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Basic 8 · Mathematics · Read and Write in Number Quantities

Numbers over a Billion and Skip Counting

In this topic you will apply place value to read and write number quantities over 1,000,000,000 and skip count forwards and backwards in 10,000s, 100,000s, 500,000s and other steps.

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

  • Read and write numbers over one billion, including trillions
  • Use numbers over a billion in real-life contexts
  • Skip count forwards and backwards in large steps

What you already know

  • Numbers beyond a billion (Basic 7)

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
Read and Write in Number Quantities
Indicator
B8.1.1.1.1 – Apply the understanding of place value to read and write in number quantities over 1,000,000,000

Introduction

National budgets, world population and distances in space need numbers far bigger than a billion. Place value lets us handle them with ease.

1. The Trillions Period

Place-value periods
TrillionsBillionsMillionsThousandsOnes
2345607089120

The number 2,345,607,089,120 is read as "two trillion, three hundred and forty-five billion, six hundred and seven million, eighty-nine thousand, one hundred and twenty". One trillion is one thousand billion, or 1,000,000,000,000, which is 10¹².

2. Writing Numbers from Words

Write in figures

Write "four trillion, twenty billion, five million, six hundred" in figures.

  1. Trillions: 4.
  2. Billions: 020.
  3. Millions: 005.
  4. Thousands: 000.
  5. Ones: 600.

Answer: 4,020,005,000,600

3. Spaces and Commas

Large numbers may be grouped with commas or with thin spaces, as in 4 020 005 000 600. Both show the same number. Never put a comma inside a period. Reading from the left, say each period and its name, and do not say "and" after every group.

A newspaper headline about the national budget
Figure 1: Numbers in the news Find a number over one billion in the news and write it in words.

4. Value of Digits

Each place is ten times the place to its right. In 7,777,777,777,777, every digit is 7, but the first 7 is worth 7 trillion and the last is worth only 7. This shows the power of place value.

5. Common Errors

Learners often forget the zeros that hold empty places. "Five billion and seven" is 5,000,000,007, not 5,007. Write three digits in every period except the first one. Another error is mixing up "million" and "billion" when reading. Say the period name slowly, and check the number of commas: one comma for thousands, two for millions, three for billions and four for trillions.

New words

trillion
One thousand billion.
period
A group of three digits.
digit
One of the symbols 0 to 9.
place value
The value of a digit's position.

Summary

  • One trillion is 1,000,000,000,000 or 10¹².
  • Read and write large numbers period by period.
  • Each place is ten times the place to its right.

Class activity: Number Dictation

  1. One partner reads out a number over one billion.
  2. The other writes it in figures.
  3. Swap roles and check using place-value cards.

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

Exercises

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

  1. 1. How many zeros are in one trillion?

    • A. 12
    • B. 9
    • C. 6
    • D. 15
    Show answer
    Answer: 1210¹².

  2. 2. 3,000,040,000,000 is…

    • A. three trillion, forty million
    • B. three trillion, forty billion
    • C. three billion, forty million
    • D. thirty trillion
    Show answer
    Answer: three trillion, forty millionPeriods.

  3. 3. One trillion is one thousand billion.

    • A. True
    • B. False
    Show answer
    Answer: True1,000 × 10⁹.

  4. 4. One trillion written as a power of ten is 10 to the power ______.

    Show answer
    Answer: 1210¹².

  5. 5. Write in figures: "six billion, three hundred million and ten".

    Show answer
    Answer: 6,300,000,010Periods.

  6. 6. Write the value of the digit 5 in 2,516,000,000,000.

    Show answer
    Answer: 500,000,000,000Hundred billions.

Lesson 2

Strand
Number
Sub-strand
Read and Write in Number Quantities
Indicator
B8.1.1.1.1 – Apply the understanding of place value to read and write in number quantities over 1,000,000,000

Introduction

Governments, companies and scientists use very large numbers every day. Understanding them helps us to follow the news and think clearly about the world.

1. Where Large Numbers Appear

Large numbers in context
ContextExample
national budgetbillions of cedis of government spending
populationAfrica has more than one billion people
distancethe Sun is about 150,000,000 km from Earth
technologya 1 TB drive holds about 1,000,000,000,000 bytes
mobile moneybillions of cedis transferred each year

2. Expanded Form

Write in expanded form

Write 8,050,300,000 in expanded form using powers of ten.

  1. 8 billions = 8 × 10⁹.
  2. 5 ten-millions = 5 × 10⁷.
  3. 3 hundred-thousands = 3 × 10⁵.

Answer: (8 × 10⁹) + (5 × 10⁷) + (3 × 10⁵)

3. Making Sense of Size

It is hard to imagine a billion. If you counted one number every second without stopping, reaching one million would take about 11.5 days, but reaching one billion would take about 31.7 years. Reaching one trillion would take more than 31,000 years. These comparisons show how much bigger each period is.

A large crowd in a stadium
Figure 2: A big crowd Estimate how many stadiums of 40,000 people would hold one million people.

4. Reading Numbers in Words and Figures Together

News reports often mix words and figures, as in "GH₵3.5 billion". To write this in full, multiply: 3.5 × 1,000,000,000 = 3,500,000,000. Similarly, "2.4 million" means 2,400,000. Knowing this helps you read budgets, reports and adverts correctly.

5. Comparing Sizes with Ratios

We can compare large numbers by dividing. One billion is one thousand times one million, because 1,000,000,000 ÷ 1,000,000 = 1,000. So a project costing GH₵1 billion costs as much as one thousand projects of GH₵1 million each. Thinking in this way helps you to judge news reports about large sums.

