Lesson 4- Decimal Place Value & Value

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 parts of a whole by separating them with a point.
• Decimal point: Is a point separating the ones and tenths 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 number 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. “.8” means 8 parts out of 10. i.e.).
• Hundredth: Is the second number on the right hand side of the decimal point. It is the second decimal place and represents parts out of 100 equal parts (E.g.“.05” means 5 parts out of 100 i.e ).
• Thousandth – Is the third number on the right hand side of the decimal point. It is the third decimal place and represents parts out of 1000 equal parts (E.g.“.009” means 9 parts out of 1000 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 above diagram, the whole number is 342,368. The

lowest place value of whole numbers is the units. Therefore, from right to left on the left hand side of the decimal point: units, tens, hundreds, thousands, ten thousands and hundred thousands.

On the right hand side of the decimal point, the highest place value of the fraction part begins: tenth, hundredth, thousandth, etc. as shown in the illustration above.

Example 1

Write the value and place value of the underlined digits in the following decimal numbers.

a) 2486.08                                       b) 35276.826

c) 359,901.620                               d) 24.241

e) 19.4211                                       f) 78 9.1515

Solution

Example 2

What is the total value of the underlined figures in each of these?

a) 24.5                                   b) 828.84

Solution

a) 24.5 = 2 tens and 5 tenths

            = 20 + 0.5

            = 20.5

b) 828.84 = 2 tens and 8 units

            = 20 + 8

            = 28

An Abacus or Notation Board can be used to illustrate decimals based on the knowledge of place value. Let’s look at the Abacus below.

Notation boards work in the same way as the Abacus. Below are some illustrations on Notation boards.