# 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 $$\frac{1}{1000}$$ 48.3050.9 53.02315.217 12.375 796.583 55.505 145.008 371 451 1 9 5 4 835 2 6 5 5 ........ 3902 3 5 5 0 021 7 8 0 0 57 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