Decimal in Expanded Form

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

Let us observe the following place value table.

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:

1. 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

2. Write the decimal number for the expansion given below:

(i) 10 + 8 + \(\frac{4}{10}\) + \(\frac{7}{1000}\)

(ii) 2000 + 200 + 0 + 2 + \(\frac{2}{10}\) + \(\frac{2}{100}\) + \(\frac{2}{1000}\)

(iii) 500 + 70 + 1 + \(\frac{3}{100}\) + \(\frac{9}{1000}\)

(iv) 80 + \(\frac{7}{10}\) + \(\frac{4}{1000}\)

Answers:

(i) 18.407

(ii) 2202.222

(iii) 571.039

(iv) 80.704

3. Write the given decimal numbers in expanded form by fractional expansion:

(i) 239.4

(ii) 16.098

(iii) 702.65

(iv) 8.006

(v) 7000.848

Answers:

(i) 200 + 30 + 9 + \(\frac{4}{10}\)

(ii) 10 + 6 + \(\frac{0}{10}\) + \(\frac{9}{100}\) + \(\frac{8}{1000}\)

(iii) 700 + 0 + 2 + \(\frac{6}{10}\) + \(\frac{5}{100}\)

(iv) 8 + \(\frac{0}{10}\) + \(\frac{0}{100}\) + \(\frac{6}{1000}\)

(v) 7000 + 0 + 0 + 0 + \(\frac{8}{10}\) + \(\frac{4}{100}\) + \(\frac{8}{1000}\)

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