✓ Revise Right course
Place value means every position in a number represents a power of 10, so the value of a digit depends on its position. Free notes and 13 questions answered.
Place Value and Number Size is part of Structure and calculation in GCSE AQA Higher Maths.
4 min
Reading time
22
Lessons in this topic
GCSE AQA Higher
Pathway
Reviewed by Revise Right
Content review
Place value means every position in a number represents a power of 10, so the value of a digit depends on its position. Free notes and 13 questions answered.
AQA GCSE Maths mock draft, 26–31 Oct. Draft coverage: Maths Paper 1 (Higher tier). Reviewed for an original-practice sitting; check student availability before registering. Marking and results will follow later, after separate approval. Eligible new accounts receive a five-day Pro trial when signup email verification completes. Previous trials keep their original expiry. After expiry, new papers need Pro unless you have an explicitly confirmed free sitting offer for this event. That offer adds no Pro time or AI learning. Saved attempts and released results remain readable. No card or automatic charge.
Use this lesson to stay inside Structure and calculation while connecting the detail back to the wider Number topic.
Read the core explanations from Place Value and Number Size before testing yourself from memory.
Place value is the foundation of our number system, yet it trips up many students when numbers get very large or very small. Think of place value as a filing system where each position has a specific job - the digit 5 means something completely different in 50, 500, or 0.05.
Every position in a number represents a power of 10. Moving left multiplies by 10, moving right divides by 10. This pattern continues infinitely in both directions, which is why we can write any number, no matter how extreme.
Understanding place value becomes crucial when dealing with very large numbers like the distance to stars, or very small numbers like the size of atoms. Without this foundation, calculations become impossible and decimal work falls apart.
Very large numbers appear everywhere in real life - population figures, distances in space, national budgets. The key is recognising that place value patterns continue indefinitely to the left. Each new position is ten times larger than the previous one.
When working with large numbers, standard form becomes essential. Instead of writing 4,500,000,000, we write $4.5 \times 10^9$. This isn't just neater - it makes calculations possible and reduces errors.
**Trap**: Many students think you can't do arithmetic with very large numbers. Actually, place value rules work the same way - you need to be more careful with your working and often use standard form to keep track.
Worked example: Converting Large Numbers to Standard Form
Write 67,000,000 in standard form.
Answer: $6.7 \times 10^7$
Very small numbers follow the same place value logic, but in reverse. Moving right from the decimal point, each position is ten times smaller. The pattern continues: tenths, hundredths, thousandths, ten-thousandths, and so on.
Small numbers appear in science constantly - the size of atoms, electrical currents, chemical concentrations. Understanding their place value is essential for calculations and comparisons.
Standard form works for small numbers too, but now the power of 10 is negative. The number 0.0045 becomes $4.5 \times 10^{-3}$. The negative power tells us how many places to move the decimal point left.
Worked example: Converting Small Numbers to Standard Form
Write 0.000034 in standard form.
Answer: $3.4 \times 10^{-5}$
Place value becomes critical when calculating with decimals. Many students make errors because they don't properly align decimal points or understand what each decimal place represents.
When adding or subtracting decimals, place value determines alignment. The decimal points must line up vertically so that tenths align with tenths, hundredths with hundredths, and so on. This ensures each calculation happens in the correct place value column.
Multiplication and division with decimals require careful tracking of place values. The position of the decimal point in the answer depends on the total number of decimal places in the original numbers.
Worked example: Adding Decimals Using Place Value
Calculate 23.47 + 8.9 + 0.156
Answer: 32.526
Place value is essential for comparing numbers accurately. Students often struggle with this when decimals are involved, especially when numbers have different numbers of decimal places.
The key principle is to compare digits in the same place value position, starting from the left. The first position where digits differ determines which number is larger. This works for whole numbers, decimals, and numbers in standard form.
**Trap**: Many students think 0.5 is smaller than 0.49 because 49 is bigger than 5. Actually, 0.5 = 0.50, and in the tenths position, 5 > 4, so 0.5 > 0.49.
Worked example: Comparing Decimal Numbers
Put these numbers in ascending order: 0.6, 0.58, 0.607, 0.06
Answer: 0.06, 0.58, 0.6, 0.607
Place value questions appear throughout GCSE maths, often disguised within other topics. Recognising when place value understanding is needed can make the difference between success and confusion.
The most common mistakes involve decimal point placement, especially in calculations. Students often lose track of place values when multiplying or dividing by powers of 10, or when converting between standard form and ordinary numbers.
Exam questions frequently test place value through rounding, significant figures, and estimation. Understanding what each digit position represents is crucial for these skills.
Published by Revise Right. Use the official specification reference to check the requirements for your course. Content updated: 2026-03-25.
Move to the related lessons or back to the topic page when you need the wider sequence before exam-style practice.
Place value means every position in a number represents a power of 10, so the value of a digit depends on its position. Moving left multiplies by 10 and moving right divides by 10, which is why the digit 5 means something completely different in 50, 500 or 0.05.
To add decimals, line up the decimal points vertically so that tenths align with tenths and hundredths with hundredths, then add each place value column. For example, 23.47 + 8.9 + 0.156 = 32.526.
To order decimals, write them with the same number of decimal places, then compare digits in the same place value position, starting from the left. For example, 0.6, 0.58, 0.607 and 0.06 become 0.600, 0.580, 0.607 and 0.060, giving the order 0.06, 0.58, 0.6, 0.607.
A small number is put into standard form by placing the decimal point after the first non-zero digit and counting how many places it moved to the right; that count is the negative power of 10. For example, 0.000034 becomes 3.4 × 10⁻⁵ because the point moves 5 places.
Each place value position represents a power of 10. Moving left multiplies by 10 and moving right divides by 10, so after the decimal point come tenths, hundredths, thousandths and ten-thousandths, and the pattern continues infinitely in both directions.
To write 67,000,000 in standard form, place the decimal point after the first non-zero digit to get 6.7, then count the places moved: 7 places to the left, so the answer is 6.7 × 10⁷. The power is positive because the decimal point moved left.
0.5 is bigger than 0.49. Writing 0.5 as 0.50 and comparing the tenths digits shows that 5 is bigger than 4, so 0.5 is bigger than 0.49, even though 49 looks bigger than 5.
67,000,000 in standard form is 6.7 × 10⁷. The decimal point goes after the first significant digit, 6, to give 6.7, and it has moved 7 places to the left, so the power of 10 is positive 7.
0.0045 in standard form is 4.5 × 10⁻³. The power of 10 is negative for small numbers, and it tells how many places the decimal point moves to give the original number.
The power of 10 is negative in standard form for small numbers because the decimal point moves to the right to reach the first significant digit. For example, 0.000034 needs the point moved 5 places right, giving 3.4 × 10⁻⁵, while large numbers have positive powers.
Decimals with different numbers of decimal places are compared by adding zeros so they have the same number of places, then comparing digits in the same position from the left. For 0.6, 0.58, 0.607 and 0.06, writing 0.600, 0.580, 0.607 and 0.060 gives the order 0.06, 0.58, 0.6, 0.607.
The value of a digit in a decimal depends on its place value position. The digit 5 means something completely different in 50, 500 or 0.05, because each position represents a different power of 10.
Standard form is used for very large numbers because it is neater, makes calculations possible and reduces errors. Instead of writing 4,500,000,000, the number becomes 4.5 × 10⁹, which keeps track of the place value.