a hint?
  • Count the decimal places for the denominator.
  • Put the digits over it, then reduce.
C4

Write 0.1 as a fraction in lowest terms.

Need a hint?
  • Count the decimal places for the denominator.
  • Put the digits over it, then reduce.
Apply

Apply (4)

A1

Write 0.125 as a fraction in lowest terms.

Need a hint?
  • Count the decimal places for the denominator.
  • Put the digits over it, then reduce.
A2

Write 0.8 as a fraction in lowest terms.

Need a hint?
  • Count the decimal places for the denominator.
  • Put the digits over it, then reduce.
A3

Write 0.4 as a fraction in lowest terms.

Need a hint?
  • Count the decimal places for the denominator.
  • Put the digits over it, then reduce.
A4

Write 0.25 as a fraction in lowest terms.

Need a hint?
  • Count the decimal places for the denominator.
  • Put the digits over it, then reduce.
Extension

Extension (4)

E1

Write 0.25 as a fraction in lowest terms.

Need a hint?
  • Count the decimal places for the denominator.
  • Put the digits over it, then reduce.
E2

Write 0.8 as a fraction in lowest terms.

Need a hint?
  • Count the decimal places for the denominator.
  • Put the digits over it, then reduce.
E3

Write 0.2 as a fraction in lowest terms.

Need a hint?
  • Count the decimal places for the denominator.
  • Put the digits over it, then reduce.
E4

Write 0.05 as a fraction in lowest terms.

Need a hint?
  • Count the decimal places for the denominator.
  • Put the digits over it, then reduce.