Compare large values
A city with 2,305,410 people has a greater population than a city with 2,295,999 people.
The hundred-thousands digit decides the comparison.
Year 6
Solve number and practical problems that involve all of the above
Use place value, comparison, rounding and negative-number reasoning to solve practical problems.
Lesson overview
Number - number and place value
Place value helps us choose sensible strategies. We can compare large numbers by starting with the greatest place, round when an estimate is useful, and use negative numbers when a problem crosses below zero.
Use rounding in context
8,651,204 is about 8,700,000 to the nearest 100,000.
An estimate helps you judge whether an answer is sensible.
Use negative numbers
A temperature moving from -3 to 5 rises by 8 degrees.
| Step | Amount |
|---|---|
| -3 to 0 | 3 |
| 0 to 5 | 5 |
| Total rise | 8 |
Crossing zero still follows the same number order.
Worked example
A stadium has 4,506,281 seats. About how many seats is that to the nearest 10,000?
| Target place | Digit to check | Rounded answer |
|---|---|---|
| 10,000 | 6 | 4,510,000 |
- The question asks for the nearest 10,000.
- Find the ten-thousands digit and check the thousands digit.
- The thousands digit is 6, so the ten-thousands digit rounds up.
- The estimate is 4,510,000 seats.
Try it
Decide which place-value idea the problem needs before choosing your answer.
Question 1
Which population is greater?
Question 2
8,651,204 rounded to the nearest 100,000 is:
Question 3
A diver moves from -5 metres to 3 metres. What is the interval?
| Part | Distance |
|---|---|
| -5 to 0 | 5 |
| 0 to 3 | 3 |
Question 4
Which statement is correct?
Question 5
A company sold 3,482,741 tickets. About how many tickets is that to the nearest 1,000?
Common mistakes
Watch for these when working through the lesson.
- Starting with smaller digits instead of checking the greatest place first.
- Rounding to the wrong place in an estimate question.
- Ignoring zero when working out an interval from a negative value.
Related topics
These ideas fit closely with this lesson.
- Round any whole number to a required degree of accuracy.
- Use negative numbers in context, and calculate intervals across zero.
- Read, write, order and compare numbers up to 10,000,000 and determine the value of each digit.