New words

expanded form
A number written as a sum of place values.
budget
A plan of income and spending.
context
The real situation of a problem.
transaction
An exchange of money.

Summary

  • Large numbers appear in budgets, population, distance and technology.
  • Expanded form with powers of ten shows the value of digits.
  • Figures such as 3.5 billion can be written in full by multiplying.

Class activity: Big Number Hunt

  1. Find large numbers in newspapers or on the internet.
  2. Write each in figures and in expanded form.
  3. Present the largest number found and explain what it measures.

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

Exercises

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

  1. 1. 2.4 million in figures is…

    • A. 2,400,000
    • B. 240,000
    • C. 24,000,000
    • D. 2,040,000
    Show answer
    Answer: 2,400,000× 1,000,000.

  2. 2. GH₵1.2 billion is…

    • A. GH₵1,200,000,000
    • B. GH₵120,000,000
    • C. GH₵12,000,000
    • D. GH₵1,020,000,000
    Show answer
    Answer: GH₵1,200,000,000× 10⁹.

  3. 3. The Sun is about 150,000,000 km from Earth.

    • A. True
    • B. False
    Show answer
    Answer: TrueApproximate.

  4. 4. A plan of income and spending is a ______.

    Show answer
    Answer: budgetMoney plan.

  5. 5. Write 3,040,000,000 in expanded form.

    Show answer
    Answer: (3 × 10⁹) + (4 × 10⁷)Powers of ten.

  6. 6. How many days would it take to count to one million at one number per second?

    Show answer
    Answer: About 11.6 days (1,000,000 ÷ 86,400).Division.

Lesson 3

Strand
Number
Sub-strand
Read and Write in Number Quantities
Indicator
B8.1.1.1.2 – Skip count forwards and backwards in 10,000s, 100,000s, 500,000s etc

Introduction

Skip counting means counting in equal jumps. It builds your sense of number and helps with mental calculation.

1. Skip Counting Forwards

Skip counting forwards
StepSequence
10,000340,000; 350,000; 360,000; 370,000
100,0002,700,000; 2,800,000; 2,900,000; 3,000,000
500,0004,500,000; 5,000,000; 5,500,000; 6,000,000
250,0001,250,000; 1,500,000; 1,750,000; 2,000,000

2. Skip Counting Backwards

Count backwards

Count back in 100,000s from 1,250,000 for four steps.

  1. 1,250,000 − 100,000 = 1,150,000.
  2. 1,150,000 − 100,000 = 1,050,000.
  3. 1,050,000 − 100,000 = 950,000.
  4. 950,000 − 100,000 = 850,000.

Answer: 1,150,000; 1,050,000; 950,000; 850,000

3. Finding the Rule

To find the step in a sequence, subtract one term from the next. In 6,500,000; 6,000,000; 5,500,000, the difference is −500,000, so the rule is "subtract 500,000". Check with another pair of terms to be sure.

Bundles of cedi notes being counted
Figure 3: Counting money Write a sequence in steps of 250,000 starting from 500,000.

4. Using a Number Line

A number line shows skip counting as jumps of equal length. Mark the start and draw arcs for each jump. This helps when crossing a boundary, such as moving from 980,000 to 1,010,000 in steps of 10,000: 980,000; 990,000; 1,000,000; 1,010,000. Watch carefully when the digit in a higher place changes.

5. Skip Counting and Multiples

Skip counting is closely linked to multiplication. Counting in 500,000s gives the multiples of 500,000: 1 × 500,000, 2 × 500,000 and so on. So the tenth term starting from 500,000 is 10 × 500,000 = 5,000,000. Using this link, you can find a term without writing out the whole sequence. Skip counting also helps with money: 40 bundles of GH₵50,000 can be counted quickly as 2,000,000.

New words

skip counting
Counting in equal jumps.
sequence
An ordered list of numbers following a rule.
term
One number in a sequence.
difference
The result of subtracting one number from another.

Summary

  • Skip counting moves forwards or backwards in equal steps.
  • Find the rule by subtracting one term from the next.
  • A number line helps when crossing a place-value boundary.

Class activity: Skip Count Circle

  1. Sit in a circle and count in 10,000s, then 100,000s, then 500,000s.
  2. Count backwards from a large number.
  3. Find the rule of sequences written by the teacher.

You need: Printed multiples-of-ten-thousand cards, Place-value chart, Bottle-top counters

Exercises

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

  1. 1. The next term in 200,000; 300,000; 400,000 is…

    • A. 500,000
    • B. 410,000
    • C. 600,000
    • D. 450,000
    Show answer
    Answer: 500,000Add 100,000.

  2. 2. Find the missing term: 3,000,000; 2,500,000; ___; 1,500,000.

    • A. 2,000,000
    • B. 1,750,000
    • C. 2,250,000
    • D. 1,000,000
    Show answer
    Answer: 2,000,000Subtract 500,000.

  3. 3. Skip counting uses equal jumps.

    • A. True
    • B. False
    Show answer
    Answer: TrueEqual steps.

  4. 4. One number in a sequence is a ______.

    Show answer
    Answer: termSequence.

  5. 5. Count in 250,000s from 750,000 for four terms.

    Show answer
    Answer: 1,000,000; 1,250,000; 1,500,000; 1,750,000Add 250,000.

  6. 6. State the rule of 7,800,000; 7,700,000; 7,600,000 and find the next two terms.

    Show answer
    Answer: Subtract 100,000; 7,500,000 and 7,400,000.Rule.

Homework

  1. Write five numbers over one billion in words and figures.
  2. Write three sequences in steps of 10,000, 100,000 and 500,000.
Numbers over a Billion and Skip Counting – Basic 8 Mathematics Notes | sirbus