Rounding large numbers means replacing a number with four or more digits by the nearest multiple of ten, a hundred, a thousand or more, such as 4,782 with 5,000. The four PDFs on this page have rounding hills, a table that rounds one number to the nearest 10, 100 and 1,000, a table of 16 numbers rounded to the nearest 1,000 and a riddle, and every sheet has an answer key. They follow standard 4.NBT.A.3 of the Common Core standards for grade 4 number and operations in base ten, and the notes below show how the rule works at every place.
A thousands hill. 4,782 rounds up to 5,000.
Rounding bigger numbers
The rule does not change as numbers get bigger: find the place, look one digit to the right, round up for 5 or more. What changes is that there are more places to choose from. Grade 4 children round multi-digit whole numbers to any place (Common Core 4.NBT.A.3).
A good habit is to underline the digit in the rounding place and circle the digit to its right before deciding. In 36,418 rounded to the nearest thousand, underline the 6 and circle the 4: round down to 36,000.
What is on this page
Thousands hills: which thousand is each number closer to?
A three-column table: the same 4-digit number rounded to the nearest 10, 100 and 1,000.
Nearest 1,000 for 4-digit and 5-digit numbers.
A rounding riddle.
Rounding large numbers worksheets: what is in the set
There are 4 rounding large numbers worksheets on this page, and every one has an answer key except for any cut-out games. One sheet is a set of thousands hills, one rounds one number three ways, one has 16 four- and five-digit numbers, and one is a riddle.
Worksheet
What children do
Standard
Rounding Hills: Nearest 1,000
Which thousand is each number closer to?.
4.NBT.A.3
Round to the Nearest 10, 100 and 1,000
Round each 4-digit number three ways.
4.NBT.A.3
Round to the Nearest 1,000
16 four- and five-digit numbers.
4.NBT.A.3
Rounding Riddle: Nearest 1,000
Round the numbers to decode a riddle.
4.NBT.A.3
Rounding large numbers: the same rule at every place
Rounding large numbers uses the rule that children already know, and only the place changes. Find the place that you are rounding to, look at the digit to its right, and round up if that digit is 5 or more. Everything to the right of the place becomes zero. Wikipedia’s article on rounding describes the rule for any base. This table shows six numbers rounded to every place from the nearest 10 to the nearest 100,000:
Number
Nearest 10
Nearest 100
Nearest 1,000
Nearest 10,000
Nearest 100,000
4,782
4,780
4,800
5,000
0
0
36,418
36,420
36,400
36,000
40,000
0
9,650
9,650
9,700
10,000
10,000
0
99,500
99,500
99,500
100,000
100,000
100,000
250,460
250,460
250,500
250,000
250,000
300,000
305,619
305,620
305,600
306,000
310,000
300,000
A good habit is to underline the digit in the rounding place and to circle the digit to its right before deciding. In 36,418 rounded to the nearest 1,000, the 6 is underlined and the 4 is circled, so the number rounds down to 36,000. The large numbers place value page explains the places.
Rounding to the nearest 1000 worksheets: which numbers round to 5,000?
The rounding to the nearest 1000 worksheets use hills between two thousands. The numbers from 4,500 to 5,499 all round to 5,000. This is the same pattern as rounding to the nearest ten, with every place scaled up. This table shows the range for four roundings:
Round to the nearest
Rounds to
Smallest number
Biggest number
How many numbers
1,000
5,000
4,500
5,499
1,000
1,000
36,000
35,500
36,499
1,000
10,000
40,000
35,000
44,999
10,000
100,000
300,000
250,000
349,999
100,000
A thousand numbers round to each thousand, and ten thousand numbers round to each ten thousand. The halfway number, such as 4,500, is the first one to round up. The diagram above shows a hill with 4,782 on it. The number line tool lets children see the same idea on a line.
