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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