Rounding Whole Numbers

What an approximation is, how to round a whole number to the nearest 10, 100, 1000, 10 000 or million, why the rule works on the number line, and which whole numbers round to a given value.

Before you start

Each digit of a whole number has a place value. In $5\,384\,276$ the 5 is in the millions place, the 3 in the hundred thousands place, the 8 in the ten thousands place, the 4 in the thousands place, the 2 in the hundreds place, the 7 in the tens place and the 6 in the ones place.

Counting in tens from 0 gives 0, 10, 20, 30, … After 0, these are the multiples of 10. Counting in hundreds gives 0, 100, 200, 300, … and counting in thousands gives 0, 1000, 2000, 3000, … For example, 3990 is followed by 4000 when we count in tens.

Exact Values and Approximations

A football match at the National Stadium is watched by exactly $48\,763$ people. The next day a newspaper says that "about $49\,000$ people" watched it. The number $49\,000$ is an approximation: a value close to the exact one, but simpler.

We use an approximation when the exact value is not needed (a headline), when it cannot be known exactly or keeps changing (the population of a country), and when a simpler number is easier to remember, to compare or to calculate with. The usual way to get an approximation is to round the number (we also say "round off").

Definition

To round a whole number to the nearest 10 is to replace it by the nearest of the numbers 0, 10, 20, 30, … A number exactly halfway between two of them is replaced by the larger one.

Rounding to the nearest 100, 1000, $10\,000$ , … or million is done in the same way, counting in hundreds, thousands, ten thousands, … or millions.

The sign $\approx$ is read "is approximately equal to". We write $48\,763 \approx 49\,000$ (to the nearest 1000). We do not write $48\,763 = 49\,000$ , which is false.

" $49\,000$ , correct to the nearest 1000" means the same: the exact value has been rounded to the nearest 1000.

Rounding on the Number Line

Count in hundreds: 0, 100, 200, 300, … Every whole number is either one of these or lies between two of them that are next to each other. To round a number to the nearest 100, mark it on the number line between these two and see which one it is closer to. The point halfway between them is where the answer changes.

Example 1: Rounding on the number line

Use a number line to round $23\,645$ to the nearest
(a) 100
(b) 1000

Solution

(a) $23\,645$ lies between $23\,600$ and $23\,700$ , the multiples of 100 on either side of it. Halfway between them is $23\,650$ .

$23\,645$ is to the left of the halfway point. It is $23\,645 - 23\,600 = 45$ away from $23\,600$ and $23\,700 - 23\,645 = 55$ away from $23\,700$ , so it is nearer to $23\,600$ .

(b) $23\,645$ lies between $23\,000$ and $24\,000$ , the multiples of 1000 on either side of it. Halfway between them is $23\,500$ .

$23\,645$ is to the right of the halfway point. It is $23\,645 - 23\,000 = 645$ away from $23\,000$ and only $24\,000 - 23\,645 = 355$ away from $24\,000$ , so it is nearer to $24\,000$ .

(a) $23\,645 \approx 23\,600$ (to the nearest 100)
(b) $23\,645 \approx 24\,000$ (to the nearest 1000)

A number can also be exactly halfway between the two. Then neither is nearer. So that everyone gives the same answer, there is an agreement: a number that is exactly halfway is rounded up, to the larger of the two.

Example 2: Exactly halfway

Round $23\,645$ to the nearest 10.

Solution

$23\,645$ lies between $23\,640$ and $23\,650$ , the multiples of 10 on either side of it.

It is $23\,645 - 23\,640 = 5$ away from $23\,640$ and $23\,650 - 23\,645 = 5$ away from $23\,650$ . It is exactly halfway.

A number that is exactly halfway is rounded up, so we take the larger multiple, $23\,650$ .

$23\,645 \approx 23\,650$ (to the nearest 10)

Rounding on the number line

To round a number to the nearest 10, 100, 1000, …, count in tens, hundreds, thousands, … from 0. Find the two numbers of the count that the number lies between, and the point halfway between them.

