Place value and rounding

The idea

Every digit in a number has a value that depends on its position. In 47,382 the digits stand for 4 ten-thousands, 7 thousands, 3 hundreds, 8 tens and 2 ones. Reading numbers from the left, in groups of three digits, makes even very large numbers manageable.

To compare two numbers, first check they have the same number of digits — more digits always means a bigger number. If they match, compare digit by digit from the left; the first position where they differ decides which is larger.

Rounding means replacing a number with the nearest tidy value. To round to the nearest thousand, look at the hundreds digit: 0–4 rounds down, 5–9 rounds up. The digit you look at is always the one immediately to the right of the place you are rounding to.

Worked example

Round 47,382 to the nearest thousand.

1. Find the thousands column: the 7 in 47,382 is the thousands digit, so the answer will be 47,000 or 48,000.
2. Look at the digit to its right, the hundreds digit: it is 3.
3. 3 is less than 5, so we round down and the thousands digit stays at 7.
4. Replace everything after the thousands with zeros.

Answer: 47,000

Watch out

• Looking at the wrong digit when rounding — always check the digit immediately to the right of the target place.
• Writing 15 ones as '15' inside a number instead of carrying: 600 + 15 must be added, giving ...615, not a digit '15'.
• Comparing numbers from the right, or comparing 9,850 with 12,300 digit by digit when 12,300 simply has more digits and is bigger.