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Basic 7 · Mathematics · Numeration Systems

Rounding Whole Numbers and Decimals

In this topic you will round whole numbers greater than one billion to the nearest ten, hundred, thousand, ten thousand and hundred thousand, decide when to round up or down in real life, and round decimals to the nearest tenth, hundredth and thousandth.

By the end of these notes you should be able to:

  • Round whole numbers to a given place value
  • Decide when to round up or down in real-life situations
  • Round decimals to the nearest tenth, hundredth and thousandth

What you already know

  • Place value of large numbers

Copy everything that has a blue line on its left into your notebook. The other parts are for reading.

Lesson 1

Strand
Number
Sub-strand
Numeration Systems
Indicator
B7.1.1.1.3 – Round (off up down) whole numbers more than 1,000,000,000 to the nearest hundred-thousand ten-thousands thousands hundreds and tens

Introduction

Newspapers often say "about 33 million people live in Ghana" instead of giving the exact number. Rounding gives a simpler number that is close to the real value.

1. The Rule for Rounding

  1. Find the digit in the place you are rounding to.
  2. Look at the digit immediately to its right.
  3. If that digit is 5 or more, add 1 to the rounding digit (round up).
  4. If it is less than 5, keep the rounding digit (round down).
  5. Replace all digits to the right with zeros.

2. Worked Examples

Round to the nearest thousand

Round 4,523,678 to the nearest thousand.

  1. Thousands digit: 3 (in 4,523,678).
  2. Digit to the right (hundreds): 6, which is 5 or more.
  3. Round up: 3 becomes 4.

Answer: 4,524,000

Round to the nearest hundred

Round 2,139,450,236 to the nearest hundred.

  1. Hundreds digit: 2.
  2. Digit to the right (tens): 3, which is less than 5.
  3. Round down: keep 2.

Answer: 2,139,450,200

A newspaper page with large numbers in headlines
Figure 1: Numbers in the news Copy two rounded numbers from a newspaper and suggest their exact values.

3. Rounding with a Number Line

A number line shows why we round. 4,523,678 lies between 4,523,000 and 4,524,000. The halfway point is 4,523,500. Since 4,523,678 is past the halfway point, it is closer to 4,524,000.

4. Rounding When the Digit Is 9

Round to the nearest ten

Round 1,999,997 to the nearest ten.

  1. Tens digit: 9; digit to the right: 7, so round up.
  2. 9 tens + 1 = 10 tens, so carry 1 to the hundreds, and so on.

Answer: 2,000,000

New words

rounding
Replacing a number with a simpler number close to it.
round up
Increase the rounding digit by 1.
round down
Keep the rounding digit the same.
halfway point
The middle value between two rounded numbers.

Summary

  • Look at the digit to the right of the rounding place: 5 or more rounds up, less than 5 rounds down.
  • Replace digits to the right of the rounding place with zeros.
  • A number line shows which rounded value is nearer.

Class activity: Rounding Race

  1. Each pair receives ten number cards.
  2. Round each number to the nearest ten, hundred and thousand.
  3. Check answers with another pair.

You need: Place-value cards, Ghana cedi play notes, Graph paper

Exercises

Answer in your exercise book first, then check your answers.

  1. 1. Round 3,476 to the nearest hundred.

    • A. 3,500
    • B. 3,400
    • C. 3,480
    • D. 4,000
    Show answer
    Answer: 3,500Tens digit 7.

  2. 2. Round 6,250,000,049 to the nearest hundred.

    • A. 6,250,000,000
    • B. 6,250,000,100
    • C. 6,250,000,050
    • D. 6,300,000,000
    Show answer
    Answer: 6,250,000,000Tens digit 4.

  3. 3. If the digit to the right is 5, we round up.

    • A. True
    • B. False
    Show answer
    Answer: True5 or more.

  4. 4. Rounding 7,349 to the nearest ten gives ______.

    Show answer
    Answer: 7,350Ones digit 9.

  5. 5. Round 8,654,321 to the nearest thousand.

    Show answer
    Answer: 8,654,000Hundreds digit 3.

