Counting, Reading and Writing Whole Numbers to Trillions for JSS 1

Whole Numbers

Performance Objectives

By the end of the lesson, students should be able to:

1. count, read and write numbers in millions and billions;
2. count and write numbers in trillions;
3. apply the counting, reading and writing of large numbers in everyday life;
4. solve problems on quantitative aptitude tasks involving large numbers.

Introduction to Large Numbers and Place Value

Whole numbers are the set of numbers starting from zero and continuing indefinitely without any fractional or decimal parts.

In everyday transactions, scientific measurements and national planning, very large quantities are encountered. To handle these large quantities, the decimal system of numeration is used. This system is based on place value, where the position of a digit determines its actual value. As one moves from right to left in a number, the value of each place increases by a factor of ten.

To make reading and writing large numbers easier, digits are grouped into periods of three, starting from the right. Each period is separated by a comma. The primary periods used for large whole numbers are Units, Thousands, Millions, Billions and Trillions.

The relationship between these periods is based on powers of ten:

1. One Thousand is represented as $1,000$ (one followed by three zeros).
2. One Million is one thousand thousands, represented as $1,000,000$ (one followed by six zeros).
3. One Billion is one thousand millions, represented as $1,000,000,000$ (one followed by nine zeros).
4. One Trillion is one thousand billions, represented as $1,000,000,000,000$ (one followed by twelve zeros).

The place value chart below illustrates the structure of large numbers up to the trillions period. Each period is subdivided into Hundreds (H), Tens (T) and Units (U).

Counting, Reading and Writing Numbers in Millions and Billions

Counting in millions and billions involves understanding how to transition from one period to the next. After reaching $999,999$ (nine hundred and ninety-nine thousand, nine hundred and ninety-nine), adding $1$ results in $1,000,000$ (one million). Similarly, after reaching $999,999,999$, adding $1$ results in $1,000,000,000$ (one billion).

To read a large number, start from the left and read each three-digit group as if it were a three-digit number, then state the name of the period (except for the units period at the end).

To write a large number in figures from words, write the digits for each period in order, inserting commas to separate the periods. If a period is missing certain place values, use zeros as placeholders to maintain the correct positions.

Worked Examples

Example 1: Write the number $45,208,315$ in words.

To solve this, identify the digits in each period:

1. The millions period contains $45$ (forty-five).
2. The thousands period contains $208$ (two hundred and eight).
3. The units period contains $315$ (three hundred and fifteen).

Combining these periods gives: Forty-five million, two hundred and eight thousand, three hundred and fifteen.

Example 2: Write the number $3,005,420,000$ in words.

Identify the digits in each period:

1. The billions period contains $3$ (three).
2. The millions period contains $005$ (five).
3. The thousands period contains $420$ (four hundred and twenty).
4. The units period contains $000$ (zero, which is not read).

Combining these periods gives: Three billion, five million, four hundred and twenty thousand.

Example 3: Write the following number in figures: “Twelve billion, seventy-five million, four hundred thousand and ten”.

Represent each period with three digits (except the leftmost period which can have fewer):

1. Twelve billion is written as $12$ in the billions period.
2. Seventy-five million is written as $075$ in the millions period (using a zero placeholder).
3. Four hundred thousand is written as $400$ in the thousands period.
4. Ten is written as $010$ in the units period (using a zero placeholder).

Combining the periods with commas gives: $12,075,400,010$.

Counting, Reading and Writing Numbers in Trillions

The trillions period is the next higher period after billions. One trillion ($1,000,000,000,000$) is a thousand times larger than one billion. Counting in trillions follows the same systematic rules of place value and period grouping.

Worked Examples

Example 1: Write the number $5,200,450,000,000$ in words.

Identify the digits in each period from left to right:

1. The trillions period contains $5$ (five).
2. The billions period contains $200$ (two hundred).
3. The millions period contains $450$ (four hundred and fifty).
4. The thousands period contains $000$ (no thousands).
5. The units period contains $000$ (no units).

Combining these periods gives: Five trillion, two hundred billion, four hundred and fifty million.

Example 2: Write the following number in figures: “Sixty-four trillion, eight hundred billion, five million and six”.

Represent each period with three digits:

1. Sixty-four trillion is written as $64$ in the trillions period.
2. Eight hundred billion is written as $800$ in the billions period.
3. Five million is written as $005$ in the millions period.
4. There are no thousands, so write $000$ in the thousands period.
5. Six is written as $006$ in the units period.

Combining the periods with commas gives: $64,800,005,000,006$.

Example 3: Find the place value of the digit $7$ in the number $7,305,120,800,000$.

Identify the position of the digit $7$ using the place value chart:

1. The number is grouped into units, thousands, millions, billions and trillions.
2. The digit $7$ is in the units column of the trillions period.

Therefore, the place value of $7$ is $7\text{ trillion}$ or $7,000,000,000,000$.

Real-Life Applications of Large Numbers

Large numbers are used to describe real-world quantities that affect society, national development and scientific discoveries. Understanding how to read and write these numbers is essential for interpreting financial, demographic and scientific data.

