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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