Unit 1: Number Sense
Topic D: Rounding Numbers
We use numbers a lot in our everyday lives. List some of the ways you use numbers.
You may have written money, shopping, time, and counting as part of your answer.
Think about time. Let’s say it takes eight minutes to walk to the bus. If someone asks you how long it takes, you will probably say, “About ten minutes.”
If you buy a sweater that costs $29, you may say, “Oh, it was around thirty dollars.”
How far is it from Vancouver to Prince George? The map says 796 km, but we would probably say, “About 800 kilometres.”
You have just read examples of rounding numbers.
We round numbers for many reasons:
- We may not know the exact number.
- The exact number may not be important for what we are doing.
- We may need a quick way to figure something out.
When you are rounding numbers, use zeros to hold the places at the end of the number. Work through the following examples and exercises carefully. Rounding is an important skill.
Rounding to the Nearest Hundred
A number rounded to the nearest hundred will have zeros in the ones place and in the tens place. The number will end with 000, 100, 200, 300, 400, 500, 600, 700, 800, or 900.
When rounding to the nearest 100, we are looking for the closest group of 100.
Example: 200, 220 and 300.
200
220300
Is 220 closer to 200 or 300? It is closer to 200.
Which gives a better estimate of 220 … 2 hundreds or 3 hundreds? 2 hundreds
If we round 220 to nearest hundred, the result would be 200.
Remember: The rounded number has zeroes in the tens and ones places.
Example: 300, 348 and 400.
300
348
400
Is 348 closer to 300 or 400? It is closest to 300.
Which gives a better estimate of 348 ….3 hundreds or 4 hundreds? 3 hundreds
If we round 348 to the nearest 100, the result would be 300.
Remember: The rounded number has zeroes in the tens and ones places.
Example: 600, 650 and 700
600
650
700
Is 650 closer to 600 or 700? It is closer to 700.
Which gives a better estimate of 650….. 6 hundreds or 7 hundreds? 7 hundreds. If we round 650 to the nearest hundred, the result would be 700.
When we round a number which has a 5 in the tens place, we always round up to the next hundred.
If we round 650 to nearest hundred, the result would be 700.
Example: Round 584 to the nearest 100.
584 is between 5 hundreds and 6 hundreds.
584 is closer to 6 hundreds.
Rounded number is 600.
Exercise One
Round each number to the nearest 100. Check your work using the answer key at the end of the exercise.
- 232 is between hundreds and hundreds.
232 is closest to hundreds.
Rounded number is . - 647 is between hundreds and hundreds.
647 is closest to hundreds.
Rounded number is . - 881 is between hundreds and hundreds.
881 is closest to hundreds.
Rounded number is . - 152 is between hundreds and hundreds.
152 is closest to hundreds.
Rounded number is . - 326 is between hundreds and hundreds.
326 is closest to hundreds.
Rounded number is .
| Number | Closer to ___ hundreds | Rounded Number | |
|---|---|---|---|
| f. | 43 | 0 hundreds | 0 |
| g. | 188 | ||
| h. | 275 | ||
| i. | 620 | ||
| j. | 750 | ||
| k. | 549 | ||
| l. | 499 | ||
| m. | 821 | ||
| n. | 999 |
Answers to Exercise One
- 2 hundreds 200
- 6 hundreds 600
- 9 hundreds 900
- 2 hundreds 200
- 3 hundreds 300
- 0 hundreds 0
- 2 hundreds 200
- 3 hundreds 300
- 6 hundreds 600
- 8 hundreds 800
- 5 hundreds 500
- 5 hundreds 500
- 8 hundreds 800
- 10 hundreds 1000
Now look at a shorter method to round to the nearest 100.
When rounding to the nearest hundred, do this:
Step 1: Underline the hundreds place.
468
Step 2: Look at the digit following in the tens place.
[latex]\begin{array}{c}\downarrow \\ \underline{4}68\end{array}[/latex]
Step 3: If the digit in the tens place is less than 5,
- write a zero in the tens place and the ones place.
- leave the hundreds digit as it is.