If the number is below the halfway point (to the left of it), round down to the smaller of the two.
If the number is at the halfway point or above it (to the right of it), round up to the larger of the two.
A number that is already in the count stays as it is: $23\,600$ to the nearest 100 is $23\,600$ .

The Rounding Rule

There is no need to draw the line every time. Look again at Example 1(a). The answer depended on whether $23\,645$ had reached the halfway point $23\,650$ , and the tens digit tells us that at once. From $23\,600$ to $23\,649$ the tens digit is 0, 1, 2, 3 or 4, and the number is below halfway. From $23\,650$ to $23\,699$ the tens digit is 5, 6, 7, 8 or 9, and the number is at halfway or above it. So one digit decides: the digit just to the right of the place we are rounding to.

Rule: rounding a whole number

Find the digit in the place you are rounding to: the tens digit for the nearest 10, the hundreds digit for the nearest 100, and so on. This is the last digit you keep: every digit after it will become 0.
Look at the next digit, the one immediately to its right. No other digit matters.
If the next digit is 0, 1, 2, 3 or 4, round down: the last digit you keep stays as it is.
If the next digit is 5, 6, 7, 8 or 9, round up: add 1 to the last digit you keep. (If that digit is 9, write 0 and carry 1 to the place on its left, as in addition.)
Replace every digit after the last digit you keep by 0.

The zeros must be written. They keep the other digits in their places: $23\,645$ to the nearest 100 is $23\,600$ , not 236.

Example 3: Using the rule

Round 6251 to the nearest
(a) 10
(b) 100

Solution

(a) The last digit kept is the tens digit, 5. The next digit is 1.

1 is less than 5, so round down: the 5 stays, and the 1 is replaced by 0.

(b) The last digit kept is the hundreds digit, 2. The next digit is 5.

5 is one of 5, 6, 7, 8 and 9, so round up: the 2 becomes 3, and the 5 and the 1 are replaced by zeros.

(a) $6251 \approx 6250$ (to the nearest 10)
(b) $6251 \approx 6300$ (to the nearest 100)

A digit of 5 is not always "exactly halfway"

In Example 3(b) the digit looked at is 5, but 6251 is not halfway between 6200 and 6300. It is $6251 - 6200 = 51$ away from 6200 and $6300 - 6251 = 49$ away from 6300, so 6300 really is nearer. Only 6250 is exactly halfway, and by the agreement it is rounded up as well. That is why the rule can say simply "5 or more, round up".

Example 4: Numbers up to millions

A city has a population of $5\,917\,648$ . Round the population to the nearest
(a) 100
(b) 1000
(c) $10\,000$
(d) million

Solution

Read the place values first: 5 millions, 9 hundred thousands, 1 ten thousand, 7 thousands, 6 hundreds, 4 tens and 8 ones. Then use the rule for each part, starting from the exact number every time.

Round to the nearest	Last digit kept	Next digit	Round	Answer
(a) 100	hundreds digit, 6	4	down: the 6 stays	$5\,917\,600$
(b) 1000	thousands digit, 7	6	up: 7 becomes 8	$5\,918\,000$
(c) $10\,000$	ten thousands digit, 1	7	up: 1 becomes 2	$5\,920\,000$
(d) million	millions digit, 5	9	up: 5 becomes 6	$6\,000\,000$

Check (d) on the number line: $5\,917\,648$ lies between $5\,000\,000$ and $6\,000\,000$ , and it is far above the halfway point $5\,500\,000$ .

(a) $5\,917\,648 \approx 5\,917\,600$ (to the nearest 100)
(b) $5\,917\,648 \approx 5\,918\,000$ (to the nearest 1000)
(c) $5\,917\,648 \approx 5\,920\,000$ (to the nearest $10\,000$ )
(d) $5\,917\,648 \approx 6\,000\,000$ (to the nearest million). The city has about 6 million people.

