Decimal Place Value System

Introduction:
Decimal place value system is slightly differing from normal place value for numbers. This decimal place value system has a decimal point and numbers on both sides of decimal point. There are different names for the numbers before and after the decimal system. We are going to see how the place value system for decimals.

Explanation to Decimal Place Value System:

General representation of decimal place value system:

Let us see the place value system for the decimal 123456 . 789

Before the decimal point:

123456

6 - ones

5 - tens

4 - hundreds

3 - thousands

2 - ten thousands

1 - hundred thousands

After the decimal point:

789

7 -tenths `1/10`

8 -hundredths `1/100`

9 - thousandths `1/1000`

The above number 123456.789 can be obtained as,

(1 x 100000) + (2 x 10000) + (3 x 1000) +(4 x 100) + (5 x 10) x (6 x 1) + ( 7 x `1/10`) + (8 x `1/100` ) + (9 x `1/1000`)

Example Problems to Decimal Place Value System:
Example: 1

Which of the following is the place value of 5 in decimal 9.5?

a) Ones

b) Tenths

c) Hundreds

d) Decimal point

Solution:

Given, 9.5

5 lie after the decimal point. So, the place value of 5 is tenths.

Answer: b

Example: 2

Which of the following is the place value of 9 for decimal 98.42?

a) Tenths

b) Ones

c) Hundreds

d) Hundredths

Solution:

9 lie before the decimal point.

98

8 – ones

9 – hundreds

Answer: c

Example: 3


How will you write the expanded form the decimal 3.36?

Solution:

Given 3.36

Before the decimal point: 3

3 - Ones

After the decimal point: 36

3 - tenths

6 - hundredths

3.36 = (3 x 1) + (3 x `1/10`) + ( 6 x `1/100`)

Practice Problems to Decimal Place Value System:
Problem: 1

Which of the following is the place value of 8 in decimal 2.08?

a) Ones

b) Tenths

c) Hundredths

d) Hundreds

Answer: c

Problem: 2

Which of the following is the place value of 1 in decimal 0.001?

a) Ones

b) Thousandths

c) Hundredths

d) Hundreds

Answer: b