Unit 1: Working with Decimals

Topic D: Rounding Numbers

If a pair of jeans cost $49.98, what amount would you say if someone asks what you paid for them? You would probably say, “They cost around $50.”

We often round cents to dollars as we go about our lives. You may already have an idea of how to do this. For example, answer these questions.

  • About how much do your groceries cost each month?
  • About how much does it cost to fill a small car’s gas tank?

Look at your answers. The amount for groceries may be quite large. When you estimated your answer, how did you round the amount? For example, if your real monthly grocery bill was $481.73 you might have said $482 or perhaps $480.  Perhaps you even have estimated to the nearest hundred dollars and said, “About $500 a month for groceries.” All those estimates would be correct.

The amount for a tank of gas is less than a month’s groceries. How did you estimate?

For example, a small car may take $54.72 of gas.

If you estimated to the nearest dollar, you would say, “About $55.”

If you estimated to the nearest ten dollars, you would say, “About $50.”

If you rounded to the nearest dollar you would say, “54 dollars.”

We round a number in different ways depending on several things:

  • the size of the number we are rounding
  • what we are going to do with the number after we have rounded it off
  • our own convenience

Carefully review the place value for whole numbers.

Thousands Ones
Hundred thousands Ten thousands One thousand Hundreds Tens Ones Decimal

Rounding Whole Numbers

We round down if the digit to the right is less than 5. We round up if the digit to the right is 5 or more.

  • Rounding numbers gives an approximate amount; it is not an accurate figure.
  • Use a different form of the equal sign (≈) which means “approximate equality.”

Review: Rounding to the Nearest Ten

  • Underline the tens digit
  • Look at the digit in the ones place (to the right). You can put an arrow above it to help you find it later.
    • If the ones digit is 5 or more, round up. Write the ones digit as zero and increase the tens digit by one.
    • If the ones digit is less than 5, round down. The tens digit does not change and the ones digit is written as a zero.

Example A

 [latex]\begin{array}{r}\downarrow\\\underline{2}3\end{array}[/latex]

23 is rounded down to 20. The tens digit stays the same.

23 ≈ 20

Here’s another example:

Example B

[latex]\begin{array}{r}\downarrow\\2\underline{8}7\end{array}[/latex]

287 is rounded up to 290. Tthe tens digit increases by 1.

287 ≈ 290.

Exercise 1

Round each of the following to the nearest ten. Use the “approximate equality” sign ≈.

  1. 46 ≈ 50
  2. 111 ≈ 110
  3. 7 ≈
  4. 116 ≈
  5. 71 ≈
  6. 89 ≈
  7. 96 ≈
  8. 4 ≈
  9. 385 ≈
  10. 108 ≈
  11. 73 ≈
  12. 17 ≈
  13. 361 ≈
  14. 8 ≈
  15. 49 ≈
  16. 148 ≈

Answers to Exercise 1

  1. 50
  2. 110
  3. 10
  4. 120
  5. 70
  6. 90
  7. 100
  8. 0
  9. 390
  10. 110
  11. 70
  12. 20
  13. 360
  14. 10
  15. 50
  16. 150

Review: Rounding to the Nearest Hundred

  • Underline the hundreds digit.
  • Look at the digit in the tens place (to the right). You can put an arrow above it to help you find it later.
    • If the tens digit is 5 or more, round up. Write the tens and ones digit as zero and increase the hundreds digit by one.
    • If the tens digit is less than 5, round down. The hundreds digit does not change and the tens and ones digit is written as a zero.

Example C

 [latex]\begin{array}{c}\downarrow\\ \underline{4}73\end{array}[/latex]

473 is rounded up to 500.

473 ≈ 500

Round down if the tens digit is less than 5 and up if it is 5 or more:

  • 728 rounded to the nearest hundred is 700. (The tens digit is 2, which is less than 5, so the hundreds digit stays the same.)
  • 758 rounded to the nearest hundred is 800. (The tens digit is 5, which is five or more, so the hundreds digit increases by 1.)

