Decimals Quizzes

GCSE Maths Foundation Quiz: Decimals Practice with Addition, Subtraction, Multiplication and Division

Difficulty: Foundation

Curriculum: GCSE

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GCSE Maths Higher Quiz: Challenging Decimals – Fractions, Operations and Problem Solving

Difficulty: Higher

Curriculum: GCSE

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Decimals Quiz 3

Difficulty: Foundation

Curriculum: GCSE

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GCSE Maths Higher Quiz: Challenging Decimals – Fractions, Operations and Problem Solving

Difficulty: Higher

Curriculum: GCSE

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Visual overview of Decimals.

Introduction

Decimals are a fundamental part of GCSE Maths and everyday calculations. They represent parts of a whole using the base-10 system, allowing precise measurements and calculations. Understanding decimals is essential for working with money, measurements, percentages, ratios, fractions, and algebraic calculations. Mastery of decimals ensures students can accurately compare numbers, perform arithmetic operations, and apply decimals in real-life and exam contexts.

Decimals are not just numbers with a dot — they encode fractional values in a way that is compatible with the number system we use daily. For example, $3.75$ represents three whole units plus seventy-five hundredths, making it an essential skill for precise problem-solving.

Core Concepts

What is a Decimal?

A decimal number has a whole part and a fractional part, separated by a decimal point. For example:

$3.75 = 3 + 0.7 + 0.05$

3 is the whole number (unit) part.
0.7 represents seven tenths.
0.05 represents five hundredths.

Decimals are closely related to fractions. For example: $0.25=\frac{1}{4},\; 0.5=\frac{1}{2},\; 0.75=\frac{3}{4}$.

Decimal Place Value

Each digit in a decimal number has a specific value depending on its position relative to the decimal point:

Place	Example: 3.476	Value
Units	3	3
Tenths	4	0.4
Hundredths	7	0.07
Thousandths	6	0.006

Key point: Each place value to the right of the decimal is ten times smaller than the one before it.

Comparing Decimals

Line up the decimal points.
Compare digits from left to right.
Add trailing zeros if necessary to make decimal places equal.

Example

$2.45 < 2.5$ because $2.45 = 2.450$ and $450 < 500$.

Rounding Decimals

Rounding simplifies decimals to a specified number of decimal places or to the nearest whole number.

Identify the place you are rounding to.
Look at the next digit:
- If it is 5 or more, round up.
- If it is less than 5, round down.
Drop all digits after the rounding place.

Examples

Round $3.746$ to 1 decimal place: $3.7$
Round $2.678$ to 2 decimal places: $2.68$

Converting Fractions to Decimals

$\text{Decimal} = \dfrac{\text{Numerator}}{\text{Denominator}}$

$\frac{3}{4} = 3 \div 4 = 0.75$
$\frac{2}{5} = 2 \div 5 = 0.4$

Converting Decimals to Fractions

Count the number of decimal places.
Write the decimal without the point as the numerator.
Denominator = 1 followed by as many zeros as decimal places.
Simplify the fraction.

$0.6 = \frac{6}{10} = \frac{3}{5}$
$0.125 = \frac{125}{1000} = \frac{1}{8}$

Adding and Subtracting Decimals

Line up decimal points.
Add or subtract as with whole numbers.
Keep the decimal point aligned in the answer.

Examples

$3.75 + 2.4 = 6.15$
$5.6 - 1.25 = 4.35$

Tip: Add trailing zeros to make decimal places equal.

Multiplying Decimals

Ignore the decimal points and multiply as whole numbers.
Count the total number of decimal places in all factors.
Place the decimal in the product so it has the same number of decimal places.

Examples

$0.6 \times 0.3 = 0.18$
$1.25 \times 0.4 = 0.50$

Dividing Decimals

If the divisor is not a whole number, multiply both dividend and divisor by a power of 10 to make the divisor a whole number.
Divide as usual.
Place the decimal in the quotient directly above the decimal in the dividend.

Examples

$4.8 \div 0.6 \rightarrow 48 \div 6 = 8$
$3.75 \div 1.5 \rightarrow 375 \div 150 = 2.5$

Worked Examples

Example 1 (Foundation): Add decimals

$2.35 + 4.7$

Step 1: Align decimals: $2.35 + 4.70$

Step 2: Add as whole numbers: $2.35 + 4.70 = 7.05$

Answer: $7.05$

Example 2 (Foundation): Multiply decimals

$0.4 \times 0.25$

Step 1: Ignore decimals: $4 \times 25 = 100$

Step 2: Count decimal places: $1 + 2 = 3$ places

Step 3: Place decimal: $100 \rightarrow 0.100$

Answer: $0.1$

Example 3 (Higher): Divide decimals

$7.2 \div 0.3$

Step 1: Make divisor whole: $7.2 \div 0.3 \rightarrow 72 \div 3$

Step 2: Divide: $72 \div 3 = 24$

Answer: $24$

Example 4 (Higher): Convert decimal to fraction

$0.875$

Step 1: Count decimal places: 3

Step 2: Numerator = 875, denominator = 1000

Step 3: Simplify: $\frac{875}{1000} = \frac{7}{8}$

Answer: $ \frac{7}{8} $

Example 5 (Higher): Convert fraction to decimal

$\frac{5}{8}$

$5 \div 8 = 0.625$

Answer: $0.625$

Common Mistakes

Misaligning decimal points when adding or subtracting.
Forgetting to count decimal places when multiplying.
Not making the divisor a whole number when dividing decimals.
Confusing decimals with fractions or percentages.
Rounding incorrectly or too early in multi-step problems.

How to avoid: Align decimal points; count places carefully; use powers of 10 for division; estimate to check reasonableness; avoid rounding until the final step.

Applications

Money: £3.75, €4.50, $12.99
Measurements: 2.5 m, 3.75 L, 0.25 kg
Percentages: $12.5\% = 0.125$
Ratios: recipe adjustments, scaling quantities
Science & Engineering: precise recorded values

Strategies & Tips

Practice mental estimation to quickly check decimal calculations.
Memorise common fraction–decimal pairs (e.g., $ \frac12=0.5, \frac34=0.75 $).
Write zeros explicitly (e.g., $2.5 + 0.75 = 3.25$).
Check units in calculations.
Use step-by-step approaches for multi-step problems.

Summary / Call-to-Action

Decimals underpin many GCSE topics. Master place value, the four operations, and conversions with fractions to solve problems confidently.

Attempt the quizzes on decimals to reinforce learning.
Practise converting between fractions, decimals, and percentages.
Apply rounding rules in real-life examples.
Use estimation to verify your answers.