When a 9 Is Rounded Up

Rounding up adds 1 to the last digit you keep. When that digit is 9, $9 + 1 = 10$ , so 0 is written in that place and 1 is carried to the place on its left, just as in addition. The number line shows the same thing more simply: rounding up takes the number to the next multiple, and the multiple of 10 after 3990 is 4000.

Example 5: A 9 that carries

Round
(a) 3996 to the nearest 10
(b) $39\,962$ to the nearest 100
(c) $99\,512$ to the nearest 1000

Solution

(a) The last digit kept is the tens digit, 9. The next digit is 6, so round up.

$9 + 1 = 10$ : write 0 in the tens place and carry 1 to the hundreds place. The hundreds digit is also 9, so it becomes 0 as well and 1 is carried to the thousands place, where 3 becomes 4. The ones digit is replaced by 0.

On the number line, the multiples of 10 on either side of 3996 are 3990 and $3990 + 10 = 4000$ , and 3996 is above the halfway point 3995.

(b) The last digit kept is the hundreds digit, 9. The next digit is 6, so round up. The multiples of 100 on either side of $39\,962$ are $39\,900$ and $39\,900 + 100 = 40\,000$ .

(c) The last digit kept is the thousands digit, 9. The next digit is 5, so round up. The multiples of 1000 on either side of $99\,512$ are $99\,000$ and $99\,000 + 1000 = 100\,000$ . The answer has one digit more than the number we started with.

(a) $3996 \approx 4000$ (to the nearest 10)
(b) $39\,962 \approx 40\,000$ (to the nearest 100)
(c) $99\,512 \approx 100\,000$ (to the nearest 1000)

Always say what you rounded to

3996 to the nearest 10 is 4000. To the nearest 100 it is also 4000 (the tens digit is 9, so the hundreds digit 9 is rounded up and carries), and to the nearest 1000 it is 4000 again (the hundreds digit is 9, so 3 becomes 4). The number 4000 alone does not tell a reader how closely it was rounded. Write the accuracy after it: $3996 \approx 4000$ (to the nearest 10).

Which Numbers Round to a Given Value?

Sometimes only the rounded value is known, and the question is what the exact number could have been. Work backwards from the halfway points on each side of the rounded value.

Example 6: The smallest and the largest

(a) A whole number is 370 when rounded to the nearest 10. Find the smallest and the largest number it could be.
(b) A whole number is 6300 when rounded to the nearest 100. Find the smallest and the largest number it could be.

Solution

(a) The multiples of 10 next to 370 are 360 and 380. Halfway between 360 and 370 is 365, and halfway between 370 and 380 is 375.

365 is exactly halfway, so it is rounded up, to 370. It is the smallest number that rounds to 370, because 364 rounds down to 360.

375 is exactly halfway too, so it is rounded up to 380, not to 370. The largest whole number that rounds to 370 is the one just before it, 374.

(b) The multiples of 100 next to 6300 are 6200 and 6400. The halfway points are 6250 and 6350.

6250 is rounded up to 6300, so it is the smallest. 6350 is rounded up to 6400, so the largest is the whole number just before it, 6349.

(a) The smallest number is 365 and the largest is 374.
(b) The smallest number is 6250 and the largest is 6349.

Rule: the whole numbers that round to a given value

Take half of the 10, 100 or 1000 that the number was rounded to: 5 for the nearest 10, 50 for the nearest 100, 500 for the nearest 1000, and so on. For a rounded value greater than 0:

the smallest number is the rounded value minus this half: $6300 - 50 = 6250$
the largest whole number is the rounded value plus this half, less 1: $6300 + 50 - 1 = 6349$

The count of these whole numbers is the 10, 100 or 1000 itself: 10 whole numbers round to 370 (to the nearest 10) and 100 whole numbers round to 6300 (to the nearest 100).