Exercise 2

Round each of the following to the nearest HUNDRED. Use the “approximate equality” sign ≈.

  1. 330  ≈  300
  2. 908
  3. 2795
  4. 1260
  5. 742
  6. 127
  7. 302
  8. 945
  9. 865
  10. 275
  11. 590
  12. 1240
  13. 214
  14. 4450
  15. 98
  16. 996

Answers to Exercise 2

  1. 300
  2. 900
  3. 2800
  4. 1300
  5. 700
  6. 100
  7. 300
  8. 900
  9. 900
  10. 300
  11. 600
  12. 1200
  13. 200
  14. 4500
  15. 100
  16. 1000

Review: Rounding to the Nearest Thousand

  • Underline the thousands digit
  • Look at the digit in the hundreds place (to the right). You can put an arrow above it to help you find it later.
    • If the hundreds digit is 5 or more, round up. Write the hundreds, tens and ones digit as zero and increase the thousands digit by one.
    • If the hundreds digit is less than 5, round down. The thousands digit does not change and the hundreds, tens and ones digit is written as a zero.

Example D

[latex]\begin{array}{l}\hspace{0.5em}\downarrow\\ \underline{3}485\end{array}[/latex]

3485 is rounded down to 3000.

3485 ≈ 3000

Round down if the hundreds digit is less than 5 and round up if it is 5 or more:

  • 2109 rounded to the nearest thousand is 2000. (The hundreds digit is 1, which is less than 5.)
  • 2643 rounded to the nearest thousand is 3000. (The hundreds digit is 6, which is more than 5.)
  • 0940 rounded to the nearest thousand is 1000. (The hundreds digit is 9, which is more than 5, so the thousands digit increases from 0 to 1.)
  • 0465 rounded to the nearest thousand is 0. (The hundreds digit is 4, which is less than 5, so the thousands digit stays at 0.)

Exercise 3

Round each of the following to the nearest thousand. Use the “approximate equality” sign ≈.

  1. 1760  ≈  2000
  2. 6250
  3. 850         
  4. 320
  5. 5544
  6. 1234         
  7. 492
  8. 6199
  9. 9883
  10. 1045
  11. 7856
  12. 500
  13. 1780
  14. 495
  15. 9300
  16. 700
  17. 2449
  18. 5555
  19. 8914
  20. 85455
  21. 6475         

Answers to Exercise 3

  1. 2000
  2. 6000
  3. 1000
  4. 0
  5. 6000
  6. 1000
  7. 5000
  8. 6000
  9. 10000
  10. 1000
  11. 8000
  12. 1000
  13. 2000
  14. 0
  15. 9000
  16. 1000
  17. 2000
  18. 6000
  19. 9000
  20. 85000
  21. 6000

Rounding Decimals to Whole Numbers

Remember, decimals are part of the whole thing. We can round the decimal to the nearest whole number. Rounding to whole numbers means rounding off to the ones place.

When rounding to the whole number:

  • Underline the ones digit
  • Look at the digit in the thenths place (to the right). You can put an arrow above it to help you find it later.
    • If the tenths digit is 5 or more, round up. Increase the ones digit by one. Do not write a decimal or any decimal digits.
    • If the tenths digit is less than 5, round down. The ones digit does not change. Do not write a decimal or any decimal digits,

Example E

[latex]\begin{array}{l}\hspace{1.3em}\downarrow\\ 3\underline{7}.482\end{array}[/latex]

37.482 rounded to the nearest whole number is 37. (The tenths digit is 4, which is less than 5.)

37.482 ≈ 37

[latex]\begin{array}{l}\hspace{1.3em}\downarrow\\ 3\underline{7}.906\end{array}[/latex]

37.906  rounded to the nearest whole number is 38. (The tenths digit is 9, which is more than 5.)

