Comparing, rounding & dividing
Rounding, ordering and comparing whole numbers
Rounding makes big numbers easier to describe and helps you estimate. You can also put numbers in order and compare them using the signs =, < and >.
How to round
To round a number, look at the digit just to the right of the place you are rounding to. • If that digit is 5 or more, round up. • If it is less than 5, round down. For the nearest 10, look at the ones digit. For the nearest 100, look at the tens digit. For the nearest 1000, look at the hundreds digit, and so on. Example: to round 5206 to the nearest 100, the tens digit is 0, so round down to 5200.
Rounding bigger numbers
The same rule works for the nearest 10 000 and 100 000. • Nearest 10 000: look at the thousands digit. • Nearest 100 000: look at the ten-thousands digit. Example: 45 678 to the nearest 10 000 — the thousands digit is 5, so round up to 50 000.
Comparing with < , > and =
To compare two whole numbers, look at the digits from left to right until they are different. • < means 'is less than' • > means 'is greater than' • = means 'is equal to' The wide open end of < or > always faces the bigger number. Example: 645 123 < 645 213.
Ordering numbers
To put numbers in order, compare them and line them up. • Smallest to largest starts with the smallest number. • Largest to smallest starts with the biggest number. Start by comparing the highest place value the numbers have.
Worked examples
Round 5206 to the nearest 1000
- You are rounding to the nearest 1000, so look at the hundreds digit: 2.
- 2 is less than 5, so round down.
- The thousands stay the same and the rest become zeros.
Answer: 5206 rounds to 5000.
Round 45 678 to the nearest 10 000
- You are rounding to the nearest 10 000, so look at the thousands digit: 5.
- 5 is 5 or more, so round up.
- 45 thousands rounds up to 50 thousands.
Answer: 45 678 rounds to 50 000.
Compare 645 123 and 645 213
- Read from the left. The hundred-thousands, ten-thousands, thousands all match.
- The next digit is the hundreds: 1 in the first number, 2 in the second.
- 1 hundred is less than 2 hundreds, so the first number is smaller.
Answer: 645 123 < 645 213.
Order 8848, 2228, 6194 smallest to largest
- Compare the thousands digit of each number.
- 2228 has the fewest thousands, then 6194, then 8848.
- Write them in that order.
Answer: 2228, 6194, 8848.
Where you see this in real life
- Saying a city is 'about 16 000 km away' instead of 16 167 km.
- Rounding a crowd size to the nearest thousand for a news report.
- Ordering the heights of mountains from shortest to tallest.
- Comparing the prices of two toys to see which is cheaper.
Key words
- Round
- To change a number to a nearby, easier number such as the nearest 10, 100 or 1000.
- Round to the nearest
- To find the closest 10, 100, 1000 and so on.
- Compare
- To decide which number is bigger or smaller.
- Order
- To arrange numbers from smallest to largest or largest to smallest.
- is less than, <
- The symbol < shows the first number is smaller.
- is greater than, >
- The symbol > shows the first number is bigger.