Page 87 - classs 6 a_Neat

DECIMALS IN EXPANDED FORM
We read them as:
point zero zero one, point zero zero two, . . . . . . , point zero zero nine, point zero one zero, point zero one one, .
. . . . . , point zero nine nine, point one zero zero, point one zero one, . . . . . . , point nine nine nine respectively. Place Value Table
Remember that .001= 0.001, .011= 0.011, ... . Tenth Hundredth Thousandth
Thousands Hundreds Tens Ones Decimal 1 1 1
72.63 point
EXAMPLES OF MIXED FRACTIONS AS DECIMALS 1,000 100 10 1 . 10 100 1000
1 17 29
EXAMPLE 2: Express the numbers 2 ,6 and 18 as decimals. 72.63 7 2 . 6 3
10 100 1000
Solution: We have: 1 1 742.375 7 4 2 . 3 7 5
2 = 2 + = 2 + 0.1 = 2.1
10 10
17 17 PRACTICE EXERCISE 6.1
6 = 6 + = 6 + 0.17 = 6.17
100 100

29 29 1. Write the following fractions in their decimal form.
18 = 18 + = 18 + 0.029 = 18.029
1000 1000 (a) 6 (b) 9 (c) 52 (d) 57 (e) 245
10 100 100 1000 1000
DECIMALS 2. Write the following in the decimal form.
a. Fifteen-hundredths
DECIMALS The numbers expressed in decimal form are called decimal numbers or simply decimals. b. Seven-tenths
EXAMPLE3: Each of the numbers 5 .8, 19.63, 7.295, 0.068, etc., is a decimal. c. Forty-five-thousandths
A decimal has two parts, namely, (1) whole-number part and (ii) decimal part. d. Eight and eight thousandth
These parts are separated by a dot(.), called the decimal point. e. Two hundred twenty-two and two hunderdth
The part on the left side of the decimal point ts the whole-number part and that on the
rightside of the decimal point ts the decimal part. 3. Write the following in decimal form.

EXAMPLE 4: In 68.49, we have , whole-number part= 68 and decimal part= .49. (a) 3 (b) 11 (c) 2036 (d) 14703 (e) 500005
10 100 10 100 100
DECIMAL PLACES The number of digits contained in the decimal part of a decimal gives the number of 4. Fill in the blanks.
decimal places.
EXAMPLE 5: 93 has two decimal places and 7.632 has three decimal places . (a) 8.53 = 8 + 5 + 3 (b) 29.175 = 29 + 1 + 7 + 5 (c) 81.81 = ‪ + 8 + 1

Chart to Depict Decimal Fractions
Decimal Position of the Decimal (d) 66.666 = ‪ + 6 + 6 + 6
Part Fraction
Fraction Point 5. Write in the expanded form
1 1 1 place from the extreme a. 5.83 b. 62.37 C. 125.4 d. 12.543 e. 326.543
One-tenth = 0.1 right number
10 10

1 1 2 places from the extreme 6. Write in the short form.
One-hundredth = 0.01 right number.
100 10 × 10 a. 0.8 + 0.08 + 0.008

1 1 3 places from the b. 3 + 0.1 + 0.02 + 0.003
One-thousandth = 0.001 extreme right number. c. 51 + 0.02 + 0.003
1,000 10 × 10 ×10 d. 100 + 10 + 1 + 0.1 + 0.01 + 0.001

1 1 4 places from the e. 900 + 80 + 9 + 0.5 + 0.009
One-ten thousandth = 0.0001 extreme right number:
10,000 10 × 10 × 10 × 10

One-hundred 1 = 1 5 places from the
thousandth 1,00,000 10 × 10 × 10 × 10 × 10 0.00001 extreme right number