[latex]\begin{array}{cl}\downarrow &\\ \underline{3}29 & \text{rounds to 300 (329 is nearer to 300 than to 400)}\\ \downarrow &\\ \underline{8}46 &\text{rounds to 800}\\ \downarrow &\\ \underline{6}08 & \text{rounds to 600}\end{array}[/latex]
Step 4: If the digit in the tens place is 5 or more,
- write a zero in the tens place and the ones place.
- add one more hundred to the hundreds place.
[latex]\begin{array}{cl}\downarrow &\\ \underline{3}62 & \text{rounds to }\textbf{4}00 \text{(362 is nearer to 400 than to 300)} \\ \downarrow &\\ \underline{8}52 & \text{rounds to } \textbf{9}00\\ \downarrow &\\ \underline{9}64 & \text{rounds to }\textbf{1 0}00 \text{(one hundred more than 9 hundreds is 10 hundreds)}\end{array}[/latex]
Note: If you are rounding to the nearest hundred, one and two-digit numerals round like this:
- the numbers from 0 to 49 round to 0
- the numbers from 50 to 99 round to 100.
Exercise Two
Round your answer to the nearest hundred. Check your work using the answer key at the end of the exercise.
- 426 =
- 395 =
- 638 =
- 95 =
- 31 =
- 211 =
- 965 =
- 438 =
- 703 =
- 796 =
Any number can be rounded to the nearest hundred.
[latex]\begin{array}{l}\phantom{4 8} \downarrow\\4\, \underline{8}27 ≈ 4\, 800\end{array}[/latex] [latex]\begin{array}{l}\phantom{92 6}\downarrow\\92\, \underline{6}59 ≈ 92\, 700\end{array}[/latex] [latex]\begin{array}{l}\phantom{3 9}\downarrow\\3\, \underline{9}75 ≈ 4\, 000\end{array}[/latex]
- 8372 =
- 2082 =
- 21639 =
- 42983 =
- 125438 =
- 12651 =
- 3888 =
- 9109 =
Answers to Exercise Two
- 400
- 400
- 600
- 100
- 0
- 200
- 1000
- 400
- 700
- 800
- 8400
- 2100
- 21600
- 43000
- 125400
- 12700
- 3900
- 9100
Rounding to the Nearest Thousand
A number rounded to the nearest thousand will have zeros in the ones, tens, and hundreds places. The number will end with 0 000, 1 000, 2 000, 3 000, 4 000, 5 000, 6 000, 7 000,
8000, or 9000.
When rounding to the nearest thousand, do this:
Step 1: Underline the thousands place.
4398
Step 2: Look at the digit following in the hundreds place.
[latex]\begin{array}{l}\phantom{4 }\downarrow\\ \underline{4}\,398\end{array}[/latex]
Step 3: If the digit in the hundreds place is less than 5,
- write a zero in the hundreds place, the tens place, and the ones place.
- leave the thousands digit as it is.
[latex]\begin{array}{ll}\phantom{4 }\downarrow&\\ \underline{4}\,398& \text{rounds to 4 000 (4 398 is nearer to 4 000 than to 5 000)}\\\phantom{325 }\downarrow&\\ 32\underline{5} \, 263& \text{rounds to 325 000} \end{array}[/latex]
Step 4: If the digit in the hundreds place is 5 or more,
- write a zero in the hundreds, tens, and ones places.
- add one more thousand to the thousands place.
[latex]\begin{array}{ll}\phantom{2 }\downarrow &\\ \underline{2}\, 884& \text{rounds to 3 000 (2884 is nearer to }\textbf{3 }\text{000 than to 2 000)}\\ \phantom{86 }\downarrow &\\8\underline{6}\, 583&\text{rounds to }\textbf{87 }000\\ \phantom{29 }\downarrow &\\2\underline{9}\, 965&\text{rounds to }\textbf{30 }000\end{array}[/latex]
Note: If you are rounding to the nearest thousand, one, two, and three-digit numerals round like this:
- numerals from 0 to 499 round to 0
- numerals from 500 to 999 round to 1000.
