# Lesson Notes By Weeks and Term - Junior Secondary School 1

WHOLE NUMBERS

SUBJECT: MATHEMATICS

CLASS:� JSS 1

DATE:

TERM: 1st TERM

WEEK TWO

TOPIC: WHOLE NUMBERS

CONTENT

• Ordering Large Numbers
• Using Mixture of Digits and Words with Large Numbers
• Problems Solving in Quantitative Aptitude Reasoning (QR) using large numbers

Ordering Large Numbers

Any 2-digit number is larger than every unit number, e.g 11 is larger than 9. Any 3-digit number is larger than every 2-digit number;e.g 132 is greater than 86, and so on.

When a set of numbers are given, it is useful to rearrange the numbers in such a way that those that start in such a way that those that start with the same digit can be compared.

Example 1

Find the smallest and the largest number from the following set of numbers:

2 675 571, 3 498 567, 2 670 781, 3 497 859

Solution�

2� � 6 � � 7 � � 5� � � 5 � � 7 � 1

2� � 6� � � 7� � 0� � � 7� � � 8 � 1

3� � 4� � 9 � � 8� � 5� � 6 � � 7

3� � 4� � 9 � � 7� � 8� � 5 � � 9

The smallest number is 2 670 781 and the largest number is 3 498 567.

The numbers in the example above can also be arranged in order of size starting with the smallest as follows:

2 670 781,� 2 675 571,� 3 497 859,� 3 498 567

This arrangement is also called ascending order. The reverse is known as descending order.

Example 2

Arrange these numbers in order of size magnitude) starting with the smallest: 13456786, 24567432, 38479871, 24558011, 13498069, 38478817.

Solution

Always group large numbers in threes.

Arranging the numbers that start with 1 in order of size: 13 456 786, 13 498 069

Arranging the numbers that start with 2: 24 558 011, 24 567 432

Arranging the numbers that start with 3: 38 478 817, 38 479 871

Hence, arranging these numbers in order of magnitude gives:� 13 456 786, 13 498 069, 24 558 011, 24 567 432, 24 558 011, 24 567 432

EVALUATION

1. Arrange the following numbers in ascending order: 89728567, 89704567, 89693670, 89776909, 89735890.
2. Arrange the following numbers in descending order: 217679057, 497378939, 234656452, 21023404895, 2100998969.

Using Mixture of Digits and Words with Large Numbers

People often get confused when reading and writing large numbers. To avoid the confusion, the editors of newspapers use a combination of digits and words to show large numbers. For example, 1 million people, \$ 1.5 billion, N 3.6 trillion.

Some newspapers headlines are as follows:

• Unemployment soaring to 10.7 million
• HIV rose to an estimated 23 million in 2010
• Cost of ID rises to �10 billion in the UK.

Example 1�

Write these numbers as a mixture of digits and words:

1. �30 000 000� � � � (b) N75 000 000 000� � (c)� \$460 000 000 � (d)� �3 400 000 000 000

Solution

1. �30 000 000� =� �30 x 1 000 000

= �30 million

1. N 75 000 000 000 =� N 75 x 1 000 000 000

������������������������������= N 75 billion

1. \$460 000 000 = \$460 x 1 000 000

������������������������= \$460 million

1. �3 400 000 000 000 = �3.4 x 1 000 000 000 000

���������������������������������= �3.4 trillion

Example 2

Write the following numbers in digits

1. 3.6 million� � � (b) 234 billion

Solution

1. 3.6 million = 3.6 x 1 000 000

�������������������= 3 600 000

1. 234 billion = 2.75 x 1 000 000 000

�����������������= 2 750 000 000

Large Numbers (QR)

The S. I system of units is an internationally agreed method of measuring quantities such as length, mass, capacity and time.

Example 1.

Express the following in millimeter.

(a) 173 cm� (b) 5.9km��� � (c ) 200m

Solution

1. 173 cm to mm

Since 1cm = 10mm

�Then, 173cm = 173 x 10�

������������������������= 1 730mm

1. 5.9km to mm

1cm = 10mm, 100cm = 1m, 1000m� = 1km. Therefore, 1 000 000mm = 1 km

1. km = 5.9 x 1 000 000mm

�������������= 5 900 000 or 5.9 million(mm)

1. 200m to mm

1m = 1000mm

200m = 200 x 1 000mm

�����������= 200 000mm or 200 thousand (mm)

EVALUATION

1. Write these numbers in digits only and group the digits of your answers in threes.
1. \$312 billion � � (b) �0.85 trillion� (c) 212 million litres
1. Write these numbers as a mixture of digits and words: (a) 780 000 barrels� (b) 900 000 km (c) \$ 900 000 000
2. Change the following to the unit in brackets: (a) 5000kg (grams) � (b) 1250 litres ( mL)

1. Essential Mathematics for JSS1 by AJS Oluwasanmi page23-35.
2. New General Mathematics for JSS 1 by M. F Macrae et al pg 15-20.

WEEKEND ASSIGNMENT

1. What is the value of 1.2 km in metres? (a) 120m (b) 1 200m (c ) 12 000m� (d ) 120 000m
2. Which of the following numbers is the largest?(a) 727345565 (b) 727245565 (c)727445565� (d) 726778876.
3. \$114 million in digits only is� (a) \$1 200 000� (b) \$1 140 000� (c) \$1 250 000� (d) \$125 000
4. Le 5 600 000 in digits and words is� (a) Le 56 million (b) Le 5.6 billion � (c) Le 0.56 billion� (d) Le 5.6 million
5. 13 500 000mm in km is (a) 13.5 km� (b) 1.35 km� (c) 1350 km (d) 13500 km

THEORY

1. Write these numbers in digits only: (a) Le 0.5 billion� (b) \$ 9.1 million
2. Write down the missing number (QR):�
1. 100 987 331, 101 987 331, 102 987 331, __________, __________, 105 987 331
2. 980 231 680, 980 231 682, ________, 980 231 686, ____________, 980 231 690.��