Rounding worksheets grade 4: underline and circle
For rounding worksheets grade 4, the standard 4.NBT.A.3 asks children to use place value understanding to round multi-digit whole numbers to any place. The underline-and-circle method makes it quick. This table shows five numbers, with the digit to underline, the digit to circle, and the answer:
When a number is rounded up and the digit before is a 9, the 9 becomes a 0 and the digit before it goes up by one. If that is also a 9, the change goes on. This is the hardest case in rounding. This table shows six numbers:
Number
Round to the nearest
Rounded
What happens
9,650
1,000
10,000
the 9s turn into 0s and the next place goes up by one
99,500
1,000
100,000
the 9s turn into 0s and the next place goes up by one
9,999
10
10,000
the 9s turn into 0s and the next place goes up by one
99,950
100
100,000
the 9s turn into 0s and the next place goes up by one
999,500
1,000
1,000,000
the 9s turn into 0s and the next place goes up by one
999,999
100,000
1,000,000
the 9s turn into 0s and the next place goes up by one
9,650 rounds to 10,000 because 9 thousands and 1 more thousand make 10 thousands. The number gets a new digit. The diagram above shows the same idea, and it is the one case where the rounded number is longer than the original.
Rounding multi digit numbers: how big can the change be?
When rounding multi digit numbers, children can ask how far the rounded number can be from the original. For every place the biggest change is half of the place, since a number that is more than halfway rounds the other way. This table shows the biggest change for each place:
Five roundings. 36,418 at every place.
Round to the nearest
Biggest change
An example that changes by that much
Number of digits that become 0
10
5
45 → 50
1
100
50
450 → 500
2
1,000
500
4,500 → 5,000
3
10,000
5,000
45,000 → 50,000
4
100,000
50,000
450,000 → 500,000
5
The bigger the place, the bigger the possible change. That is why a rounded number is only an approximation, and why rounding to a bigger place gives a simpler number but a rougher estimate. The estimating with rounding page uses this idea.
Rounding in real life: which place to round to
The place to round to depends on the job. A news story about a city rounds to the nearest 10,000 or 100,000, and a report about a crowd rounds to the nearest 1,000. This table shows five jobs and the place that each rounds to:
Situation
Round to
Why
A news headline about a city
nearest 10,000 or 100,000
a quick idea of the size
The crowd at a game
nearest 1,000
a number that is easy to say
The distance to the moon
nearest 1,000
about 384,000 km
A price in a report
nearest 100
a clear picture of the cost
A bank statement
not rounded
every cent counts
This table shows how five numbers of people look when they are rounded to different places:
People in
Exact number
Nearest 1,000
Nearest 10,000
Nearest 100,000
a city
305,619
306,000
310,000
300,000
a stadium crowd
12,458
12,000
10,000
0
a school district
87,236
87,000
90,000
100,000
a county
450,982
451,000
450,000
500,000
a town
9,650
10,000
10,000
0
The 305,619 people of the city is about 306,000, 310,000 or 300,000, depending on the place. Each is correct, and each is useful for a different reason. The comparing large numbers page compares large numbers, and the comparing and rounding decimals page rounds decimals.
Common mistakes with rounding large numbers
The most common mistake is to ignore the digit to the right. This table shows five mistakes, what went wrong and the fix:
What the child writes or says
What went wrong
The fix
4,782 rounds to 4,000
ignores the digit to the right
the hundreds digit is 7, so round up: 5,000
9,650 rounds to 9,000
does not round up because the thousands digit is 9
the hundreds digit 6 says round up: 10,000
36,418 rounds to 36,400 to the nearest 1,000
rounds to the nearest 100
to the nearest 1,000 the answer ends in three zeros: 36,000
5,500 rounds to 5,000
rounds the halfway number down
5,500 is halfway, so it rounds up to 6,000
The 4 in 4,782 is changed to a 5, and the rest is kept
keeps the other digits
every digit to the right becomes a 0: 5,000
Rounding large numbers word problems
Large numbers come up in crowds, cities and distances. Ask children to underline the place, to circle the digit to its right, and then to round:
Word problem
Working
Answer
A stadium holds 36,418 people. What is that to the nearest 1,000?
hundreds digit 4, round down
36,000 people
A trip is 4,782 miles. What is that to the nearest 1,000?
hundreds digit 7, round up
5,000 miles
A town has 9,650 people. Round the number to the nearest 1,000.
hundreds digit 6, round up
10,000 people
A city has 305,619 people. Round the number to the nearest 10,000.
thousands digit 5, round up
310,000 people
A mountain is 14,505 feet high. What is that to the nearest 1,000?
hundreds digit 5, round up
15,000 feet
A school sold 87,236 tickets. Round the number to the nearest 100.