Exercise Three
Round your answer to the nearest thousand. Check your work using the answer key at the end of the exercise.
- 3829 =
- 2499 =
- 8309 =
- 4520 =
- 9724 =
- 386 =
- 2096 =
- 23719 =
- 45245 =
- 8129 =
- 123542 =
- 91871 =
Answers to Exercise Three
- 4000
- 2000
- 8000
- 5000
- 10000
- 0
- 2000
- 24000
- 45000
- 8000
- 124000
- 92000
Rounding to the Nearest Ten Thousand
A number rounded to the nearest ten thousand will have zeros in the ones, tens, hundreds and thousands places. The number will end with 0 000, 10000, 20000, 30000, 40000, 50000, 60000, 70000, 80000, or 90000.
When rounding to the nearest ten thousand, do this:
Step 1: Underline the ten thousands place.
42398
Step 2: Look at the digit following in the thousands place.
[latex]\begin{array}{l}\phantom{4}\downarrow\\ \underline{4}2\, 398\end{array}[/latex]
Step 3: If the digit in the thousands place is less than 5,
- write a zero in the thousands place, the hundreds place, the tens place, and the ones place.
- leave the ten thousands digit as it is.
[latex]\begin{array}{ll}\phantom{4}\downarrow&\\ \underline{4}2\, 398&\text{rounds to 40 000 (42 398 is nearer to 40 000 than to 50 000)}\\ \phantom{25}\downarrow&\\ 2\underline{5}3\, 263& \text{rounds to 250 000}\end{array}[/latex]
Step 4: If the digit in the thousands place is 5 or more,
- write a zero in the thousands, hundreds, tens, and ones places.
- add one more thousand to the thousands place.
[latex]\begin{array}{ll}\phantom{2}\downarrow&\\ \underline{2}8\, 884&\text{rounds to 2}\textbf{9 }000 \text{(28 884 is nearer to 29 000 than to 28 000)}\\ \phantom{86}\downarrow&\\ 8\underline{6}7\, 583& \text{rounds to }\textbf{870 } 000\\ \phantom{29}\downarrow&\\ 2\underline{9}9\, 965& \text{rounds to }\textbf{300 } 000\end{array}[/latex]
Note: If you are rounding to the nearest ten thousand, one, two, three and four- digit numerals round like this:
- numerals from 0 to 4 999 round to 0
- numerals from 5000 to 9999 round to 10000.
Exercise Four
Round your answer to the nearest ten thousand. Check your work using the answer key at the end of the exercise.
- 123542
- 91871
- 41724
- 80910
- 14639
- 73816
- 41171
- 52963
- 829527
- 1624099
Answers to Exercise Four
- 120000
- 90000
- 40000
- 80000
- 10000
- 70000
- 40000
- 50000
- 830000
- 1620000
Rounding to the Nearest Hundred Thousand
A number rounded to the nearest hundred thousand will have zeros in the ones, tens, hundreds, thousands and ten thousands places. The number will end with 000 000, 100000, 200000, 300000, 400000, 500000, 600000, 700000, 800000, or 900000.
When rounding to the nearest hundred thousand, do this:
Step 1: Underline the hundred thousands place.
414 398
Step 2: Look at the digit following in the ten thousands place.
[latex]\begin{array}{l}\phantom{4}\downarrow \\ \underline{4}14\, 398\end{array}[/latex]
Step 3: If the digit in the ten thousands place is less than 5,
- write a zero in the ten thousands place, the thousands place, the hundreds place, the tens place, and the ones place.
- leave the hundred thousands digit as it is.
[latex]\begin{array}{ll}\phantom{4}\downarrow&\\ \underline{4}14\, 398&\text{rounds to 400 000 (414 398 is nearer to 400 000 than to 500 000)}\\ \phantom{53}\downarrow&\\ \underline{5}36\, 263& \text{rounds to 500 000}\end{array}[/latex]
Step 4: If the digit in the thousands place is 5 or more,
- write a zero in the ten thousands place, thousands place, hundreds place, tens place, and ones place.
- add one more thousand to the hundred thousands place.
