MATHEMATICSNumber & Arithmetic
Decimals
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● Master Topic Guide Verified 11+ Curriculum
Decimals Master Guide ✏️
Master decimal place value, ordering, rounding, four operations, and decimal-fraction conversions for 11+ exams!
✏️
DECIMALS OVERVIEW
Decimals are another way to show parts of a whole. They use a decimal point to separate the whole number from the fractional part.
1. PLACE VALUE
Each digit in a decimal has a place value.
| Ones (1) | Tenths (1/10) | Hundredths (1/100) | Thousandths (1/1000) |
|---|---|---|---|
| 3 | . 4 | 6 | 7 |
3.467 ═ 3 + 0.4 + 0.06 + 0.007
2. DECIMAL MODELS
Decimals can be shown using visual models.
0.1 (one tenth)
0.25 (twenty-five hundredths)
0.75 (seventy-five hundredths)
3. READING DECIMALS
Read whole number, then "and", then decimal part.
2.3 two and three tenths
4.56 four & 56 hundredths
0.7 zero and seven tenths
4. COMPARING DECIMALS
Line up decimal points and compare each place value.
3.45 > 3.41 (5 hundredths > 1 hundredth)
2.075 < 2.08 (75 thousandths < 80 thousandths)
5. ORDERING DECIMALS
Ascending (smallest to largest):0.12, 0.28, 0.5, 0.9
Descending (largest to smallest):3.7, 3.65, 3.6, 3.56
6. ROUNDING DECIMALS
Round 3.456 to nearest tenth:3.456 ≈ 3.5 (look at 5)
Round 7.892 to nearest hundredth:7.892 ≈ 7.89 (look at 2)
7. ADDING & SUBTRACTING DECIMALS
Addition:12.34 + 5.678
═ 18.018
═ 18.018
Subtraction:9.50 − 2.367
═ 7.133
═ 7.133
8. MULTIPLYING & DIVIDING DECIMALS
Multiply:2.4 × 0.3
═ 0.72 (2 d.p.)
═ 0.72 (2 d.p.)
Divide:4.92 ÷ 3
═ 1.64
═ 1.64
TOP DECIMALS TIPS
- • Always line up decimal points when adding/subtracting!
- • Add zeros to make equal decimal places (e.g., $9.50$).
- • Place value gets 10 times smaller as you move right.
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DECIMAL FRACTIONS
Decimals and fractions are different ways of showing parts of a whole. They are equal when they represent the same value.
1. FRACTIONS
Shows parts of a whole.
1/4 (one quarter)
2. DECIMALS
Use place value to show parts of a whole.
0.23 (23 hundredths)
3. EQUIVALENT VALUES
Fractions and decimals can be equal.
1/4 ═ 0.25
5. CONVERTING BETWEEN DECIMALS & FRACTIONS
Decimal ➔ Fraction:
0.1 ═ 1/10
0.25 ═ 1/4
0.5 ═ 1/2
0.75 ═ 3/4
0.2 ═ 1/5
Fraction ➔ Decimal:
1/2 ═ 0.5
1/4 ═ 0.25
3/5 ═ 0.6
3/4 ═ 0.75
7/10 ═ 0.7
7. COMMON DECIMAL-FRACTION EQUIVALENTS
| Fraction | Decimal | Fraction | Decimal |
|---|---|---|---|
| 1/2 | 0.5 | 3/4 | 0.75 |
| 1/4 | 0.25 | 1/3 | 0.333… |
| 1/5 | 0.2 | 2/3 | 0.666… |
| 2/5 | 0.4 | 3/5 | 0.6 |
| 1/10 | 0.1 | 9/10 | 0.9 |
INTERACTIVE DECIMALS CHAMPION QUIZ11+ Exam Practice
1. Convert 3/4 to a decimal:
2. Round 3.456 to nearest tenth:
3. Calculate: 12.34 + 5.678:
4. Calculate: 2.4 × 0.3:
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