Example 7: An attendance

A newspaper reports that $49\,000$ people watched a football match at the National Stadium, correct to the nearest 1000.
(a) What is the smallest number of people who could have watched the match?
(b) What is the largest number?
(c) Could exactly $49\,500$ people have watched it?

Solution

The number was rounded to the nearest 1000, and half of 1000 is 500.

(a) Smallest: $49\,000 - 500 = 48\,500$ . Check: the hundreds digit of $48\,500$ is 5, so it is rounded up to $49\,000$ , while $48\,499$ is rounded down to $48\,000$ .

(b) Largest: $49\,000 + 500 - 1 = 49\,499$ . Check: the hundreds digit of $49\,499$ is 4, so it is rounded down to $49\,000$ .

The exact attendance at the start of this lesson, $48\,763$ , is one of the numbers from $48\,500$ to $49\,499$ .

(a) The smallest number is $48\,500$ people.
(b) The largest number is $49\,499$ people.
(c) No. An attendance of $49\,500$ would be reported as $50\,000$ .

Rounding in Everyday Settings

How closely a number is rounded depends on what it is for. A school with 1284 students has "about 1300 students". The price of a flat may be given to the nearest thousand dollars, and the population of a country in millions. Read the question for the accuracy it asks for, round once from the exact number, and give the answer with its unit (dollars) or what it counts (people, views).

Example 8: A price

A four-room flat in Tampines is sold for $ $598\,500$ .
(a) Round the price to the nearest $1000.
(b) Round the price to the nearest $ $10\,000$ .
(c) Round the price to the nearest $ $100\,000$ .
(d) How far is each rounded price from the exact price?

Solution

(a) The last digit kept is the thousands digit, 8. The next digit is 5, so round up: 8 becomes 9. (The price is exactly halfway between $ $598\,000$ and $ $599\,000$ .)

(b) The last digit kept is the ten thousands digit, 9. The next digit is 8, so round up. $9 + 1 = 10$ : write 0 and carry 1 to the hundred thousands place, where 5 becomes 6.

Each answer comes from the exact price, $ $598\,500$ , not from the answer before it.

(d) $599\,000 - 598\,500 = 500$ and $600\,000 - 598\,500 = 1500$ . The answers to (b) and (c) are the same value, so they are equally far from the exact price. Here $ $600\,000$ is the simpler number, and it is further from the exact price than $ $599\,000$ is.

(a) The price is $ $599\,000$ , to the nearest $1000.
(b) The price is $ $600\,000$ , to the nearest $ $10\,000$ .
(c) The price is $ $600\,000$ , to the nearest $ $100\,000$ .
(d) $ $599\,000$ is $500 from the exact price. $ $600\,000$ is $1500 from it.

Common Mistakes

Using the equals sign. $6251 = 6300$ is false. Write $6251 \approx 6300$ , and say what you rounded to: (to the nearest 100).
Lowering the last digit kept when rounding down. $23\,645$ to the nearest 100 is $23\,600$ , not $23\,500$ . "Round down" means the last digit you keep stays as it is.
Leaving out the zeros. $23\,645$ to the nearest 100 is $23\,600$ , not 236. The zeros keep the other digits in their places.
Rounding in stages. $23\,449$ to the nearest 100 is not found by going first to $23\,450$ and then to $23\,500$ . Look at the tens digit of the number itself: it is 4, so the answer is $23\,400$ .
Losing the carry. 3996 to the nearest 10 is 4000, not 3990 or 3900. Rounding up takes you to the next multiple of 10: $3990 + 10 = 4000$ .
Taking the halfway point as the largest. The largest whole number that rounds to 6300 (to the nearest 100) is 6349, not 6350. The number 6350 is rounded up to 6400.

Practice

Work each question on paper before you open its solution.

Question 1

Use a number line to round
(a) 4372 to the nearest 100
(b) $61\,480$ to the nearest 1000

ShowHide solution

(a) 4372 lies between 4300 and 4400. The halfway point is 4350, and 4372 is to the right of it: it is $4372 - 4300 = 72$ away from 4300 and only $4400 - 4372 = 28$ away from 4400.

