Page 89 - classs 6 a_Neat

7. Complete the given sequences by writing the next three decimal numbers. SOME EXAMPLES

a. 2.1,2.2,2.3, _________ EXAMPLE 4: Convert 5.3, 7.19, 0.376 and 84 into like decimals.
b. 7.123, 7.124, 7.125, _________
c. 15.8, 15.9, 16.0, _________ SOLUTION: In the given numbers, the maximum number of decimal places is 3. So, we convert each one of
d. 20.01, 20.02, 20.03, ________ the given numbers into one having 3 decimal places by annexing suitable number of zeros to the extreme right
e. 152.1, 152.2, 152.3, _________ of the decimal part.
5.3 = 5.300, 7.19 = 7.190, 0.376 = 0.376 and 84 = 84.000.
8. Write three equivalent decimals for each of the following. Thus, 5.300, 7. 190, 0.376 and 84.000 are the required like decimals.
a.0.5 b.3.6 c.20.7 d.62.35 e.146.9
EXAMPLE 5: Arrange the digits of 269.374 in the place-value chart. Write the place value of each
9.Write each of the following fractions as decimals by converting the denominators into multiples of 10. digit. Also, write 269.374 in expanded form.
1 3 17 4 29 SOLUTION: We may arrange the digits of the given number in the place-value chart as shown
(a) (b) (c) (d) (e) below.
2 5 20 25 500

10. Use a graph paper to illustrate the following decimal fractions. Hundreds Tens Ones Decimal Tenths Hundredths Thousandths
point
7 3 21 47 3
(a) (b) (c) (d) (e) 2 6 9 . 3 7 4
10 10 100 100 100
LIKE AND UNLIKE DECIMALS

LIKE DECIMALS Decimals having the same number of decimal places are called like decimals. In 269.374, we have:

EXAMPLE 1: 9.82, 6.03, 14.58 are like decimals, each having two decimal places. Place value of 2 = 2 hundreds = 200.
Place value of 6 = 6 tens = 60.
UNLIKE DECIMALS Decimals having dl[ferent number of decimal places are called unlike place value of 9 = 9 ones = 9
decimals. 3
place value of 3 = 3 tenths = .
10
EXAMPLE 2: Clearly, 6.4, 8.93, 12.065 are unlike decimals.
Place value of 7 = 7 hundredths = 7 .
AN IMPORTANT RESULT 100
We shall show that 0.6 = 0.60 = 0.600, etc. 4
6 6 × 10 60 Place value of 4 = 4 thousandths = 1000 .
0.6 = = = = 0.60
10 10 × 10 100 269.374 = 2 hundreds+ 6 tens+ 9 ones+ 3 tenths+ 7 hundredths. + 4 thousandths
6 6 × 100 600
0.6 = = = = 0.600 3 7 4
10 10 × 100 1000 = 200 + 60 + 9 + + +
0.6 = 0.60 = 0.600 etc. 10 100 1000
COMPARING DECIMALS
RESULT Putting any number of zeros to the extreme right of the decimal part of a decimal does not Suppose we have to compare two decimals. Then, we proceed according to the following steps.
change its value. Step 1. Convert the given decimals into like decimals.
Step 2. First compare the whole-number part.

Thus, we may write 2.64 = 2.640 = 2.6400, etc. The decimal with the greater whole-number part is greater.
Thus, we may convert unlike decimals into like decimals by annexing the required number of zeros to the
extreme right of the decimal part. Step 3. If the whole-number parts are equal, compare the tenths digits.
The decimal with the bigger digit in the tenths place is greater.
Step 4. If the tenths digits are also equal, compare the hundredths digits, and so on. The following examples
will make the ideas more clear.