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.

1. 232 is between          hundreds and          hundreds.
232 is closest to          hundreds.
Rounded number is          .
2. 647 is between          hundreds and          hundreds.
647 is closest to          hundreds.
Rounded number is         .
3. 881 is between          hundreds and          hundreds.
881 is closest to          hundreds.
Rounded number is         .
4. 152 is between          hundreds and          hundreds.
152 is closest to          hundreds.
Rounded number is         .
5. 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

1. 2 hundreds    200
2. 6 hundreds    600
3. 9 hundreds    900
4. 2 hundreds    200
5. 3 hundreds    300
6. 0 hundreds    0
7. 2 hundreds    200
8. 3 hundreds    300
9. 6 hundreds    600
10. 8 hundreds    800
11. 5 hundreds    500
12. 5 hundreds    500
13. 8 hundreds    800
14. 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.

$\begin{array}{c}\downarrow \\ \underline{4}68\end{array}$

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.

$\begin{array}{cl}\downarrow &\\ \underline{3}29 & \text{rounds to 300 (329 is nearer to 300 than to 400)}\\ \downarrow &\\ \underline{8}46 &\text{rounds to 800}\\ \downarrow &\\ \underline{6}08 & \text{rounds to 600}\end{array}$

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.

$\begin{array}{cl}\downarrow &\\ \underline{3}62 & \text{rounds to }\textbf{4}00 \text{(362 is nearer to 400 than to 300)} \\ \downarrow &\\ \underline{8}52 & \text{rounds to } \textbf{9}00\\ \downarrow &\\ \underline{9}64 & \text{rounds to }\textbf{1 0}00 \text{(one hundred more than 9 hundreds is 10 hundreds)}\end{array}$

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

1. 426 =
2. 395 =
3. 638 =
4. 95 =
5. 31 =
6. 211 =
7. 965 =
8. 438 =
9. 703 =
10. 796 =

Any number can be rounded to the nearest hundred.

$\begin{array}{l}\phantom{4 8} \downarrow\\4\, \underline{8}27 ≈ 4\, 800\end{array}$    $\begin{array}{l}\phantom{92 6}\downarrow\\92\, \underline{6}59 ≈ 92\, 700\end{array}$    $\begin{array}{l}\phantom{3 9}\downarrow\\3\, \underline{9}75 ≈ 4\, 000\end{array}$

1. 8372 =
2. 2082 =
3. 21639 =
4. 42983 =
5. 125438 =
6. 12651 =
7. 3888 =
8. 9109 =

1. 400
2. 400
3. 600
4. 100
5. 0
6. 200
7. 1000
8. 400
9. 700
10. 800
11. 8400
12. 2100
13. 21600
14. 43000
15. 125400
16. 12700
17. 3900
18. 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.

$\begin{array}{l}\phantom{4 }\downarrow\\ \underline{4}\,398\end{array}$

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.

$\begin{array}{ll}\phantom{4 }\downarrow&\\ \underline{4}\,398& \text{rounds to 4 000 (4 398 is nearer to 4 000 than to 5 000)}\\\phantom{325 }\downarrow&\\ 32\underline{5} \, 263& \text{rounds to 325 000} \end{array}$

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.

$\begin{array}{ll}\phantom{2 }\downarrow &\\ \underline{2}\, 884& \text{rounds to 3 000 (2884 is nearer to }\textbf{3 }\text{000 than to 2 000)}\\ \phantom{86 }\downarrow &\\8\underline{6}\, 583&\text{rounds to }\textbf{87 }000\\ \phantom{29 }\downarrow &\\2\underline{9}\, 965&\text{rounds to }\textbf{30 }000\end{array}$

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

1. 3829 =
2. 2499 =
3. 8309 =
4. 4520 =
5. 9724 =
6. 386 =
7. 2096 =
8. 23719 =
9. 45245 =
10. 8129 =
11. 123542 =
12. 91871 =

1. 4000
2. 2000
3. 8000
4. 5000
5. 10000
6. 0
7. 2000
8. 24000
9. 45000
10. 8000
11. 124000
12. 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.

$\begin{array}{l}\phantom{4}\downarrow\\ \underline{4}2\, 398\end{array}$

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.

$\begin{array}{ll}\phantom{4}\downarrow&\\ \underline{4}2\, 398&\text{rounds to 40 000 (42 398 is nearer to 40 000 than to 50 000)}\\ \phantom{25}\downarrow&\\ 2\underline{5}3\, 263& \text{rounds to 250 000}\end{array}$

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.