[latex]\begin{array}{ll}\phantom{2}\downarrow&\\ \underline{2}81\, 884&\text{rounds to }\textbf{300 }000 \text{ (281 884 is nearer to 300 000 than to 200 000)}\\ \phantom{67}\downarrow&\\ 6\underline{7}2\, 583& \text{rounds to }\textbf{700 } 000\\ \phantom{99}\downarrow&\\ 9\underline{9}9\, 965& \text{rounds to }\textbf{1 000 } 000\end{array}[/latex]
Note: If you are rounding to the nearest hundred thousand, one, two, three, four and five-digit numerals round like this:
- numerals from 0 to 49 999 round to 0
- numerals from 50 000 to 99 999 round to 100 000.
Exercise Five
Round your answer to the nearest hundred thousand. Check your work using the answer key at the end of the exercise.
- 143829
- 12499
- 861309
- 472520
- 96724
- 386174
- 221096
- 283716
- 457245
- 87129
Answers to Exercise Five
- 100 000
- 0
- 900000
- 500000
- 100000
- 400000
- 200000
- 300000
- 500000
- 100000
Rounding to the Nearest Million
A number rounded to the nearest million will have zeros in the ones, tens, hundreds, thousands, ten thousands and hundred thousands places. The number will end with 000 000, 1000000, 2000000, 3000000, 4000000, 5000000, 6000000, 7000000, 8000000, or 9000000.
When rounding to the nearest million, do this:
Step 1: Underline the millions place.
4214398
Step 2: Look at the digit following in the hundred thousands place.
[latex]\begin{array}{l}\phantom{4 }\underline{4}\, 214\, 398\end{array}[/latex]
Step 3: If the digit in the hundred thousands place is less than 5,
- write a zero in the hundred thousands place, the ten thousands place, the thousands, the hundreds place, the tens place, and the ones place.
- leave the millions digit as it is.
4214398 rounds to 4000000 (4214398 is nearer to 4000000 than to 500000)
5367263 rounds to 5000000
[latex]\begin{array}{ll}\phantom{4 }\downarrow&\\ \underline{4}\, 214\, 398&\text{rounds to 4 000 000 (4 214 398 is nearer to 4 000 000 than to 5 000 000)}\\ \phantom{5 }\downarrow&\\ \underline{5}\,367\, 263& \text{rounds to 5 000 000}\end{array}[/latex]
Step 4: If the digit in the hundred thousands place is 5 or more,
- write a zero in the hundred thousands place, the ten thousands place, the thousands place, the hundreds place, tens place, and ones place.
- Add one more thousand to the Thousand place.
2818884 rounds to 3000000 (2818884 is nearer to 3000000 than to 2000000)
6729583 rounds to 7000000
9991965 rounds to 10000000
[latex]\begin{array}{ll}\phantom{2 }\downarrow&\\ \underline{2}\, 818\, 884&\text{rounds to }\textbf{3 }000\,000 \text{ (281 884 is nearer to 300 000 than to 200 000)}\\ \phantom{6 }\downarrow&\\ \underline{6}\, 729\, 583& \text{rounds to }\textbf{700 } 000\\ \phantom{9}\downarrow&\\ \underline{9}\, 991\, 965& \text{rounds to }\textbf{10 }000\, 000\end{array}[/latex]
Exercise Six
Round your answer to the nearest million.
Note: If you are rounding to the nearest million, one, two, three, four, five and six-digit numerals round like this:
- numerals from 0 to 499999 round to 0
- numerals from 500000 to 999999 round to 1000000.
- 6123542
- 2391871
- 5419724
- 2801910
- 941639
- 3736816
- 3413171
- 4525963
- 1829527
- 1624099
Answers to Exercise Six
- 6000000
- 2000000
- 5000000
- 3000000
- 1000000
- 4000000
- 3000000
- 5000000
- 2000000
- 2000000
Exercise Seven
For each problem, round to the number asked. Check your work using the answer key at the end of the exercise.