37. 906 ≈ 38

Example F

  1. Round to a whole number.
    [latex]\begin{array}{l}\hspace{5.58em}\downarrow\\ 42.123\rightarrow4\underline{2}.123\approx42\end{array}[/latex]
  2. Round 960.802 to the nearest whole number.
    [latex]\begin{array}{l}\hspace{6.6em}\downarrow\\ 960.802\rightarrow96\underline{0}.802\approx961\end{array}[/latex]
  3. Round 39.5 to the nearest ones.
    [latex]\begin{array}{l}\hspace{4.6em}\downarrow\\ 39.5\rightarrow3\underline{9}.5\approx40\end{array}[/latex]

Zeros again –

You know that zeros at the end of a decimal do not change the value of the amount. You can add as many as you like.

But when a decimal has been rounded, drop any zeros after the place where you have rounded.

Instead of 39.52  ≈ 40.0, do 39.52 ≈ 40

Instead of 960.802 ≈ 961.000, do 960.802 ≈ 961

Exercise 4

Round each of the following to the nearest whole number. Use the “approximate equality” sign ≈.

  1. 11.3  ≈  11
  2. 2.679
  3. 403.8
  4. 7.6
  5. 65.91
  6. 22.2
  7. 3.76
  8. 9.2
  9. 1.7
  10. 0.6
  11. 2.63
  12. 5.09
  13. 19.8
  14. 2.1
  15. 0.7
  16. 74.2
  17. 3.61
  18. 12.3
  19. 34.5
  20. 17.82
  21. 2.45
  22. 1.792
  23. 2.01
  24. 5.55
  25. 10.3
  26. 9.9
  27. 8.15

Answers to Exercise 4

  1. 11
  2. 3
  3. 404
  4. 8
  5. 66
  6. 22
  7. 4
  8. 9
  9. 2
  10. 1
  11. 3
  12. 5
  13. 20
  14. 2
  15. 1
  16. 74
  17. 4
  18. 12
  19. 35
  20. 18
  21. 2
  22. 2
  23. 2
  24. 6
  25. 10
  26. 10
  27. 8

Important Information

If these exercises on rounding are becoming tiresome, please do not despair—there is a purpose. When you do operations (+ − × ÷) with decimals, you will often end up with answers in the ten-thousandths place when you really only need the accuracy of a tenth or a hundredth place decimal. If you do decimal operations on a calculator, you may end up with 6 decimal places (millionths)—not too practical if you are working with money and only want two decimal places! You will know how to round the answer to the decimal place you need for that question or situation.

Rounding Decimals to the Nearest Tenth

  • Underline the tenths place digit.
  • Look at the digit (to the right) in the hundredths place. You can put an arrow above it to help you find it later.
    • If the hundredths digit is less than 5, the tenths digit does not change and the hundredths digit (and all other decimals numbers after the hundredths) are not written at all.
    • If the hundredths digit is 5 or more, increase the tenths digit by one and write no more decimals in the hundredths spot or after.

Example G

Round to the nearest tenth.

  • [latex]\begin{array}{l}\hspace{6.2em}\downarrow\\13.432\rightarrow13.\underline{4}32\approx13.4\end{array}[/latex]
  • [latex]\begin{array}{l}\hspace{6.2em}\downarrow\\13.476\rightarrow13.\underline{4}76\approx13.5\end{array}[/latex]
  • [latex]\begin{array}{l}\hspace{5.1em}\downarrow\\0.263\rightarrow0.\underline{2}63\approx0.3\end{array}[/latex]
  • [latex]\begin{array}{l}\hspace{7.6em}\downarrow\\234.0399\rightarrow234.\underline{0}399\approx234.0\end{array}[/latex]
Keep the 0 because you have accurately rounded off to that zero. It is called a significant figure.

Exercise 5

Round each of the following to the nearest tenth.

