__Objective__

At the end of this lesson, students should know and understand the place value and value of decimal numbers.

__Decimal Vocabulary__

**Decimal/Decimal number**: – Is a number that represents a whole number and part of a whole by separating them with a point.**Decimal point**: – Is a point separating the ones and tenths place in a decimal number.**Ones**: – Is the place value of the digit on the immediate left hand side of the decimal point.**Tenth**: – Is the first digit on the immediate right hand side of the decimal point. It is the first decimal place and represents parts out of 10 equal parts. (**E.g.0.8 means 8 parts out of 10, i.e. )****Hundredth**: – Is the second number on the right hand side of the decimal point. It represents parts out of 100 equal parts. (**E.g. 0.03 means 3 parts out of 100, i.e. )****Thousandth**: – Is the third number on the right hand side of the decimal point. It represents parts out of 1000 equal parts. (**E.g. 0.007 represents 7 parts out of 1000, i.e. )****Ten thousandth**: – Is the fourth number on the right hand side of the decimal point. It represents parts out of 10,000 equal parts. (**E.g. 0.0002 means 2 parts out of 10000, i.e. )****Decimal place**: – Is the number of digits after the decimal point.

The decimal point separates the whole number from the fraction part of a decimal number.

In the diagram shown above, the whole number is 5,638,742. The lowest place value of the whole numbers is the units. Hence, from right to left (on the left hand side of the decimal point) we have: units, tens, hundreds, thousands, ten thousands, hundred thousand millions.

The fraction part of the decimal number lies on the right hand side of the decimal point. The highest place value of the fraction part or decimal is the tenth and it reduces towards the far right as follows: tenth, hundredth, thousandth, ten thousandth etc. as shown in the illustration above.

__Example 1__

**What is the place value and value of the underlined digits in the decimal numbers below?**

(a) 14.__2__04 (b) 849.91__6__ (c) 14__7__6.8

(d) 0.1__4__36 (e) 532.753__9__ (f) 4__8__.231

__Solution__

__Example 2__

**What is the total value of the underlined digits?**

(a) 53__.____2__ (b) 6__4__.8__5__ (c) __6__8__9__3.2638

__Solution__

(a) __5__3__.____2__

=5 tens and 2 tenths

=50 + 0.2

=50.2

(b) 6__4__.8__5__

=4 units and 5 hundredths

=4 + 0.05

=4.05

__(c) 6__8__9__2638

= 6 thousands and 9 tens

=6000 + 90

=6090

** **

**The knowledge of decimal place value and value can be applied when illustrating decimals on an Abacus or Notation Board.**

**NB: The decimal point always comes between the units and tenths.**

__Notation Board__

The Notation Board is similar to the Abacus.

__Unit 10 Lesson 3: Exercise 1__

**Write the place value and value of the underlined digits.**

- 7.
__9__2 __6__.344- 684
__7__ - 56.2
__3__ - 62
__5__ - 2
__8__9.9327 - 71
__0__5 __3__98.73- 068
__1__ - 9.0
__2__37 - 1
__4__57 __8__411630.45- 70
__6__4 - 5163.
__8__15 __2__05- 8.37
__4__9 - 1
__1__81 - 1.7
__1__08 - 2
__3__27 - 3
__5__81267.89

__Unit 10 Lesson 3: Exercise 2__

**Find the total value of the underlined digits in each of the decimals below.**

- 42
__6__.__2__8 __7__8__.____5__2- 5
__0__.74__6__ - 2
__9__8__4__ - 1
__4__.28__7__9 - 56.3
__9__4__7__ __1__34__8__- 429.14
__72__ - 5
__4__0__8__ - 4
__2__2.60__8__3

1) 6.2 2) 70.5

3) 0.006 4) 90.04

5) 4.007 6) 0.0907

7) 1000.008 8) 0.0072

9) 0.0408 10) 20.008

3) 0.006 4) 90.04

5) 4.007 6) 0.0907

7) 1000.008 8) 0.0072

9) 0.0408 10) 20.008

__Unit 10 Lesson 3: Exercise 3__

**Write the decimals illustrated on these notation boards.**

**Make abacus pictures to illustrate these decimal numbers.**

5) 47.2

6) 2463.38

7) 32.608

8) 9.6347

9) 15.008

10) 710.0235

1) 73.15 2) 4.2613

3) 905.01 4) 106.245

3) 905.01 4) 106.245

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