(b) $61\,480$ lies between $61\,000$ and $62\,000$ . The halfway point is $61\,500$ , and $61\,480$ is to the left of it: it is $61\,480 - 61\,000 = 480$ away from $61\,000$ and $62\,000 - 61\,480 = 520$ away from $62\,000$ .

(a) $4372 \approx 4400$ (to the nearest 100)
(b) $61\,480 \approx 61\,000$ (to the nearest 1000)

Question 2

Round $24\,891$ to the nearest
(a) 10
(b) 100
(c) 1000
(d) $10\,000$

ShowHide solution

(a) The last digit kept is the tens digit, 9. The next digit is 1, so round down: the 9 stays, and the 1 is replaced by 0.

(b) The last digit kept is the hundreds digit, 8. The next digit is 9, so round up: 8 becomes 9.

(d) The last digit kept is the ten thousands digit, 2. The next digit is 4, so round down: the 2 stays.

(a) $24\,891 \approx 24\,890$ (to the nearest 10)
(b) $24\,891 \approx 24\,900$ (to the nearest 100)
(c) $24\,891 \approx 25\,000$ (to the nearest 1000)
(d) $24\,891 \approx 20\,000$ (to the nearest $10\,000$ )

Question 3

Round
(a) 765 to the nearest 10
(b) 8350 to the nearest 100
(c) $46\,500$ to the nearest 1000
(d) $2\,500\,000$ to the nearest million

ShowHide solution

Each of these numbers is exactly halfway between two multiples, so each is rounded up. The rule with digits says the same: in each number the next digit is 5.

(a) 765 is halfway between 760 and 770 (5 away from each).

(b) 8350 is halfway between 8300 and 8400 (50 away from each).

(d) $2\,500\,000$ is halfway between $2\,000\,000$ and $3\,000\,000$ ( $500\,000$ away from each).

(a) $765 \approx 770$ (to the nearest 10)
(b) $8350 \approx 8400$ (to the nearest 100)
(c) $46\,500 \approx 47\,000$ (to the nearest 1000)
(d) $2\,500\,000 \approx 3\,000\,000$ (to the nearest million)

Question 4

A video of the National Day Parade has been watched $2\,517\,394$ times. Round the number of views to the nearest
(a) 10
(b) 1000
(c) $100\,000$
(d) million

ShowHide solution

(a) The last digit kept is the tens digit, 9. The next digit is 4, so round down: the 9 stays.

(b) The last digit kept is the thousands digit, 7. The next digit is 3, so round down: the 7 stays.

(d) The last digit kept is the millions digit, 2. The next digit is 5, so round up: 2 becomes 3. ( $2\,517\,394$ is above $2\,500\,000$ , the halfway point between 2 million and 3 million.)

(a) $2\,517\,390$ views (to the nearest 10)
(b) $2\,517\,000$ views (to the nearest 1000)
(c) $2\,500\,000$ views (to the nearest $100\,000$ )
(d) $3\,000\,000$ views, or 3 million views (to the nearest million)

Question 5

Round
(a) 597 to the nearest 10
(b) 6982 to the nearest 100
(c) $49\,950$ to the nearest 100
(d) $999\,631$ to the nearest 1000

ShowHide solution

In each part the last digit kept is 9 and it is rounded up, so there is a carry.

(a) The tens digit is 9 and the next digit is 7, so round up. The multiples of 10 on either side of 597 are 590 and $590 + 10 = 600$ .

(b) The hundreds digit is 9 and the next digit is 8, so round up. The multiples of 100 on either side of 6982 are 6900 and $6900 + 100 = 7000$ .

(c) The hundreds digit is 9 and the next digit is 5, so round up. The multiples of 100 on either side of $49\,950$ are $49\,900$ and $49\,900 + 100 = 50\,000$ . ( $49\,950$ is exactly halfway between them.)