  1. 4.23 ≈ 4.2
  2. 5.18
  3. 8.54
  4. 16.09
  5. 3.52
  6. 4.14  
  7. 6.24
  8. 1.76
  9. 1.74
  10. 7.19
  11. 2.15
  12. 1.44
  13. 3.172
  14. 9.99
  15. 5.09
  16. 4.111
  17. 6.046
  18. 0.71
  19. 3.63
  20. 9.45
  21. 12.36
  22. 202.305
  23. 2.66
  24. 9.492
  25. 7.388
  26. 5.249
  27. 2.45        

Answers to Exercise 5

  1. 4.2
  2. 5.2
  3. 8.5
  4. 16.1
  5. 3.5
  6. 4.1
  7. 6.2
  8. 1.8
  9. 1.7
  10. 7.2
  11. 2.2
  12. 1.4
  13. 3.2
  14. 10.0
  15. 5.1
  16. 4.1
  17. 6.0
  18. 0.7
  19. 3.6
  20. 9.5
  21. 12.4
  22. 202.3
  23. 2.7
  24. 9.5
  25. 7.4
  26. 5.2
  27. 2.5

Rounding Decimals to the Nearest Hundredth

Rounding decimals to the nearest hundredth is similar to rounding to the nearest tenth.

  • Underline the hundredths place digit.
  • Look at the digit (to the right) in the thousandths place. You can put an arrow above it to help you find it later.
    • If the thousandths digit is less than 5, the hundredths digit does not change and the thousandths digit (and all other decimals numbers after the hundredths) are not written at all.
    • If the thousandths digit is 5 or more, increase the hundredths digit by one and write no more decimals in the thousandths spot or after.

Example H

Round to the nearest hundredth.

[latex]\begin{array}{l}\hspace{7.1em}\downarrow\\35.4524\rightarrow35.4\underline{5}24\approx35.45\end{array}[/latex]

[latex]\begin{array}{l}\hspace{7.1em}\downarrow\\35.4567\rightarrow35.4\underline{5}67\approx35.46\end{array}[/latex]

[latex]\begin{array}{l}\hspace{7.1em}\downarrow\\47.9873\rightarrow47.9\underline{8}73\approx47.99\end{array}[/latex]

[latex]\begin{array}{l}\hspace{7.6em}\downarrow\\23.99609\rightarrow23.9\underline{9}609\approx24.00\end{array}[/latex]

Keep these zeros because you have accurately rounded off to them.
These zeros are significant.

Exercise 6

Round to the nearest hundredth. Keep significant zeros!

  1. 128.409 ≈ 128.41
  2. 0.909
  3. 98.024
  4. 3.001
  5. 76.3333
  6. 0.229
  7. 100.999
  8. 0.756

Answers to Exercise 6

  1. 128.41
  2. 0.91
  3. 98.02
  4. 3.00
  5. 76.33
  6. 0. 23
  7. 101.00
  8. 0.76

More Dollars and Cents

A cent is what fraction of a dollar?

Yes, a cent is [latex]\tfrac{1}{100}[/latex] of a dollar (one hundredth).

You may be asked to round amounts of money to the nearest cent. What you are actually doing is rounding to the nearest hundredth of a dollar.

  • [latex]\begin{array}{l}\hspace{2.3em}\downarrow\\\$3.2\underline{8}6\approx\$3.29\end{array}[/latex]
  • [latex]\begin{array}{l}\hspace{2.7em}\downarrow\\\$14.9\underline{2}3\approx\$14.92\end{array}[/latex]

one cent = one hundredth of a dollar

Exercise 7

Round to the nearest cent.

  1. $42.008 ≈ $42.01
  2. $ 0.233 ≈ $0.23
  3. $25.255
  4. $10.141
  5. $0.706
  6. $100.999
  7. $0.9834
  8. $2.8977

Answers to Exercise 7

  1. $42.01
  2. $0.23
  3. $25.26
  4. $10.14
  5. $0.71
  6. $101.00
  7. $0.98
  8. $2.90

Rounding Decimals to the Nearest Thousandth

Example  I

Round to the nearest thousandth (1000th).

2.0486 ⇒ 2.0486  ≈   2.049

Round to the nearest thousandth (1000th).

29.4324 ⇒ 29.4324 ≈ 29.432

Use rounded numbers to estimate answers in daily situations, in math problem solving, and to get an idea of the answer before you figure something out on a calculator. Numbers that are rounded off make calculations simpler.

