# Lesson 8 – Decimal Number Lines And Sequences

Objectives:

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

a) Know the set of decimal numbers that exist between any two consecutive whole numbers.

b) Know the set of decimal numbers that exist between any two consecutive decimal numbers.

c) Read and write decimals on a line.

d) Fill in the gaps in decimal sequences by identifying and applying the rule.

Decimal number lines are number lines that helps us to figure out the set of decimals that lies within given numbers. Here’s a part of the number line (1 to 2). Between 1 and 2, there are nine (9) other decimal numbers as shown on the number line.

Now, lets look at the set decimal that lie between 1 and 1.1 Between 1 and 1.1, there are also nine (9) other decimal numbers as shown on the number line.

There are nine (9) other decimal numbers between 1 and 1.0 as shown below. Considering number line A; 1.1, 1.2, 1.2, AND 1.4 are nearest to 1 whole 1.9, 1.8, 1.7 and 1.6 are nearer to 2.

It can therefore be said that the 1.5 is the half-way between 1 and 2.

A similar thing can be said about number lines B and C; hence, 1.05 and 1.005 are mid-point (half-way) on B and C respectively.

Decimal Number Sequences

Decimal number sequences are a set of decimal numbers that graduate (move) from one number to the next number based on a particular pattern. The pattern is known as the rule of sequence.

Decimal number sequences can be continued by counting in decimal steps.

Lets look at some examples.

Example;

a) 0.2, 0.4, 0.6, 0.8.

In the sequence above, the difference between the first two decimal numbers is 0.2. The same difference can be seen in any two consecutive numbers in the sequence. It is evident that the decimal number increases from smaller to bigger. Hence, the rule is +0.2. You may also count in .02s to complete the sequence.

b) 8.0, 7.5, 7.0, 6.5, 6.0, 5.5….

In this sequence, the first thing we realise is that the decimal numbers reduce as you move towards the right-hand side.

There is a difference of 0.5 between and number and the number next to it.

We can therefore say that the rule is -0.5 or counting backwards in 0.5.

c) 6.2, 7.2, 8.2, 9.2,

The rule is +1 or counting on in decimal 10. From 6.2

Unit 10 Lesson 8: Exercise 1

Complete the number line below.     Unit 10 Lesson 8: Exercise 2

Fill in the blanks in the sequences below.

1. 5, 3.0, 3.5, ………, ………., ………
2. 3, 4.6, 4.9, 5.2, ………, ………, ………
3.  0, 5.4, 4.8, 4.2, ………, ………, ………
4. 9, 8.2, 8.5, ………, ………, ………
5. 6, 13.6, 12.6, ………, ………, ………
6. 4, 0.8, 1.2, ………, ………, ………
7. 7, 5.4, 5.1, 4.8, ………, ………., ………
8. 02, 3.05, 3.08, ………, ………, ………
9. 4, 12.08, 12.12, ………., ………, ………
10. 2, 37.9, 37.6, ………, ………, ………

(1) 2.5, 3.0, 3.5, 4.0, 4.5, 5.0
(2) 4.3, 4.6, 4.9,5.2, 5.5, 5.8, 6.1
(3) 6.0, 5.4, 4.8, 4.2, 3.6, 3.0, 2.4
(4) 7.9, 8.2, 8.5, 8.8, 9.1, 9.4
(5) 14.6, 13.6, 12.6, 11.6, 10.6, 9.6
(6) 0.4, 0.8, 1.2, 1.5, 2.0, 2.4
(7) 5.7, 5.4, 5.1, 4.8, 4.5, 4.2, 3.9
(8) 3.02, 3.05, 3.08, 3.11, 3.14, 3.17
(9) 1204, 12.08, 12.12, 12.16, 12.20, 12.24
(10) 38.32, 37.9, 37.6, 37.3, 3.7.0, 36.4

Unit 10 Lesson 8: Exercise 3

What the letters represent in the number line? Write down the missing numbers in each sequence.

6) 2, 2.4, 3.6, ………, 6.0, 7.2, ………

7) 12, 5.15, ………, 5.21, ………, ………

8) 472, 12.475, ………, ………, ……..

9) ………, 6.35, 6.35, 6.47, ………, 6.71, ……..

10) ………, ………, 8.74, 8.94, 9.14, ………

(1) a=4.9   b=5.4   c=6.2
(2) d=6.9   e=7.7   f=8.4
(3) g=3.05   h=3.09   i=3.1
(4) j=8.12   k=8.23
(5) l=25.004   m=25.009   n=25.012
(6) 1.2, 2.4, 3.6, 4.8, 6.0, 7.2, 8.4,
(7) 5.12, 5.15, 5.18, 5.21, 5.24, 5.27
(8) 12.472, 12.475, 12.478, 12.481, 12.484
(9) 3.23, 6.35, 6.47, 6.59, 6.71, 6.83
(10) 8.34, 8.54, 8.74, 8.94, 9.14, 9.34

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