tens digit 3, round down
87,200 tickets
Games and activities for rounding large numbers
Children learn rounding large numbers best when they play with it. These games use things that are found at home or in a classroom:
Underline and circle: write a large number on a card, and have a partner underline the place and circle the next digit
Rounding hill race: roll five dice for a number, and say which thousand it rolls to
Nines challenge: find as many numbers as possible that round to 10,000
Round it three ways: round a number to the nearest 10, 100 and 1,000
Rounding bingo: a bingo card with rounded numbers, and calling cards with numbers to round
Headline writer: find a big number in the news, and write the headline with a rounded number
Extra support and extra challenge with rounding large numbers
For children who need more support: make sure that rounding to the nearest 10 and 100 is secure. Use a place value chart, and mark the place to round to. Underline the digit in that place, circle the digit to its right, and say whether the circled digit is less than 5. Start with numbers with four digits and no nines, and use the answer key to check each hill.
For children who need more challenge: ask for all the numbers that round to 36,000, for the smallest number that rounds to 100,000 when rounded to the nearest 10,000, and for a number that has the same rounded value at every place. The sheet that rounds one number three ways, and the riddle, are good challenges.
How to tell that a child is ready to move on from rounding large numbers
Before moving on from rounding large numbers, check that the child can do all four of these things:
Through the nines. 9,650 rounds up to 10,000.
The child underlines the rounding place and circles the digit to its right.
The child rounds 4-digit and 5-digit numbers to the nearest 1,000.
The child rounds numbers such as 9,650 up through the nines.
The child rounds the same number to different places.
A short lesson is the best way to introduce rounding large numbers. This 20-minute plan can be used in a classroom, at a tutoring session or at home, and it uses the worksheets at the end:
Minutes
Activity
What to say or ask
0 to 3
Show 4,782 on a number line between 4,000 and 5,000
Which thousand is it closer to?
3 to 8
Underline the thousands digit and circle the hundreds digit
Is the circled digit 5 or more?
8 to 13
Round 36,418 to the nearest 10, 100 and 1,000
What happens to the digits to the right?
13 to 18
Round 9,650 to the nearest 1,000
Why does the number get a new digit?
18 to 20
Start a worksheet and check one answer
Check the circled digit.
Where rounding large numbers fits across the grades
No skill stands alone. This table shows what children learn before and after rounding large numbers, with the standard that goes with each step:
This page is the last of the whole number rounding pages. The whole sequence is on the rounding worksheets page.
Helping at home with rounding large numbers
Parents do not need to be experts to help with rounding large numbers. These suggestions work well, and each takes only a few minutes:
Round the numbers in the news, such as the size of a crowd.
Ask “which thousand is it closer to?” about a distance.
Use a place value chart to underline the place.
Play the nines game: find numbers that round up to a new digit.
Check the answers with the answer key, and ask the child to explain one.
How to check progress in rounding large numbers
A teacher or parent can check progress in rounding large numbers with the answer key and a few questions. This table shows three common situations, what they mean and what to do next:
What you see
What it means
What to do next
The child ignores the digit to the right
The rule has not yet moved from the tens to larger places
Underline the place, circle the next digit, and say the rule aloud
The child gets 9 of 10 right in every set
Rounding large numbers is secure
Move on to estimating with rounding
The child does not change the zeros
The digits to the right are kept
Say “every digit to the right becomes a zero”
A five-day plan for rounding large numbers
Most children need about a week of short sessions for rounding large numbers. This plan follows the order of the worksheets on this page:
Day
What to do
Practice
Day 1
Review rounding to 10 and 100, and use thousands hills
Rounding Hills: Nearest 1,000
Day 2
Round one number three ways
Round to the Nearest 10, 100 and 1,000
Day 3
Round 4-digit and 5-digit numbers to the nearest 1,000
10,000. The hundreds digit is 6, so round up, and 9 thousands become 10 thousands.
Which place should I round to?
It depends on how exact you need to be. Rounding to a bigger place gives a simpler number but a rougher estimate.
What is 9,650 rounded to the nearest thousand?
10,000. The hundreds digit is 6, so round up, and 9 thousands become 10 thousands.
How do you round a large number?
Underline the digit in the place you are rounding to, and circle the digit to its right. If the circled digit is 5 or more, add one to the underlined digit. Then change every digit to the right of it to 0.
Which place should I round to?
It depends on how exact you need to be. Rounding to a bigger place gives a simpler number but a rougher estimate. A crowd is usually rounded to the nearest thousand, and a city to the nearest ten thousand.
