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.

Remember: The rounded number has zeroes in the tens and ones places.

Remember: The rounded number has zeroes in the tens and ones places.

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.

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.

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.

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.

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]

Topic D: Self-Test

Mark /36    Aim 30/36

1. Round your answer to the nearest hundred. (4 marks)
   1. 329
   2. 2481
   3. 8065
   4. 3916
2. Round your answer to the nearest thousand. (4 marks)
   1. 5521
   2. 21813
   3. 46499
   4. 34860
3. Round your answer to the nearest ten thousand. (4 marks_
   1. 15521
   2. 26318
   3. 176994
   4. 86486
4. Round your answer to the nearest hundred thousand. (4 marks)
   1. 523521
   2. 821932
   3. 761949
   4. 464051
5. Round your answer to the nearest million. (4 marks)
   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
      Vancouver, Canada

Answers to Topic D Self-Test

1. 1. 300
   2. 2500
   3. 8100
   4. 4000
2. 1. 6000
   2. 22000
   3. 46000
   4. 35000
3. 1. 20000
   2. 30000
   3. 180000
   4. 860000
4. 1. 500000
   2. 800000
   3. 800000
   4. 500000
5. 1. 7000000
   2. 6000000
   3. 9000000
   4. 1000000

6. 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