Aligning, rounding off and finding your position on a graduated line

Placing a number between two others

Placing an integer between two other numbers means finding a number just below it and a number just above it, often a ten, a hundred or a thousand.

Example: placing 674 between two hundreds: 600 < 674 < 700. Placing 674 between two tens: 670 < 674 < 680.

Rounding a number

Rounding involves replacing a number with a simpler approximate value, whilst retaining the required place value.

Rule: look at the digit immediately following the chosen place value.

• if it is 0, 1, 2, 3 or 4 -> round ‘down’ (the place value remains the same)
• if it is 5, 6, 7, 8 or 9 -> round ‘up’ (add 1 to the carry-over digit)

Example: round 674 to the nearest ten. The units digit is 4 (< 5) -> round to 670.

Example: round 674 to the nearest hundred. The tens digit is 7 (>= 5) -> we round to 700.

The number line

A number line allows us to position and compare numbers visually. The further to the right a number is placed, the larger it is.

Example: on a number line from 0 to 10 with increments of 1, the number 7 lies between 6 and 8, closer to 8 than to 5.

Common pitfall

Don’t confuse ‘rounding to the nearest ten’ with ‘rounding to the nearest hundred’: the digit you choose to round to completely changes the result. Always check which digit you’re being asked to round to before looking at the next digit.

Another common mistake: thinking that 675, when rounded to the nearest ten, is 670. In fact, the units digit is 5, so we round up to 680.