Page 97 - Start Up Mathematics_5

Expanded Form of Decimal Numbers

Example 1: Write (a) 78.65, (b) 135.024 and (c) 8,562.913 in the expanded form.

Solution: Short form Expanded form
(a) 78.65 = 7 tens + 8 ones + 6 tenths + 5 hundredths
6 5
= 70 + 8 + + = 70 + 8 + 0.6 + 0.05
10 100
(b) 135.024 = 1 hundred + 3 tens + 5 ones + 2 hundredths + 4 thousandths
2 4
= 100 + 30 + 5 + + = 100 + 30 + 5 + 0.02 + 0.004
100 1000
(c) 8,562.913 = 8 thousands + 5 hundreds + 6 tens + 2 ones + 9 tenths +
1 hundredth + 3 thousandths
9 1 3
= 8,000 + 500 + 60 + 2 + + +
10 100 1000
= 8,000 + 500 + 60 + 2 + 0.9 + 0.01 + 0.003

Reading Decimal Numbers

In a decimal number, the whole number is read in the usual manner and the decimal part
is read digitwise. Look at the following examples,

5
10 = 0.5 is read as zero point five Common Mistake!

11
100 = 0.11 is read as zero point one one 68.12 is read as sixty-eight
2485 = 24.85 is read as twenty-four point eight five point one two and not
100 sixty-eight point twelve.
76
1000 = 0.076 is read as zero point zero seven six

EXERCISE 6.1

1. Write the place value of the circled digits.
(a) 3 1.0 2 5 (b) 20 2 .9 6 (c) 9. 0 2 4 (d) 1 8. 3 07 (e) 6 3 1 2.41 9

2. Write in the expanded form.
(a) 57.69 (b) 24.306 (c) 130.045 (d) 196.27 (e) 814.025

(f) 2,014.38 (g) 9,824.07 (h) 600.714 (i) 304.189 (j) 99.075
3. Write the following in the short form.

3 2 7
(a) 2 + (b) 10 + 5 + +
10 10 100
8 6 5
(c) 7,000 + 500 + 20 + + (d) 6,000 + 50 + 1 +
10 1000 1000
4 7
(e) 1,000 + 300 + 5 + (f) 200 + 30 +
100 1000

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