Decimal in Expanded Form

We will discuss here about how to express decimal in expanded form.

Let us observe the following place value table.

Numerals

Hundreds

100

Tens

10

Ones

1

(.)

.

Tenths

\(\frac{1}{10}\)

Hundredths

\(\frac{1}{100}\)

Thousandths

\(\frac{1}{1000}\)

48.305

0.9

53.02

315.217

12.375

796.583

55.505

145.008




3


7


1

4


5

1

1

9

5

4

8


3

5

2

6

5

5

.

.

.

.

.

.

.

.

3

9

0

2

3

5

5

0

0


2

1

7

8

0

0

5



7

5

3

5

8

Now, consider the expanded form of the above numerals.

48.305 = 40 + 8 + 0.3 + 0.005

0.9 = 0.9

53.02 = 50 + 3 + 0.02

315.217 = 300 + 10 + 5 + 0.2 + 0.01 + 0.007

12.375   = 10 + 2 + 0.3 + 0.07 + 0.005

796.583 = 700 + 90 + 6 + 0.5 + 0.08 + 0.003

55.505   = 50 + 5 + 0.5 + 0.005

145.008 = 100 + 40 + 5 + 0.008


Solved examples:

Express the decimals in the expanded form:

(i) 1.569

= 1 + 0.5 + 0.06 + 0.009

(ii) 14.4502

= 10 + 4 + 0.4 + 0.05 + 0.0002

(iii) 0.256

= 0.2 + 0.05 + 0.006

(iv) 138.048

= 100 + 30 + 8 + 0.04 + 0.008

(v) 956.369

= 900 + 50 + 6 + 0.3 + 0.06 + 0.009


Now we will learn how to express the expanded form of a decimal in short form.


Solved examples:

Express the expanded form in short form of decimals:

(i) 200 + 20 + 3 + 0.3 + 0.05 + 0.001

= 223.351

(ii) 10 + 8 + 0.1 + 0.002 + 0.0008

= 18.1028

(iii) 300 + 10 + 5 + 0.5 + 0.02 + 0.005

= 315.525





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