(d) The thousands digit is 9 and the next digit is 6, so round up. The multiples of 1000 on either side of $999\,631$ are $999\,000$ and $999\,000 + 1000 = 1\,000\,000$ .

(a) $597 \approx 600$ (to the nearest 10)
(b) $6982 \approx 7000$ (to the nearest 100)
(c) $49\,950 \approx 50\,000$ (to the nearest 100)
(d) $999\,631 \approx 1\,000\,000$ (to the nearest 1000)

Question 6

Round each number to the nearest 1000.
(a) 962
(b) 438

ShowHide solution

Counting in thousands gives 0, 1000, 2000, … Both numbers are less than 1000, so they lie between 0 and 1000. The halfway point is 500.

(a) 962 is above 500, so it is rounded up to 1000.

(b) 438 is below 500, so it is rounded down to 0.

The rule with digits agrees if a 0 is written in the thousands place. In 0962 the last digit kept is 0 and the next digit is 9, so the 0 becomes 1. In 0438 the next digit is 4, so the 0 stays.

(a) $962 \approx 1000$ (to the nearest 1000)
(b) $438 \approx 0$ (to the nearest 1000)

Question 7

Ravi rounds 6449 to the nearest 100 in two steps. First he rounds it to the nearest 10 and gets 6450. Then he rounds 6450 to the nearest 100 and gets 6500. Is his answer right? Explain.

ShowHide solution

To round to the nearest 100, look only at the tens digit of the number itself. The tens digit of 6449 is 4, so round down: the hundreds digit 4 stays.

6449 is $6449 - 6400 = 49$ away from 6400 and $6500 - 6449 = 51$ away from 6500, so 6400 is nearer.

Ravi's first step moved the number up to 6450, which is exactly halfway, and his second step then rounded it up again. Always round once, from the exact number.

Ravi is wrong. $6449 \approx 6400$ (to the nearest 100).

Question 8

Find the smallest and the largest whole number that is
(a) 480 when rounded to the nearest 10
(b) 4000 when rounded to the nearest 10
(c) 4000 when rounded to the nearest 1000

ShowHide solution

(a) Half of 10 is 5. Smallest: $480 - 5 = 475$ . Largest: $480 + 5 - 1 = 484$ . (The next number, 485, is rounded up to 490.)

(b) Half of 10 is 5. Smallest: $4000 - 5 = 3995$ . Largest: $4000 + 5 - 1 = 4004$ .

The same rounded value, 4000, stands for only 10 possible numbers in (b) and for 1000 possible numbers in (c). This is why the accuracy must always be stated.

(a) Smallest 475, largest 484
(b) Smallest 3995, largest 4004
(c) Smallest 3500, largest 4499

Question 9

A secondary school has 1300 students, correct to the nearest 100.
(a) Find the smallest and the largest possible number of students.
(b) Before the exact number is known, the school orders one locker for each student. How many lockers must it order to be sure of having enough?

ShowHide solution

(a) The number was rounded to the nearest 100, and half of 100 is 50. Smallest: $1300 - 50 = 1250$ . Largest: $1300 + 50 - 1 = 1349$ .

Check: 1250 is rounded up to 1300 (its tens digit is 5), and 1349 is rounded down to 1300 (its tens digit is 4). 1350 would be rounded up to 1400.

(b) To be sure of having enough, the school must allow for the largest possible number of students, 1349.

(a) The smallest possible number is 1250 students and the largest is 1349 students.
(b) The school must order 1349 lockers.

Question 10

Mr Lim buys a second-hand car for $ $74\,963$ .
(a) Round the price to the nearest $100.
(b) Round the price to the nearest $ $10\,000$ .
(c) How far is each rounded price from the exact price? Which one is closer?

ShowHide solution

(a) The last digit kept is the hundreds digit, 9. The next digit is 6, so round up. The multiples of 100 on either side of $74\,963$ are $74\,900$ and $74\,900 + 100 = 75\,000$ .