Exercise 8

Round the following numbers as called for at the left of the chart.

  1. Round to the nearest tenth.
    1. 2.34 ≈ 2.3
    2. 3.75
    3. 1.028
  2. Round to the nearest thousandth.
    1. 0.1234
    2. 1.8032
    3. 7.0052
  3. Round to the nearest whole number.
    1. 21.1
    2. 2.7
    3. 12.05
  4. Round to the nearest hundred.
    1. 275
    2. 490
    3. 1260
  5. Round to the nearest hundredth.
    1. 1.732
    2. 2.466
    3. 3.074
  6. Round to the nearest ten.
    1. 68
    2. 32
    3. 824
  7. Round to the nearest thousandth.
    1. 0.7286
    2. 0.5027
    3. 1.2345

Answers to Exercise 8

  1. Round to the nearest tenth.
    1. 2.3
    2. 3.8
    3. 1.0
  2. Round to the nearest thousandth.
    1. 0.123
    2. 1.803
    3. 7.005
  3. Round to the nearest whole number.
    1. 21
    2. 3
    3. 12
  4. Round to the nearest hundred.
    1. 300
    2. 500
    3. 1300
  5. Round to the nearest hundredth.
    1. 1.73
    2. 2.47
    3. 3.07
  6. Round to the nearest ten.
    1. 70
    2. 30
    3. 820
  7. Round to the nearest thousandth.
    1. 0.729
    2. 0.503
    3. 1.235

Exercise 9

Round the numbers to estimate the answer. Circle the estimate that is the best answer.

  1. 47 × 52 ≈ 240, 2500 , 250, 2600
    Estimation: 50 × 50 = 2500
  2. 3.2 × 4.875 ≈ 6, 8, 15, 17
  3. 4149 ÷ 20 ≈ 2000, 200, 20, 230
  4. 2895 + 2895 ≈ 600, 6000, 4000, 5000
  5. 91 × 79 ≈ 720, 800, 8000, 80000
  6. 347 ÷ 50 ≈ 7, 70, 700, 8
  7. 4892 − 3012 ≈ 1500, 1000, 2000, 2500
  8. Nathan drives to Terrace and back once a week. He averages 286 km per week. Estimate how many kilometres he drives in one year (52 weeks).

Answers to Exercise 9

  1. 2500
  2. 15
  3. 200
  4. 6000
  5. 8000
  6. 7
  7. 2000
  8. 15000 km

Topic D: Self-Test

Mark /10     Aim 8/10

  1. Round to the nearest hundred. (2 marks)
    1. 749
    2. 691
  2. Round to the nearest whole number. (2 marks)
    1. 0.831
    2. 6.24
  3. Round to the nearest tenth. (2 marks)
    1. 8.29
    2. 6.533
  4. Round to the nearest hundredth. (2 marks)
    1. 34.792
    2. 6.459
  5. Round to the nearest thousandth. (2 marks)
    1. 5.4392
    2. 0.8208
  6. Estimate the answer. (2 marks)
    1. Mary baby-sat for her twin nephews for 6.75 hours on Saturday. She is paid $8.40 an hour. Estimate her earnings by rounding the numbers in the problem to whole numbers. Show how you worked out the estimate.

Answers to Topic H Self-Test

  1. Round to the nearest hundred. (2 marks)
    1. 700
    2. 700
  2. Round to the nearest whole number. (2 marks)
    1. 1
    2. 6
  3. Round to the nearest tenth. (2 marks)
    1. 8.3
    2. 6.5
  4. Round to the nearest hundredth. (2 marks)
    1. 34.79
    2. 6.46
  5. Round to the nearest thousandth. (2 marks)
    1. 5.439
    2. 0.821
  6. Estimate the answer. (2 marks)
    1. Estimation: 7 hours × $8 ≈ $56
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Adult Literacy Fundamental Mathematics: Book 4 - 2nd Edition Copyright © 2023 by Katherine Arendt; Mercedes de la Nuez; and Liz Girard is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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