__Objectives:__

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

- Identify decimal numbers between any two consecutive whole numbers.
- Know the decimal numbers that exist between any two consecutive decimals.
- Read and write decimals on a number line.
- Fill in gaps in decimal sequences by identifying and applying the rule.

Decimal number lines help to compute the set of decimals that lie within any two or more given numbers. The knowledge used in comparing and ordering decimals may be essential in this lesson.

**Let’s take a look at the number line below showing the set of decimals between 0 and 1.**

**Now let’s take a look at the set of decimals that exist between 5 and 5.1**

**Below are the set of decimals between 8 and 8.01**

- Considering number line A, there are nine (9) decimal numbers indicated between 0 and 1.
- There are also 9 decimal numbers indicated between 5 and 5.1 as shown on the number line B.
- There are 9 decimal numbers indicated between 8 and 8.01 as seen on the number line C.

On the first number line (A) above, 0.1, 0.2, 0.3 and 0.4 are nearer to 0 while 0.9, 0.8, 0.7 and 0.6 are nearer to 1.

We can therefore say that 0.5 is half way between 0 and 1 and therefore it is the mid-point.

A similar conclusion can be drawn for number lines B and C that 5.05 and 8.005 are their mid-points respectively.

__Decimal Number Sequences__

Decimal number sequences are a set of decimal numbers that graduate from one number to the next based on a particular pattern or rule. Decimal number sequences can be created or continued by counting in decimal steps. Let’s look at some examples below.

__Example 1__

0.3, 0.6, 0.9, 1.2…..

__Unit 10 Lesson 7: Exercise 1__

**What decimal number does each letter represent?**

a=6.5 b=7.9 c=9.1

d=9.8 e=4.17 f=4.31

g=4.46 h=29.32 i=29.46

j=29.66 k=29.78 l=78.7

m=79.3 n=80.1 o=82.9

p=2.308 q=2.322 r=2.345

s=0.006 t=0.039 u=11.999

v= 12.009 w= 8.0 y=39.93

z=9.110

d=9.8 e=4.17 f=4.31

g=4.46 h=29.32 i=29.46

j=29.66 k=29.78 l=78.7

m=79.3 n=80.1 o=82.9

p=2.308 q=2.322 r=2.345

s=0.006 t=0.039 u=11.999

v= 12.009 w= 8.0 y=39.93

z=9.110

__Unit 10 Lesson 7: Exercise 2__

**Write the next two terms in each sequence.**

**Fill in the blanks in these sequences.**

1) 2.32, 2.39 2) 8.97, 9.03

3) 0.48, 0.39 4) 8.69, 7.69

5) 4.346, 4.335 6) 0.020 and 0.030

7) 12.24 and 12.15 8) 40.98 and 42.00

9) 23.536 and 23.544 10) 5.432 and 5.426

3) 0.48, 0.39 4) 8.69, 7.69

5) 4.346, 4.335 6) 0.020 and 0.030

7) 12.24 and 12.15 8) 40.98 and 42.00

9) 23.536 and 23.544 10) 5.432 and 5.426

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