Step-by-step worked examples and graded practice questions on place value — reading and writing large numbers and decimals, multiplying and dividing by powers of 10, and ordering numbers by size.
📚 Foundation & Higher✅ 15 Practice Questions🔍 Full Worked Examples⚠️ Common Mistakes
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Place value is the value a digit has because of its position in a number. The same digit can represent a very different amount depending on where it sits — the 4 in 4,000 is worth four thousand, but the 4 in 0.04 is worth four hundredths.
The table below shows the column headings you need for GCSE, from millions down to thousandths:
Millions
Hundred Thousands
Ten Thousands
Thousands
Hundreds
Tens
Units
·
Tenths
Hundredths
Thousandths
3
4
7
2
9
0
5
·
8
1
6
Read from this table, the number is 3,472,905.816. Each column is worth ten times the column to its right — moving one column left multiplies the value by 10; moving one column right divides it by 10.
The value of a digit in a large number
Worked Example 1
In the number 5,472,930, what is the value of the digit 7?
1
Write the number in a place value table and find the column the 7 sits in: 5 (millions), 4 (hundred thousands), 7 (ten thousands), 2 (thousands), 9 (hundreds), 3 (tens), 0 (units)
2
The 7 is in the ten thousands column, so its value is 7 × 10,000
Answer70,000
Place value in decimals
The columns continue past the decimal point using tenths, hundredths and thousandths — each is ten times smaller than the last, following the same pattern as whole numbers.
Worked Example 2
In the number 6.375, what is the value of the digit 7?
1
Identify the columns after the decimal point: 3 (tenths), 7 (hundredths), 5 (thousandths)
2
The 7 is in the hundredths column, so its value is 7 hundredths
Answer0.07 (7 hundredths)
Multiplying and dividing by powers of 10
Multiplying by 10, 100 or 1000 moves every digit to the left by 1, 2 or 3 columns. Dividing by 10, 100 or 1000 moves every digit to the right by 1, 2 or 3 columns. The digits themselves never change — only their position does.
Worked Example 3
Work out (a) 3.6 × 100 and (b) 452 ÷ 1000
1
(a) Multiplying by 100 shifts every digit 2 columns left: 3.6 → 360
2
(b) Dividing by 1000 shifts every digit 3 columns right: 452 → 0.452
Answer(a) 360 (b) 0.452
Multiplying by 100 shifts every digit two places to the left. A placeholder zero is needed to keep the units column in the right place.
Ordering and comparing decimals
Worked Example 4
Write these numbers in order, smallest first: 0.6, 0.45, 0.099, 0.5
1
Give every number the same number of decimal places by adding placeholder zeros: 0.600, 0.450, 0.099, 0.500
2
Compare column by column, starting with the tenths: 0.099 has 0 tenths, so it is smallest; then compare 0.450, 0.500, 0.600
Answer0.099, 0.45, 0.5, 0.6
Common trap: 0.45 is larger than 0.099, even though "45" looks smaller than "099" — always compare the value of each column, not the number of digits.
Practice questions
Work through each question before checking the answers.
Foundation (Grade 3–5)
Q1Write the number 4,706 in words.Foundation
Q2In the number 82,914, what is the value of the digit 9?Foundation
Q3In the number 5.238, what is the value of the digit 3?Foundation
Q4Work out 7.2 × 10 and 7.2 × 1000.Foundation
Q5Put these numbers in order, smallest first: 0.7, 0.07, 0.77, 0.077Foundation
Higher (Grade 5–7)
Q6Work out 630 ÷ 100 and 630 ÷ 10,000.Higher
Q7Write the number three million, forty thousand and six using digits.Higher
Q8In the number 0.0508, what is the value of the digit 8?Higher
Q9Put these numbers in order, largest first: 3.09, 3.9, 3.099, 3.19Higher
Q10A number is multiplied by 1000 to give 45,000. What was the original number?Higher
Higher — Hard (Grade 8–9)
Q11A number has 3 in the hundreds column, 0 in the tens column, and its value in the tens column contributes 0 to the total. Explain why a placeholder is still needed, using a specific example.Grade 8–9
Q12The digit 4 in a number has a value of 400,000. The digit 4 also appears in the tenths column of the same number. Write a number that satisfies both conditions.Grade 8–9
Q13Work out (2.5 × 100) ÷ 1000, giving your answer as a decimal.Grade 8–9
Q14Without a calculator, work out 0.006 × 4000.Grade 8–9
Q15Explain why 0.5 and 0.50 represent the same value, but 0.5 and 0.05 do not.Grade 8–9
Answers
Foundation (Q1–Q5)
Q1Four thousand, seven hundred and six
Q2900(9 is in the hundreds column)
Q30.03 (3 hundredths)
Q472 and 7200
Q50.07, 0.077, 0.7, 0.77
Higher (Q6–Q10)
Q66.3 and 0.063
Q73,040,006
Q80.0008 (8 ten-thousandths)
Q93.9, 3.19, 3.099, 3.09
Q1045(45,000 ÷ 1000)
Higher — Hard (Q11–Q15)
Q11E.g. in 305, the 0 in the tens column is needed to keep the 3 in the hundreds column and the 5 in the units column — without it, "35" means something completely different from "305".
Q12E.g. 400,000.4(any number with 4 in the hundred-thousands column and 4 in the tenths column)
Q130.25(2.5 × 100 = 250, then 250 ÷ 1000 = 0.25)
Q1424(0.006 × 4000 = 6 × 4 ÷ 1000 × 1000 = 24)
Q15A zero placed after the last non-zero decimal digit doesn't change the value (0.50 = 0.5), because it's in a column worth nothing extra. But 0.05 has the 5 in a different column (hundredths, not tenths), so it represents a genuinely different, smaller value.
Common mistakes
Common Mistake 1
Comparing decimals by counting digits instead of place value
Students often think 0.099 is bigger than 0.45 because "99" looks bigger than "45". Always line up the decimal points and compare column by column, starting with the tenths.
Common Mistake 2
Forgetting the placeholder zero
When multiplying 3.6 by 100, it's easy to write "36" instead of 360. A placeholder zero is needed whenever a column would otherwise be empty.
Common Mistake 3
Shifting digits the wrong way
Multiplying makes digits move left (bigger); dividing makes digits move right (smaller). Mixing these up is one of the most common errors at GCSE.
Common Mistake 4
Confusing "thousand" and "thousandth"
The thousands column is to the left of the decimal point (a large value); the thousandths column is three places to the right of it (a very small value). Read the question carefully.
Exam tips
💡 Exam Tip 1
Line up decimal points before comparing
When ordering decimals, rewrite each one with the same number of decimal places using placeholder zeros — it makes the comparison far less error-prone.
💡 Exam Tip 2
Say the column name out loud
When asked for the "value" of a digit, name its column first (e.g. "the 7 is in the hundredths column") before writing the final answer — this avoids careless slips.
💡 Exam Tip 3
Check your answer is a sensible size
After multiplying or dividing by a power of 10, check the answer is bigger (for ×) or smaller (for ÷) than you started with. This catches shifted-digit errors immediately.
💡 Exam Tip 4
Write numbers in words carefully
Commas group digits in threes from the right (thousands, millions). Reading the groups aloud — "four hundred and six thousand" — helps avoid missing or repeating a group.
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