Revision notes for Edexcel GCSE Maths Place Value. Open the guide for explanations and worked examples. Written against the Edexcel GCSE Maths (1MA1) specification, so the content matches what's examinable rather than general Maths background.
Place Value
What you'll learn
- How to find the value of a digit in a whole number or decimal.
- How to write numbers from clues, including millions.
- How to arrange and order numbers, including decimals and number cards.
Digits and place value
Numbers are made from digits. The position of a digit tells you how much it is worth.
For example, in 642:
| Hundreds | Tens | Ones |
|---|---|---|
| 6 | 4 | 2 |
The 6 means 6 hundreds, so it is worth 600.
The 4 means 4 tens, so it is worth 40.
The 2 means 2 ones, so it is worth 2.
Definition
Digit and place value
- A digit is a single symbol used to make numbers, like 0, 1, 2, 3, 4, 5, 6, 7, 8 or 9.
- Place value means the value a digit has because of its position in the number.
Key Idea
Column position matters
The same digit can have different values in different places. In 50 the 5 is worth 50, but in 500 the 5 is worth 500.
Example
Finding the value of a digit
Find the value of the 7 in 274.
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Write the number in columns: hundreds, tens, ones.
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The number 274 has 2 hundreds, 7 tens and 4 ones.
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The 7 is in the tens column.
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7 tens are worth 70, so the value of the 7 is 70.
Common Mistake
Writing the digit instead of its value
If the question asks for the value of the 7 in 274, the answer is 70, not just 7.
Zeros as placeholders
Sometimes a zero is used to show that a column is empty. It still matters because it keeps the other digits in the correct places.
For example, in 3058, the zero shows there are no hundreds.
Definition
Placeholder
A placeholder is a digit, often 0, that holds a position in a number so the other digits keep their correct place values.
Example
Finding a value when there is a zero
Find the value of the 9 in 5096.
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Read the columns from right to left: ones, tens, hundreds, thousands.
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In 5096, the 6 is in the ones column and the 9 is in the tens column.
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The zero is in the hundreds column, but you still count that column.
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The 9 is worth 90.
Decimals and the decimal point
A decimal is a number with a decimal point. The decimal point separates the whole-number part from the part that is smaller than 1.
In 36.8:
- 36 is the whole-number part.
- The 8 is after the decimal point, so it is in the tenths column.
Definition
Decimal point
The decimal point is the dot in a decimal number. Digits to the left are whole numbers. Digits to the right are tenths, hundredths, thousandths and so on.
Example
Value of a digit after the decimal point
Find the value of the 6 in 42.6.
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Look at the decimal point in 42.6.
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The first digit to the right of the decimal point is the tenths column.
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The 6 is in the tenths column.
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The value of the 6 is 6 tenths, written as 0.6.
Tip
Say the column name
For decimals, say “tenths” for the first digit after the decimal point and “hundredths” for the second digit. This helps you avoid treating decimal digits like normal ones.
Making a number from a clue
You may be asked to write a number with a certain digit in a certain place.
A 5-digit number has five digits. For example, 28,451 is a 5-digit number. The comma is just there to make it easier to read; it is not a digit.
Example
Writing a number with a given thousands digit
Write a 5-digit number with 4 as its thousands digit. Use the digit 4 only once.
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A 5-digit number has these columns: ten-thousands, thousands, hundreds, tens, ones.
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The thousands digit must be 4, so put 4 in the second column from the left.
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Choose other digits that are not 4.
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One possible answer is 24,056.
Common Mistake
Mixing up thousands and ten-thousands
In a 5-digit number, the first digit is the ten-thousands digit. The second digit is the thousands digit.
Writing millions in figures
Figures means digits instead of words.
So “three million” in figures is 3,000,000.
Definition
Million
One million is written as 1,000,000. It is a 1 followed by six zeros.
Example
Writing a decimal million in figures
Write 6.4 million in figures.
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6 million is 6,000,000.
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0.4 million is 400,000.
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Add them together: 6,000,000 + 400,000 = 6,400,000.
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So 6.4 million is 6,400,000.
Tip
Count the zeros
For a whole number of millions, write the number, then add six zeros. For example, 8 million is 8,000,000.
Ordering whole numbers
To order whole numbers, compare from left to right.
Start with the largest place value. If the first digits are the same, compare the next digit.
Example
Putting whole numbers in order
Put these numbers in order, starting with the smallest:
128, 172, 205, 139, 170
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Look at the hundreds digits first.
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The numbers starting with 1 are smaller than 205, because they have 1 hundred instead of 2 hundreds.
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Now compare the numbers starting with 1: 128, 172, 139, 170.
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Compare the tens digits: 2, 7, 3, 7. So 128 comes first, then 139.
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For 170 and 172, compare the ones digits: 0 is smaller than 2.
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The order is 128, 139, 170, 172, 205.
Ordering decimals
Decimals can be tricky because a longer decimal is not always bigger.
For example, 0.4 is the same as 0.400. Adding zeros at the end of a decimal does not change its value.
Key Idea
Make decimal lengths match
When ordering decimals, add zeros to the end so they all have the same number of decimal places. Then compare from left to right.
Example
Putting decimals in order
Put these numbers in order, starting with the smallest:
0.42, 0.402, 0.24, 0.024, 0.204
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Make them all have three decimal places by adding zeros to the end where needed.
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Write them as: 0.420, 0.402, 0.240, 0.024, 0.204.
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Compare the digits after the decimal point from left to right.
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The smallest is 0.024, then 0.204, then 0.240, then 0.402, then 0.420.
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Write the original numbers in order: 0.024, 0.204, 0.24, 0.402, 0.42.
Common Mistake
Thinking more decimal digits means bigger
0.307 is smaller than 0.37 because 0.37 can be written as 0.370.
Number cards
Sometimes you are given digit cards and asked to make the largest or smallest number.
To make the largest number, put the biggest digits in the biggest place-value columns.
To make the smallest number, put the smallest digits in the biggest place-value columns.
Example
Making the largest three-digit number
Use the cards 8, 1, 6 and 4 to make the largest possible three-digit number.
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A three-digit number has hundreds, tens and ones.
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To make the number as large as possible, use the biggest digit in the hundreds column.
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The three biggest digits are 8, 6 and 4.
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Put them in descending order: 864.
Definition
Sum
A sum is an addition calculation, or the answer to an addition calculation.
For a two-digit plus two-digit card sum, the tens columns are more important than the ones columns.
Example
Arranging cards to make the smallest sum
Use the cards 9, 5, 2 and 1 to make the smallest possible answer to a two-digit plus two-digit sum.
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The tens digits matter most because each tens digit is worth ten times as much as a ones digit.
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To make the sum as small as possible, put the smallest digits in the tens columns.
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Put 1 and 2 in the tens columns.
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Put 5 and 9 in the ones columns.
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One smallest arrangement is 15 + 29 = 44.
Exam technique
In the exam
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Underline the digit the question asks about, then name its column before writing its value.
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For decimals, add zeros at the end to help compare them fairly.
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For number cards, decide first whether you need the largest or smallest answer, then fill the biggest place-value columns first.
Self review
Check yourself
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What is the value of the 6 in 4,638?
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Write a 5-digit number with 2 as the hundreds digit, using 2 only once.
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Put these in order from smallest to largest: 0.7, 0.07, 0.707, 0.77.
Recap questions
Test yourself with 5 quick questions on this guide. Answer them all correctly to complete it.
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