Common real-life applications include:

1. National Budgets: Governments plan their annual spending in trillions of Naira. For instance, a national budget might be written as $\text{₦}27,500,000,000,000$ (twenty-seven trillion, five hundred billion Naira).
2. Population Census: The population of the world is over $8,000,000,000$ (eight billion) people. Individual countries like Nigeria have populations exceeding $200,000,000$ (two hundred million) people.
3. Astronomy: Distances in space are extremely large. For example, a light-year (the distance light travels in one year) is approximately $9,460,000,000,000\text{ kilometres}$ (nine trillion, four hundred and sixty billion kilometres).
4. Corporate Revenue: Large multinational companies and banks report their annual earnings and assets in billions or trillions of Naira.

Worked Examples

Example 1: A country’s revenue for a particular year is estimated at fifteen trillion, eight hundred and sixty billion Naira. Write this amount in figures with the currency symbol ($\text{₦}$).

Break down the verbal description into periods:

1. Trillions period: $15$
2. Billions period: $860$
3. Millions period: $000$
4. Thousands period: $000$
5. Units period: $000$

Combining these gives: $\text{₦}15,860,000,000,000$.

Example 2: The population of three African countries are $220,000,000$, $45,000,000$ and $115,000,000$. Find the total population of the three countries and write the answer in words.

First, perform the addition of the numbers:

$$220,000,000 + 45,000,000 + 115,000,000 = 380,000,000$$

Next, convert the sum into words:

The number $380,000,000$ has $380$ in the millions period and zeros in all other periods. Therefore, the total population in words is: Three hundred and eighty million.

Quantitative Aptitude Tasks Involving Large Numbers

Quantitative aptitude tasks test the ability to identify patterns, apply logical reasoning and perform operations on large numbers. These tasks often use symbols, shapes or sequences to represent mathematical relationships.

Worked Examples

Example 1: Study the pattern below and find the missing number.

The sequence of numbers is:

$$5,000 \rightarrow 5,000,000 \rightarrow 5,000,000,000 \rightarrow \text{?}$$

To solve this, analyze the relationship between consecutive terms:

1. The first term is $5,000$ (five thousand).
2. The second term is $5,000,000$ (five million), which is $5,000 \times 1,000$.
3. The third term is $5,000,000,000$ (five billion), which is $5,000,000 \times 1,000$.

The pattern shows that each term is multiplied by $1,000$ to get the next term. Therefore, the missing term is:

$$5,000,000,000 \times 1,000 = 5,000,000,000,000$$

The missing number is $5,000,000,000,000$ (five trillion).

Example 2: In a quantitative aptitude game, the symbol $\otimes$ represents the operation: multiply the number by one million ($1,000,000$). Find the value of $450 \otimes$.

Apply the defined operation to the given number:

$$450 \otimes = 450 \times 1,000,000$$
$$450 \otimes = 450,000,000$$

The value is $450,000,000$ (four hundred and fifty million).

Example 3: Study the relationship in the diagram below and find the value of $x$.

To find the value of $x$, analyze the mathematical relationship shown in the diagram:

The product of the numbers in the outer circles equals the number in the central circle.

$$3,000 \times 1,000,000 \times x = 3,000,000,000$$

First, multiply the two known outer numbers:

$$3,000 \times 1,000,000 = 3,000,000,000$$

Now, substitute this back into the equation:

$$3,000,000,000 \times x = 3,000,000,000$$

Divide both sides by $3,000,000,000$ to solve for $x$:

$$x = \frac{3,000,000,000}{3,000,000,000}$$
$$x = 1$$

The value of $x$ is $1$.

Exercises

Section A: Multiple Choice Questions

Choose the correct option for each of the following questions:

1. What is the place value of the digit $8$ in the number $48,500,210,000$?
   1. Eight hundred million
   2. Eight billion
   3. Eighty billion
   4. Eight trillion
2. Which of the following represents the number “Two trillion, forty billion and five hundred” in figures?
   1. $2,040,000,000,500$
   2. $2,400,000,000,500$
   3. $2,040,000,500,000$
   4. $2,004,000,000,500$
3. How many zeros are there in one billion?
   1. $6$
   2. $9$
   3. $12$
   4. $15$
4. A state government generated a revenue of $\text{₦}125,000,000,000$ in a year. Write this amount in words.
   1. One hundred and twenty-five million Naira
   2. One hundred and twenty-five billion Naira
   3. Twelve billion, five hundred million Naira
   4. One trillion, twenty-five billion Naira
5. Complete the pattern: $700,000 \rightarrow 700,000,000 \rightarrow \text{?}$
   1. $700,000,000,000$
   2. $700,000,000,000,000$
   3. $7,000,000,000$
   4. $70,000,000,000$

Section B: Essay and Theory Questions

Solve the following problems, showing all workings clearly:

1. Write the following numbers in words:
   1. $805,400,120$
   2. $12,003,950,000$
   3. $6,500,000,000,000$
2. Write the following numbers in figures, using commas correctly:
   1. Nine hundred and twelve billion, forty-five million, two hundred thousand and eight.
   2. Thirty-one trillion, six hundred million and fifty.
   3. Four hundred and five billion, eight thousand.
3. The federal government of a country allocated $\text{₦}8,400,000,000,000$ for education and $\text{₦}5,200,000,000,000$ for health.
   1. Find the total allocation for both sectors in figures.
   2. Write the total allocation in words.
4. If the symbol $\oplus$ means “multiply the number by one billion ($1,000,000,000$)”, find the value of:
   1. $15 \oplus$
   2. $0.5 \oplus$