The value of a digit depends on its column: in 4673.2 the 7 is in the tens column, so it is worth 70. To order decimals, give them the same number of decimal places and compare. Negative numbers get smaller the further they are from zero, so −7 is less than −3. The symbols < and > always point towards the smaller number.
Place value essentials
- Columns: … thousands, hundreds, tens, units . tenths, hundredths, thousandths …
- Value of a digit = digit × the value of its column
- < means “is less than”; > means “is greater than”
- × 10, × 100, × 1000: digits move 1, 2, 3 places to the left
- ÷ 10, ÷ 100, ÷ 1000: digits move 1, 2, 3 places to the right
What is place value?
Every digit in a number sits in a column, and the column decides what the digit is worth. Moving one column to the left makes a digit ten times bigger; moving one column to the right makes it ten times smaller. After the decimal point the columns are tenths, hundredths and thousandths.
So in 5.243 the 2 is worth 2 tenths and the 3 is worth 3 thousandths.
How do you order decimals?
Write all the numbers with the same number of decimal places by adding zeros at the end, which does not change their value. Then compare them as if they were whole numbers. For example, 0.6 becomes 0.600 and 0.56 becomes 0.560, which shows that 0.56 is smaller.
A common mistake is to think a decimal with more digits is bigger. 0.605 has more digits than 0.65, but it is smaller.
Ordering negative numbers
Negative numbers lie to the left of zero on a number line, and the further left a number is, the smaller it is. So −9 is smaller than −4, even though 9 is bigger than 4. To order a mixed list, place the negatives first, starting with the one furthest from zero, then zero, then the positives.
Using < and >
The symbol < means “is less than” and > means “is greater than”. The open end faces the bigger number and the point faces the smaller one. Reading from left to right, −2 < 1 says “negative 2 is less than 1”.
Multiplying and dividing by 10, 100 and 1000
Multiplying by 10 moves every digit one place to the left; multiplying by 100 moves them two places. Dividing moves them to the right. Fill any empty columns with zeros: 3.06 × 100 = 306 and 52 ÷ 1000 = 0.052. This is the same idea used in standard form and unit conversions.
Worked examples
Example 1. Write down the value of the 7 in 4673.2.
- Count the columns from the decimal point: 3 is units, so 7 is in the tens column.
- Value = 7 × 10.
Answer: 70.
Example 2. Put these in order, smallest first: 0.6, 0.56, 0.605, 0.65.
- Give each three decimal places: 0.600, 0.560, 0.605, 0.650.
- Compare as thousandths: 560 < 600 < 605 < 650.
Answer: 0.56, 0.6, 0.605, 0.65.
Example 3. Order these numbers, smallest first: −4, 3, −9, 1.
- The negatives come first, starting furthest from zero: −9, then −4.
- Then the positives: 1, then 3.
Answer: −9, −4, 1, 3.
Example 4. The temperature at midnight is −8 °C. By noon it has risen by 5 degrees. What is the temperature at noon?
- Start at −8 on the number line and move 5 places to the right.
Answer: −3 °C.
Example 5. Work out (a) 3.06 × 100 and (b) 52 ÷ 1000.
- (a) Move the digits two places left: 306.
- (b) Move the digits three places right, filling with zeros: 0.052.
Answer: (a) 306, (b) 0.052.
Common mistakes
- Thinking more digits means bigger. 0.605 is smaller than 0.65; compare with equal decimal places.
- Ordering negatives like positives. −9 is smaller than −4, because it is further left of zero.
- Moving the decimal point the wrong way. Multiplying by 100 makes a number bigger, so digits move left.
- Reversing < and >. The point of the symbol faces the smaller number.
- Giving the digit instead of its value. The 7 in 4673.2 is worth 70, not 7.
How place value is examined
Place value and ordering are Foundation skills on the Edexcel 1MA1 GCSE and the 4MA1 International GCSE, usually tested without a calculator. Expect to:
- write down the value of a digit, including in decimals
- order a list of decimals or negative numbers
- work with temperature changes using negative numbers
- multiply or divide by 10, 100 or 1000
Practise these skills in the GCSE number revision engine, which generates new questions every time, and with the rounding and estimation worksheet.
Place value underpins rounding and estimation and standard form.
Frequently asked questions
What is the value of a digit?
Find which column the digit is in, then multiply the digit by the value of that column.
Is 0.7 bigger than 0.68?
Yes. Written with the same decimal places, 0.70 is bigger than 0.68.
Which is smaller, −5 or −2?
−5, because it is further to the left of zero on the number line.