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:

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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