Place Value
Get to grips with place value using these Foundation GCSE Maths practice questions. The worksheet focuses on understanding place value, and the accompanying mark scheme breaks down each solution clearly. Suitable for AQA, Edexcel and OCR. Download the questions and answers for free. Each place to the left is ten times bigger; each to the right is ten times smaller.
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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.
Challenge / Extension
Stretch yourself beyond the basics.
Topic overview
Place value is the idea that a digit's worth depends on its position. In \(3\,742\), the \(3\) is worth three thousand, while in \(4\,371\) the same digit is worth three hundred.
Each column is ten times the one to its right. Moving left multiplies by ten, and moving right divides by ten. That single pattern continues past the decimal point into tenths, hundredths and thousandths.
Understanding place value underpins almost everything else in number. Ordering decimals, multiplying by powers of ten, rounding and standard form all depend on knowing what each digit is actually worth.
Revision notes
The column headings
From the decimal point leftwards the columns are units, tens, hundreds, thousands and so on. Rightwards they are tenths, hundredths and thousandths.
In \(52.36\), the \(5\) is five tens, the \(2\) is two units, the \(3\) is three tenths and the \(6\) is six hundredths.
Multiplying and dividing by powers of ten
Multiplying by \(10\) moves every digit one column to the left; dividing by \(10\) moves them one to the right. The decimal point stays put and the digits move.
So \(3.6 \times 100 = 360\) and \(45 \div 1000 = 0.045\). Zeros are used to fill any empty columns.
Ordering numbers
Compare the largest place value first. If those digits match, move right and compare the next.
For decimals, line up the decimal points and compare column by column. Adding trailing zeros can help: \(0.4\) is \(0.40\), which is clearly larger than \(0.35\).
Key points
- A digit's value depends on its column.
- Each column is ten times the one to its right.
- Multiplying by 10 moves digits one place left.
- Dividing by 10 moves digits one place right.
- Compare the largest place value first when ordering.
- Zeros hold empty columns so the other digits keep their value.
Worked examples
Example 1
Write down the value of the \(7\) in \(4\,726\).
Working
Example 2
Work out \(2.45 \times 1000\).
Working
Example 3
Put \(0.4\), \(0.38\) and \(0.409\) in ascending order.
Working
Common mistakes
Thinking a longer decimal is always larger.
0.38 has more digits than 0.4 but is smaller. Compare column by column, not by length.
Moving the decimal point instead of the digits.
It gives the same answer but causes confusion later. The point stays fixed and the digits shift.
Forgetting to fill empty columns with zeros.
2.45 × 1000 is 2450, not 245. The zero holds the units column.
Reading the digit rather than its value.
The 7 in 4726 is worth 700, not 7.
Exam tips
- Write column headings above the digits if you are unsure of a value.
- Add trailing zeros so decimals have the same length before comparing.
- Check the size of your answer after multiplying or dividing by a power of ten.
- Say the number aloud — it often reveals the place value immediately.
Key terms
- Place value
- The value of a digit determined by its position.
- Digit
- A single numeral from 0 to 9.
- Ascending order
- Arranged from smallest to largest.
- Decimal point
- The marker separating whole numbers from parts of a whole.
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.