Page 117 - Maths Class 06

Decimals

Introduction

In our everyday life, decimal numbers are commonly used to represent the units of mass, length, weight,
distance, currency. Have you ever come across the price tags with fractions on it? The reason for this is
that decimals are much easier to “visualise” than fractions.

Decimal Fraction
A decimal fraction is a fraction whose denominator is a power of ten say 10, 100, 1000, 10000,…e g. .,
23 2341
, are the decimal fractions that can also be written as 2.3 and 23.41 using the decimal point (.).
10 100
A decimal number has two parts : whole number part and a decimal part. The digits to the left of the
decimal point stand for whole numbers and the digits to the right indicate the fractional part, e g. ., 3.45
has 3 as whole and 45 fractional parts.

Place Value in Decimals

The decimal system is an extension of the place value system of whole numbers. Each digit in a decimal
part has different place value. The digits after the decimal are assigned the place values of tenths,
hundredths, thousandths, ten thousandths and so on. The place value chart for a decimal number is as
below :
s
s h
d s s t
n s s ) . h h d
a d d ( t t n
s n e s s l s d d a
u a r n e a h t e n s
o s d e n m n r a u
h u n T O i e d s o
T o u c T n u h
h H e u o T
n T D H h -
e T n
T e
T
10000 1000 100 10 1 1 1 1 1
10 100 1000 10000
2
e g. ., 47.2 = 40 + +7
10

Representation of Decimals on Number Line
Let us represent 2.3 on a number line.
We know that 2.3 is more than 2 but less than 3. There are 3 tenths in 2.3. We divide the unit length
between 2 and 3 into 10 equal parts and take 3 parts as shown below:
2.3

0 1 2 3 4 5 6 7 8 9 10 11 12
117 Mathematics-6