Page 90 - classs 6 a_Neat

EXAMPLE 9: Convert each of thefollowtng decimals as a mixed fraction:
EXAMPLE:5 Compare 63.84 and 57.98. (i) 7.5 (ii) 24.8 (iii) 13.25 (iv) 6.375

SOLUTION: The given decimals are 63.84 and 57.98. Let us compare their whole-number parts. SOLUTION: (i) 7.5 = 75 15 = 15 = 7 1 (ii) 24.8 = 248 124 = 124 = 24 4
Clearly, 63 > 57. 10 2 2 2 10 5 5 5
63.84 > 57.98. 1325 53 53 1 6375 285 51 53 3
EXAMPLE:6 Compare 24.7 and 24.58. (iii) 13.25 = 100 = 4 = 13 4 (iv) 6.375 = 1000 = 8 = 6 8
SOLUTION: Converting the given decimals into like decimals, they become 24. 70 and 24.58. The 4 40 8
whole-number parts of these numbers are equal.
So, we compare their tenths digits. CONVERTING A FRACTION INTO A DECIMAL
Clearly, 7 tenths > 5 tenths.
24. 70 > 24.58. When the denominator of afraction ls a power of l0 then we can convert the fraction into a decimal,
Hence, 24. 7 > 24.58. as shown below:

EXAMPLE 10: Convert 7 each of the following fractions into a decimal:
EXAMPLE: 7 Write the following decimals in ascending order: 17 239 2103 3001
4.83, 6.07, 0.9, 0.465 and 7.4. (i) 10 (ii) 100 (iii) 100 (iv) 1000
SOLUTION: we have:
SOLUTION: Converting the given decimals into like decimals, we get them as 17 7 7 239 39 39
4.830, 6.070, 0.900, 0.465 and 7.400. (i) = 1 = 1 + = 1 + 0.7 = 1.7 (ii) = 2 = 2 + = 2 + 0.39 = 2.39
Clearly, 0.465 < 0.900 < 4.830 < 6.070 < 7.400. 10 10 10 100 100 100
0.465 < 0.9 < 4.83 < 6.07 < 7.4. (iii) 2103 = 21 3 = 21 + 3 = 21 + 0.03 = 21.03.
Hence, the given decimals in ascending order are: 100 100 100
0.465, 0.9, 4.83, 6.07 and 7.4. 3001 1 39
(iv) 1000 = 3 1000 = 3 + 1000 = 3 + 0.001 = 3.001
CONVERTING A DECIMAL INTO A FRACTION
GENERAL METHOD OF CONVERTING A FRACTION INTO A DECIMAL
METHOD: Step 1. Write the given decimal without the decimal point as the numerator of the
fraction. Step 1. Divide the numerator by the denominator till a nonzero remainder ls obtained.
Step 2. In the denominator, write 1 followed by as many zeros as there are decimal Step 2. Put a decimal point in the dividend as well as in the quotient.
places in the given decimal. Step 3. Put a zero on the right of the decimal point in the dividend as well as on the right of the remainder.
Step 3. Convert the above fraction to the simplest form. Step 4. Divide againjust as we do in whole numbers.
The following examples will make the ideas more clear. Step 5. Repeat step 4 till the remainder ls zero.

EXAMPLE 8: Convert each of the following decimals into afractton in tts simplestform: SOME MORE EXAMPLES
(i) .4 (ii) .25 (iii) 0.06 (iv) .075 (v) 0.625
29
SOLUTION: We have: EXAMPLE 11: Convert 4 into a decimal fraction.
4 2 2
(i) .4 = 25 5 SOLUTION: On dividing, we get:
10 5 625 5
5 (v) .075 = 4 29.00 7.25
25 1 1 1000 8 - 28
(ii) .25 = 40 8
100 4 4 10
6 3 3
(iii) .06 = - 8
100 50 50 20
75 3 3
(iv) .075 = - 20
1000 40
40 ×
29 = 7.25.
4