  6. 6. Round 49,996 to the nearest ten and explain what happens.

    Show answer
    Answer: 50,000; rounding up the 9 tens makes 10 tens, which carries into the thousands and ten thousands.Carrying.

Lesson 2

Strand
Number
Sub-strand
Numeration Systems
Indicator
B7.1.1.1.3 – Round (off up down) whole numbers more than 1,000,000,000 to the nearest hundred-thousand ten-thousands thousands hundreds and tens

Introduction

Governments, businesses and journalists round very large numbers to the nearest ten thousand, hundred thousand or million to make them easy to understand.

1. Rounding to Ten Thousands and Hundred Thousands

Round to the nearest ten thousand

Round 3,872,615,904 to the nearest ten thousand.

  1. Ten-thousands digit: 1 (in 615,904, the 1).
  2. Digit to the right (thousands): 5, so round up.
  3. 1 becomes 2; replace the rest with zeros.

Answer: 3,872,620,000

Round to the nearest hundred thousand

Round 3,872,615,904 to the nearest hundred thousand.

  1. Hundred-thousands digit: 6.
  2. Digit to the right: 1, so round down.

Answer: 3,872,600,000

2. Rounding Up and Rounding Down in Real Life

In real life, the rule is sometimes replaced by common sense. If 1,250 learners must travel and each bus carries 50 learners, 1,250 ÷ 50 = 25 buses exactly. But if 1,260 learners travel, 1,260 ÷ 50 = 25.2, and we must round up to 26 buses, because no learner can be left behind. If each cake needs 3 eggs and you have 20 eggs, 20 ÷ 3 = 6.67, so you can only make 6 cakes: you round down.

A school bus parked at a school
Figure 2: School bus Write a problem in which you must round up the answer.

3. Estimation

Rounding helps us estimate answers quickly. To estimate 4,987 + 3,012, round each to the nearest thousand: 5,000 + 3,000 = 8,000. The exact answer, 7,999, is close to the estimate, so the calculation is reasonable. Estimating first helps you check whether your exact answer makes sense.

Rounding the same number
Round 2,746,385,512 to the nearestAnswer
ten2,746,385,510
hundred2,746,385,500
thousand2,746,386,000
ten thousand2,746,390,000
hundred thousand2,746,400,000

New words

estimate
A sensible approximate answer.
reasonable
Making sense in the situation.
round off
To round using the 5-or-more rule.
context
The real-life situation of a problem.

Summary

  • The same rule rounds numbers to ten thousands, hundred thousands and beyond.
  • In real life, decide whether to round up or down by thinking about the situation.
  • Rounding helps estimate answers and check calculations.

Class activity: Real-Life Rounding Problems

  1. Write two problems where the answer must be rounded up and two where it must be rounded down.
  2. Exchange with another group and solve.
  3. Explain why each answer was rounded that way.

You need: Place-value cards, Ghana cedi play notes, Graph paper

Exercises

Answer in your exercise book first, then check your answers.

  1. 1. Round 5,438,700 to the nearest hundred thousand.

    • A. 5,400,000
    • B. 5,500,000
    • C. 5,440,000
    • D. 5,000,000
    Show answer
    Answer: 5,400,000Ten-thousands digit 3.

  2. 2. 230 people need taxis that carry 4 passengers each. How many taxis are needed?

    • A. 58
    • B. 57
    • C. 57.5
    • D. 60
    Show answer
    Answer: 58Round up.

  3. 3. Estimation helps check whether an exact answer is reasonable.

    • A. True
    • B. False
    Show answer
    Answer: TrueCompare with the estimate.

  4. 4. A sensible approximate answer is an ______.

    Show answer
    Answer: estimateRough answer.

  5. 5. Round 9,876,543,210 to the nearest ten thousand.

    Show answer
    Answer: 9,876,540,000Thousands digit 3.

  6. 6. You have GH₵50 and each exercise book costs GH₵7. How many books can you buy? Explain.

    Show answer
    Answer: 7 books, because 50 ÷ 7 ≈ 7.1 and you cannot buy part of a book, so round down.Round down.