Example: Juan had 1094 baseball cards. Adamo has 2106 baseball cards. Ho has 1589 baseball cards. Round each number to the nearest 100.
| Name | Number | Rounded Number |
|---|---|---|
| Juan | 1094 | 1100 |
| Adamo | 2106 | 2100 |
| Ho | 1589 | 1600 |
- On Friday, 5479 people went the football game. On Saturday, 4388 people went to the football game. On Sunday, 4834 people went to the basketball game. Round each number to the nearest hundred.
Day Number Rounded Number Friday Saturday Sunday - Mount Logan in the Yukon is the highest mountain in Canada. It is 5956 meters. Mount Waddington is the highest mountain in British Columbia. It is 4019 meters. Mount Columbia is the highest mountain in Alberta. It is 3741 meters. Round each number to the nearest hundred.
Mountain Number Rounded Number Mount Logan Mount Waddington Mount Columbia - The Connaught Tunnel is 8082 meters long. The Mount MacDonald Tunnel is 14700 meters long. The Deas Island Tunnel is 629 meters. Round each number to the nearest thousand.
Tunnel Number Rounded Number Connaught Tunnel Mount MacDonald Tunnel Deas Island Tunnel
Answers to Exercise Seven
-
Day Number Rounded Number Friday 5479 5500 Saturday 4388 4400 Sunday 4834 4800 -
Mountain Number Rounded Number Mount Logan 5965 meters 6000 meters Mount Waddington 4019 meters 4000 meters Mount Columbia 3741 meters 3700 meters -
Tunnel Number Rounded Number Connaught Tunnel 8082 meters 8000 meters Mount MacDonald Tunnel 14700 meters 15000 meters Deas Island Tunnel 692 meters 1000 meters
Topic D: Self-Test
Mark /36 Aim 30/36
- Round your answer to the nearest hundred. (4 marks)
- 329
- 2481
- 8065
- 3916
- Round your answer to the nearest thousand. (4 marks)
- 5521
- 21813
- 46499
- 34860
- Round your answer to the nearest ten thousand. (4 marks_
- 15521
- 26318
- 176994
- 86486
- Round your answer to the nearest hundred thousand. (4 marks)
- 523521
- 821932
- 761949
- 464051
- Round your answer to the nearest million. (4 marks)
- 7312908
- 6009280
- 9152801
- 576679
- For each problem, round to the number asked. 16 Marks
- The longest river in North America is the Mississippi River which is 6275 kilometers long. The longest river in Canada is the Mackenize River which is 4 242 kilometers long. The Yukon River is 3701 kilometers long. The St. Lawrence River is 3058 kilometers long. Round each number to the nearest hundred.
River Number Rounded Number Mississippi River Mackenzie River Yukon River St. Lawrence River - In 2009, the population of Shanghai, China was 13831900. The population of Moscow, Russia was 10 508 971. The population of New York City, United States of America was 8363710. The population of Vancouver, Canada was 578041. Round each of these numbers to the nearest hundred thousand.
City Number Rounded Number Shanghai, China Moscow, Russia New York City, USA Vancouver, Canada
- The longest river in North America is the Mississippi River which is 6275 kilometers long. The longest river in Canada is the Mackenize River which is 4 242 kilometers long. The Yukon River is 3701 kilometers long. The St. Lawrence River is 3058 kilometers long. Round each number to the nearest hundred.
Answers to Topic D Self-Test
-
- 300
- 2500
- 8100
- 4000
-
- 6000
- 22000
- 46000
- 35000
-
- 20000
- 30000
- 180000
- 860000
-
- 500000
- 800000
- 800000
- 500000
-
- 7000000
- 6000000
- 9000000
- 1000000
-
-
River Number Rounded Number Mississippi River 6275 kilometers 6300 kilometers Mackenzie River 4242 kilometers 4200 kilometers Yukon River 3701 kilometers 3700 kilometers St. Lawrence River 3058 kilometers 3100 kilometers -
City Number Rounded Number Shanghai, China 13831900 people 13800000 people Moscow, Russia 10508971 people 10500000 people New York City, USA 8363710 people 8400000 people Vancouver, Canada 578041 people 600000 people
-