(b) The last digit kept is the ten thousands digit, 7. The next digit is 4, so round down: the 7 stays.

(c) $75\,000 - 74\,963 = 37$ and $74\,963 - 70\,000 = 4963$ . A number rounded to the nearest 100 is never further from its exact value than the same number rounded to the nearest $10\,000$ , and here it is much closer.

(a) The price is $ $75\,000$ , to the nearest $100.
(b) The price is $ $70\,000$ , to the nearest $ $10\,000$ .
(c) $ $75\,000$ is $37 from the exact price and $ $70\,000$ is $4963 from it, so $ $75\,000$ is closer.

Question 11

Town A has a population of $284\,615$ and Town B has a population of $279\,380$ .
(a) Round each population to the nearest $10\,000$ .
(b) A website says, "The two towns have the same population." Explain why this is misleading, and find the difference between the two populations.
(c) Round each population to the nearest 1000. Do the rounded values now show which town is larger?

ShowHide solution

(a) Town A: the last digit kept is the ten thousands digit, 8, and the next digit is 4, so round down. Town B: the last digit kept is the ten thousands digit, 7, and the next digit is 9, so round up: 7 becomes 8. Both are $280\,000$ .

(b) The rounded values are equal, but the exact populations are not: $284\,615 - 279\,380 = 5235$ . Every whole number from $275\,000$ to $284\,999$ is $280\,000$ to the nearest $10\,000$ , so two numbers with the same rounded value can be thousands apart.

(c) Town A: the last digit kept is the thousands digit, 4, and the next digit is 6, so round up: 4 becomes 5. Town B: the last digit kept is the thousands digit, 9, and the next digit is 3, so round down: the 9 stays.

(a) Town A: $284\,615 \approx 280\,000$ . Town B: $279\,380 \approx 280\,000$ (both to the nearest $10\,000$ ).
(b) The populations only look equal because of the rounding. Town A has 5235 more people than Town B.
(c) Town A: $284\,615 \approx 285\,000$ . Town B: $279\,380 \approx 279\,000$ (both to the nearest 1000). Yes, they now show that Town A is larger.

Question 12

A whole number is 7000 when rounded to the nearest 1000, and 6500 when rounded to the nearest 100. Find the smallest and the largest number it could be.

ShowHide solution

Rounded to the nearest 1000 it is 7000, so it is one of the whole numbers from $7000 - 500 = 6500$ to $7000 + 500 - 1 = 7499$ .

Rounded to the nearest 100 it is 6500, so it is one of the whole numbers from $6500 - 50 = 6450$ to $6500 + 50 - 1 = 6549$ .

The number must be in both lists, so it is one of the whole numbers from 6500 to 6549.

Check: 6500 is 7000 to the nearest 1000 (its hundreds digit is 5) and 6500 to the nearest 100. 6549 is 7000 to the nearest 1000 (its hundreds digit is 5) and 6500 to the nearest 100 (its tens digit is 4).

The smallest number is 6500 and the largest is 6549.

Key Points

An approximation is a value close to the exact one. The sign $\approx$ means "is approximately equal to", and the accuracy is written after the answer: $48\,763 \approx 49\,000$ (to the nearest 1000).
To round to the nearest 10 is to take the nearest of the numbers 0, 10, 20, 30, … (for the nearest 100, of 0, 100, 200, …, and so on). A number exactly halfway between two of them is rounded up.
Look at the next digit, just to the right of the last digit you keep: 0 to 4, the last digit kept stays; 5 to 9, add 1 to it.
Replace every digit after the last digit you keep by 0.
When a 9 is rounded up, write 0 and carry 1 to the left: $3996 \approx 4000$ (to the nearest 10).
Round once, from the exact number, never in stages.
To find the whole numbers that round to a given value, take half of the 10, 100 or 1000 rounded to. They run from (the value minus this half) to (the value plus this half, less 1): 6250 to 6349 round to 6300 (to the nearest 100).