Place Value Worksheet - GCSE - Intermediate
Place Value 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 Place Value: Intermediate Maths Challenges
Key Stage 4 / GCSE (Ages 14-16) - Intermediate Level
Instructions: This worksheet focuses on enhancing your understanding of place value in various numerical contexts. Tackle each activity carefully, showing all your working out and reasoning. Use the provided answer spaces to record your solutions.
Understanding Standard Form
Convert the following numbers into standard form. Standard form is a way of writing very large or very small numbers easily. Express each number as a product of a number between 1 and 10 and a power of 10.
1. 450,000
2. 0.0056
3. 7,890,000
4. 0.00032
5. 123,000,000
Converting Between Forms
Convert each number from standard form back to its ordinary number form. Write your answers clearly in the space provided.
1. 3.5 × 10^4
2. 6.02 × 10^-3
3. 9.1 × 10^6
4. 2.75 × 10^-2
5. 5.67 × 10^3
Rounding and Bounds
Round each number to the nearest ten and calculate the upper and lower bounds. Use the bounds to express the range of possible values.
1. 467
2. 3,582
3. 7,849
4. 92
5. 1,234
Prime Factorisation
Express each number as a product of its prime factors. Use index notation where applicable.
1. 60
2. 84
3. 210
4. 144
5. 98
Calculating with Surds
Simplify the following surds. Show your working clearly and express your answers in simplest form.
1. √50
2. √72
3. √18
4. √98
5. √32
Error Intervals and Estimation
For each measurement, determine the error interval. Assume each measurement is given to the nearest whole number.
1. 25 cm
2. 47 kg
3. 180 m
4. 9.5 litres
5. 320 seconds
Recurring Decimals to Fractions
Convert each recurring decimal into a fraction. Show all steps of your conversion process.
1. 0.333...
2. 0.666...
3. 0.142857...
4. 0.8181...
5. 0.2727...
Comparing Values in Standard Form
Compare the following pairs of numbers in standard form and determine which is larger. Use >, <, or = to show your answer.
1. 3 × 10^5 and 2.5 × 10^6
2. 7.1 × 10^-3 and 8.2 × 10^-4
3. 9 × 10^2 and 1.2 × 10^3
4. 5.6 × 10^4 and 5.6 × 10^5
5. 4.3 × 10^-1 and 4.3 × 10^-2
Activity 1: 4.5 × 10^5 ; 5.6 × 10^-3 ; 7.89 × 10^6 ; 3.2 × 10^-4 ; 1.23 × 10^8
Activity 2: 35,000 ; 0.00602 ; 9,100,000 ; 0.0275 ; 5,670
Activity 3: 470 ; 3,580 ; 7,850 ; 90 ; 1,230
Activity 4: 2^2 × 3 × 5 ; 2^2 × 3 × 7 ; 2 × 3 × 5 × 7 ; 2^4 × 3^2 ; 2 × 7^2
Activity 5: 5√2 ; 6√2 ; 3√2 ; 7√2 ; 4√2
Activity 6: 24.5 ≤ x < 25.5 ; 46.5 ≤ x < 47.5 ; 179.5 ≤ x < 180.5 ; 9.45 ≤ x < 9.55 ; 319.5 ≤ x < 320.5
Activity 7: 1/3 ; 2/3 ; 1/7 ; 9/11 ; 3/11
Activity 8: < ; > ; < ; < ; >
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