Decimals Worksheet - GCSE - Intermediate
Decimals worksheet for Key Stage 4 / GCSE (Ages 14-16). Intermediate level maths practice, aligned to the UK National Curriculum. Print-ready with answer key included.
Mastering Decimals: Intermediate Maths Challenges
Key Stage 4 / GCSE (Ages 14-16) - Intermediate Level
Instructions: This worksheet focuses on enhancing your understanding of decimals, covering conversion, calculation, and application in various contexts. Tackle each problem with precision and show all your working clearly.
Converting Recurring Decimals to Fractions
Convert each recurring decimal into a fraction. Show all steps in your working to ensure clarity. Remember to simplify your answers where possible.
1. 0.333...
2. 0.666...
3. 0.7272...
4. 0.8181...
5. 0.4545...
Decimal Operations
Perform the following operations involving decimals. Ensure you keep track of decimal places and show all calculations clearly.
1. 12.5 + 3.75
2. 15.8 - 7.32
3. 6.4 × 2.5
4. 9.6 ÷ 1.2
Solving Decimal Equations
Solve each equation for x. Provide a step-by-step solution and check your answers by substituting back into the original equation.
1. 0.5x + 2.3 = 4.8
2. 1.2x - 3.6 = 2.4
3. 3.4x + 1.5 = 10.7
4. 2.8x - 1.4 = 5.6
Decimal Place Value Analysis
Analyse the following numbers and identify the value of the underlined digit. Provide your answers with a brief explanation.
1. 4.5_7_8
2. 12.3_4_6
3. 0.9_8_1
4. 7.6_5_2
Comparing Decimals
Compare the following pairs of decimals. Use symbols <, >, or = to indicate the relationship between each pair.
1. 0.75 ___ 0.750
2. 1.23 ___ 1.230
3. 0.456 ___ 0.465
4. 2.89 ___ 2.890
Rounding Decimals
Round each decimal to the nearest whole number, tenth, and hundredth. Show your working for each step.
1. 3.456
2. 7.891
3. 0.234
4. 5.678
Decimal Word Problems
Solve these real-world problems involving decimals. Show all your calculations and provide clear reasoning for your answers.
1. A piece of ribbon is 3.75 metres long. If it is cut into 0.25 metre pieces, how many pieces can be made?
2. A book costs £12.99 and a pen costs £1.49. If you buy 3 books and 4 pens, what is the total cost?
3. A car travels 8.4 miles on 0.7 gallons of fuel. What is the car's fuel efficiency in miles per gallon?
Decimal Error Analysis
Identify and correct the errors in the following decimal calculations. Explain the mistake and provide the correct answer.
1. 5.6 × 3 = 15.8
2. 7.4 + 2.3 = 9.9
3. 10.5 ÷ 0.5 = 5.25
Activity 1: 1/3 ; 2/3 ; 8/11 ; 9/11 ; 5/11
Activity 2: 16.25 ; 8.48 ; 16 ; 8
Activity 3: x = 5 ; x = 5 ; x = 2.7 ; x = 2.5
Activity 4: 0.07 ; 0.04 ; 0.08 ; 0.05
Activity 5: = ; = ; < ; =
Activity 6: 3 ; 3.5 ; 3.46 ; 8 ; 7.9 ; 7.89 ; 0 ; 0.2 ; 0.23 ; 6 ; 5.7 ; 5.68
Activity 7: 15 pieces ; £45.93 ; 12 miles per gallon
Activity 8: 16.8 ; 9.7 ; 21
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