Year 6 · Place Value and Negative Numbers · Lesson 1.3

Year 6: Rounding to a degree of accuracy

Part of the Year 6 place value and negative numbers chapter. Chapter overview · whole chapter on one page

1.3

Rounding to a degree of accuracy

Year 6
Round any whole number to a required degree of accuracy, Use rounding to estimate, Use the halfway point to decide

We round a number when an exact answer is not needed, or when a number is too long to use easily. The degree of accuracy tells you the place value to round to: the nearest 10, 100, 1,000, 10,000, 100,000 or 1,000,000.

To round, find the two multiples of that place value either side of the number. Look at the digit just to the right of the rounding digit. If it is 5 or more, the number is nearer to the bigger multiple, so round up. If it is less than 5, round down. Every digit after the rounding digit then becomes a zero in the answer for that place.

When the number is exactly halfway, for example 350,000 to the nearest 100,000, we round up.

The same method works for negative whole numbers. Ignore the minus sign, round the number, then put the minus sign back. So −6,548 rounds to −7,000 to the nearest 1,000, because 6,548 rounds to 7,000.

Rounding 6,548,213 to the nearest 10,000. The number is past the halfway point of 6,545,000, so it rounds up to 6,550,000.

Key ideas

To round, find the two multiples of the place value on each side of the number.
Look at the digit to the right of the rounding digit. 5 or more means round up. 4 or less means round down.
The digits after the rounding place become zeros: 6,548,213 to the nearest 10,000 is 6,550,000.
Halfway (for example 500,000 to the nearest 1,000,000) rounds up.
For a negative number, ignore the minus sign, round, then put the minus sign back.
Rounding is for estimates and checks. Use the exact number when a question asks for it.

Worked example 1.3.1

Round 6,548,213 to the nearest 10,000.

Key words. To round a number to a given place value, find the two multiples of that place value either side of it. Then choose the one the number is nearer to. If the number is exactly halfway, we round up.

Method. Find the two multiples of 10,000 either side of the number, then choose the nearer one.

Find the two multiples. The number lies between two multiples of 10,000.
6,540,000 < 6,548,213 < 6,550,000
Check the digit after the rounding digit. Halfway is 5,000. Look at how far the number is past 6,540,000.
6,548,213 − 6,540,000 = 8,213, and 8,213 is at least 5,000
Round up or down. Five or more means round up. Less than five means round down.
Round up to 6,550,000

Check. 6,550,000 is a multiple of 10,000 and is the closer one to 6,548,213. ✓

Watch out. Look at the digit just to the right of the place you are rounding to. The other digits do not matter for the rule.

Worked example 1.3.2

Round 2,497,650 to the nearest 100,000.

Method. Find the two multiples of 100,000 either side of the number, then choose the nearer one.

Find the two multiples. The number lies between two multiples of 100,000.
2,400,000 < 2,497,650 < 2,500,000
Check the digit after the rounding digit. Halfway is 50,000. Look at how far the number is past 2,400,000.
2,497,650 − 2,400,000 = 97,650, and 97,650 is at least 50,000
Round up or down. Five or more means round up. Less than five means round down.
Round up to 2,500,000

Check. 2,500,000 is a multiple of 100,000 and is the closer one to 2,497,650. ✓

Watch out. Look at the digit just to the right of the place you are rounding to. The other digits do not matter for the rule.

Worked example 1.3.3

Round 3,499,999 to the nearest 1,000,000.

Method. Find the two multiples of 1,000,000 either side of the number, then choose the nearer one.

Find the two multiples. The number lies between two multiples of 1,000,000.
3,000,000 < 3,499,999 < 4,000,000
Check the digit after the rounding digit. Halfway is 500,000. Look at how far the number is past 3,000,000.
3,499,999 − 3,000,000 = 499,999, and 499,999 is less than 500,000
Round up or down. Five or more means round up. Less than five means round down.
Round down to 3,000,000

Check. 3,000,000 is a multiple of 1,000,000 and is the closer one to 3,499,999. ✓

Watch out. Look at the digit just to the right of the place you are rounding to. The other digits do not matter for the rule.

Watch out

Do not stop at the rounding digit. To round 3,499,999 to the nearest 1,000,000, look at the 499,999 part: it is less than 500,000, so the answer is 3,000,000, not 4,000,000. Also, a digit of 5 rounds up, even when it is the last digit: 1,250 to the nearest 100 is 1,300.

Exercise 1C Rounding

Non-calculator

FRound 4,736 to the nearest 10.

Done

FRound 58,265 to the nearest 100.

Done

FRound each number to the nearest 1,000.

(a)362,489

(b)84,650

Done

FRound each number to the nearest 10,000.

(a)2,753,600

(b)6,473,000

Done

FRound each number to the nearest 100,000.

(a)5,249,999

(b)1,640,000

Done

FRound each number to the nearest 1,000,000.

(a)7,321,000

(b)8,600,000

Done

PSA football stadium holds 45,786 people. Round this to the nearest 1,000 to estimate how many people it holds.

Done

RWhich whole numbers round to 4,000,000 to the nearest 1,000,000? Write the smallest and the largest.

Done

PSThere are 86,400 seconds in a day. Round this to the nearest 1,000 to estimate.

Done

RAli says 5,449,999 rounds to 6,000,000 to the nearest 1,000,000. Is he right? Explain your answer.

Done

PSRound −6,548 to the nearest 1,000.

Done

RWhat is the smallest whole number that rounds to 3,000,000 to the nearest 100,000 and also rounds to 3,000,000 to the nearest 1,000,000?

Done