Decimal place value — Mathematics, 11–13 years
Understand what each digit means after the decimal point, and use that meaning to compare, round and calculate with decimal numbers.
What decimal places mean
A decimal number is built from parts of one whole. In 3.47, the 3 means three wholes, the 4 means four tenths, and the 7 means seven hundredths. Each step to the right makes the place ten times smaller, just as each step to the left makes it ten times larger.
Why place value matters
Without place value, 4.8 and 4.08 can look almost the same, even though they are different amounts. Place value was developed to write quantities between whole numbers clearly and to calculate them efficiently. It solves the problem of recording parts of a unit without inventing a new symbol for every possible amount.
Comparing two decimals
Compare 2.7 and 2.65. First compare the whole-number parts: both are 2. Write 2.7 as 2.70, because adding a zero at the end does not change its value. Now compare hundredths: 70 hundredths is greater than 65 hundredths, so 2.70 is greater than 2.65.
The longer number trap
A common mistake is thinking 3.125 is greater than 3.8 because 125 is greater than 8, or because it has more digits. That feels reasonable when comparing whole numbers, where more digits often means a larger number. But after the decimal point, digits show smaller parts: 3.125 is three and 125 thousandths, while 3.8 is three and eight tenths.
Decimals in real life
Decimals appear whenever a whole unit is split into measured parts. Prices, lengths, masses, temperatures and sports times all use them: 1.5 litres, 2.49 euros or 12.36 seconds. Reading the places correctly helps you judge whether a measurement is precise and whether a result or price makes sense.
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