$\begin{array}{ll}\phantom{2}\downarrow&\\ \underline{2}8\, 884&\text{rounds to 2}\textbf{9 }000 \text{(28 884 is nearer to 29 000 than to 28 000)}\\ \phantom{86}\downarrow&\\ 8\underline{6}7\, 583& \text{rounds to }\textbf{870 } 000\\ \phantom{29}\downarrow&\\ 2\underline{9}9\, 965& \text{rounds to }\textbf{300 } 000\end{array}$

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

1. 123542
2. 91871
3. 41724
4. 80910
5. 14639
6. 73816
7. 41171
8. 52963
9. 829527
10. 1624099

1. 120000
2. 90000
3. 40000
4. 80000
5. 10000
6. 70000
7. 40000
8. 50000
9. 830000
10. 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.

$\begin{array}{l}\phantom{4}\downarrow \\ \underline{4}14\, 398\end{array}$

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.

$\begin{array}{ll}\phantom{4}\downarrow&\\ \underline{4}14\, 398&\text{rounds to 400 000 (414 398 is nearer to 400 000 than to 500 000)}\\ \phantom{53}\downarrow&\\ \underline{5}36\, 263& \text{rounds to 500 000}\end{array}$

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.

$\begin{array}{ll}\phantom{2}\downarrow&\\ \underline{2}81\, 884&\text{rounds to }\textbf{300 }000 \text{ (281 884 is nearer to 300 000 than to 200 000)}\\ \phantom{67}\downarrow&\\ 6\underline{7}2\, 583& \text{rounds to }\textbf{700 } 000\\ \phantom{99}\downarrow&\\ 9\underline{9}9\, 965& \text{rounds to }\textbf{1 000 } 000\end{array}$

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

1. 143829
2. 12499
3. 861309
4. 472520
5. 96724
6. 386174
7. 221096
8. 283716
9. 457245
10. 87129

1. 100 000
2. 0
3. 900000
4. 500000
5. 100000
6. 400000
7. 200000
8. 300000
9. 500000
10. 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.

$\begin{array}{l}\phantom{4 }\underline{4}\, 214\, 398\end{array}$

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

$\begin{array}{ll}\phantom{4 }\downarrow&\\ \underline{4}\, 214\, 398&\text{rounds to 4 000 000 (4 214 398 is nearer to 4 000 000 than to 5 000 000)}\\ \phantom{5 }\downarrow&\\ \underline{5}\,367\, 263& \text{rounds to 5 000 000}\end{array}$

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

$\begin{array}{ll}\phantom{2 }\downarrow&\\ \underline{2}\, 818\, 884&\text{rounds to }\textbf{3 }000\,000 \text{ (281 884 is nearer to 300 000 than to 200 000)}\\ \phantom{6 }\downarrow&\\ \underline{6}\, 729\, 583& \text{rounds to }\textbf{700 } 000\\ \phantom{9}\downarrow&\\ \underline{9}\, 991\, 965& \text{rounds to }\textbf{10 }000\, 000\end{array}$

Exercise six

Round 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.
1. 6123542
2. 2391871
3. 5419724
4. 2801910
5. 941639
6. 3736816
7. 3413171
8. 4525963
9. 1829527
10. 1624099

1. 6000000
2. 2000000
3. 5000000
4. 3000000
5. 1000000
6. 1000000
7. 3000000
8. 5000000
9. 2000000
10. 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
Ho 1589 1600
1. 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 Round each number to the nearest hundred.
Day Number Rounded Number
Friday
Saturday
Sunday
2. Mount Logan in the Yukon is the highest mountain in 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 Columbia
3. 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

1. Day Number Rounded Number
Friday 5479 5500
Saturday 4388 4400
Sunday 4834 4800
2. Mountain Number Rounded Number
Mount Logan 5965 meters 6000 meters
Mount Waddington 4019 meters 4000 meters
Mount Columbia 3741 meters 3700 meters
3. 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

1. 329
2. 2481
3. 8065
4. 3916
1. 5521
2. 21813
3. 46499
4. 34860
1. 15521
2. 26318
3. 176994
4. 86486
1. 523521
2. 821932
3. 761949
4. 464051
1. 7312908
2. 6009280
3. 9152801
4. 576679
6. For each problem, round to the number asked. 16 Marks
1. 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
2. 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

## Answers to Topic D Self-Test

1. 300
2. 2500
3. 8100
4. 4000
1. 6000
2. 22000
3. 46000
4. 35000
1. 20000
2. 30000
3. 180000
4. 860000
1. 500000
2. 800000
3. 800000
4. 500000
1. 7000000
2. 6000000
3. 9000000
4. 1000000
1. 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
2. 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