Lesson 3

Strand
Number
Sub-strand
Numeration Systems
Indicator
B7.1.1.1.4 – Round decimals to the nearest tenth hundredth thousandths etc

Introduction

Prices, measurements and sports times often have decimals. A sprinter's time of 10.537 seconds may be reported as 10.54 seconds. This is rounding decimals.

1. Decimal Place Value

Decimal places in 3.4728
Ones.TenthsHundredthsThousandthsTen-thousandths
3.4728

2. Rounding to the Nearest Tenth, Hundredth or Thousandth

Round to the nearest tenth

Round 3.4728 to the nearest tenth.

  1. Tenths digit: 4.
  2. Digit to the right (hundredths): 7, so round up.

Answer: 3.5

Round to the nearest hundredth

Round 3.4728 to the nearest hundredth.

  1. Hundredths digit: 7.
  2. Digit to the right (thousandths): 2, so round down.

Answer: 3.47

Round to the nearest thousandth

Round 3.4728 to the nearest thousandth.

  1. Thousandths digit: 2.
  2. Digit to the right: 8, so round up.

Answer: 3.473

A digital stopwatch showing a time with decimals
Figure 3: Stopwatch Round three race times to the nearest tenth of a second.

3. Do Not Add Zeros at the End

When rounding decimals, we drop the digits to the right instead of replacing them with zeros. Rounding 5.639 to the nearest tenth gives 5.6, not 5.600. However, if rounding gives a zero in the last place, keep it to show accuracy: 2.396 to the nearest hundredth is 2.40.

4. Rounding Money

Money in cedis and pesewas has two decimal places, because 100 pesewas make 1 cedi. If a calculation gives GH₵12.4567, round it to the nearest pesewa (hundredth): GH₵12.46.

5. Rounding Measurements

Measurements are often rounded. A length of 1.786 m measured with a ruler marked in centimetres would be recorded as 1.79 m, to the nearest hundredth of a metre. A mass of 2.3459 kg on a kitchen scale may be shown as 2.35 kg. Rounding to a sensible place keeps measurements useful without pretending to be more accurate than the instrument allows.

New words

decimal
A number with a decimal point, such as 3.47.
tenth
The first place after the decimal point.
hundredth
The second place after the decimal point.
pesewa
One hundredth of a cedi.

Summary

  • Round decimals using the digit to the right of the rounding place.
  • Drop digits to the right instead of writing zeros, but keep a final zero created by rounding.
  • Money is rounded to the nearest pesewa, which is two decimal places.

Class activity: Decimal Rounding Chart

  1. Write five decimals with four decimal places.
  2. Round each to the nearest tenth, hundredth and thousandth.
  3. Record your answers in a table.

You need: Decimal place-value chart, Digit-and-rounding cards, Graph paper

Exercises

Answer in your exercise book first, then check your answers.

  1. 1. Round 6.78 to the nearest tenth.

    • A. 6.8
    • B. 6.7
    • C. 7.0
    • D. 6.79
    Show answer
    Answer: 6.8Hundredths digit 8.

  2. 2. Round 0.4449 to the nearest thousandth.

    • A. 0.445
    • B. 0.444
    • C. 0.44
    • D. 0.4
    Show answer
    Answer: 0.445Ten-thousandths 9.

  3. 3. Rounding 4.25 to the nearest tenth gives 4.3.

    • A. True
    • B. False
    Show answer
    Answer: TrueDigit to the right is 5.

  4. 4. One hundredth of a cedi is one ______.

    Show answer
    Answer: pesewa100 pesewas = 1 cedi.

  5. 5. Round GH₵23.4561 to the nearest pesewa.

    Show answer
    Answer: GH₵23.46Two decimal places.

  6. 6. Round 7.996 to the nearest hundredth and explain why the answer has a zero.

    Show answer
    Answer: 8.00; rounding 99 hundredths up makes 100 hundredths, and the zeros show accuracy to two places.Carrying.

Homework

  1. Round the prices of five items in a shop to the nearest cedi and the nearest pesewa.
Rounding Whole Numbers and Decimals – Basic 7 Mathematics Notes | sirbus