Express each of the following decimals in the form p/q:
¯ ¯¯ ¯¯ ¯¯¯ ¯ ¯ ¯
(i)0. 4 (ii)0.37 (iii)0.54 (iv) 0.621 (v) 125.3 (vi) 4.7(vii) 0.47
Answers
(i) Given : 0.4(bar on 4)
Let x = 0.4
or x = 0.4 = 0.444 ……... (1)
Here only one digit is repeating so we multiply by 10 on both sides :
10x = 4.444 ………...(2)
On subtracting eq (1) from eq (2)
10x – x = 4.444… – 0.444…...
9x = 4
x = 4/9
Hence, 0.4 is 4/9
(ii) Given : 0.37….(bar on 37)
Let x = 0.3737… …….. (1)
Here two digit is repeating so we multiply by 100 on both sides :
100x = 37.37… …..(2)
On subtracting eq (1) from eq (2) :
100x – x = 37.37… – 0.3737…
100x – x = 37
99x = 37
x = 37/99
Hence, 0.3737….(bar on 37) is 37/99
(iii) Given : x = 0.54… (bar on 54)
Let x = 0.5454… ………. (1)
Here two digit is repeating so we multiply by 100 on both sides :
100x = 54.5454…. ………..(2)
On subtracting eq (1) from eq (2) :
100x – x = 54.5454…. – 0.5454….
99x = 54
x = 54/99
Hence, 0.54… (bar on 54) is 54/99.
(iv) Given : 0.621621…… (bar on 621)
Let x = 0.621621… …………..(1)
Here three digit is repeating so we multiply by 1000 on both sides :
1000x = 621.621621…. ……….. (2)
On subtracting eq (1) from eq (2) :
1000x – x = 621.621621…. – 0.621621….
999x = 621
x = 621/999
x = 23/37
Hence, 0.621621…… (bar on 621) is 23/37
(v) Given : 125.3 (bar on 3)
Let x = 125.3333…. ………..(1)
Here one digit is repeating so we multiply by 10 on both sides :
10x = 1253.3333…. ………..(2)
On subtracting eq (1) from eq (2) :
10x – x = 1253.3333…. – 125.3333….
9x = 1128
x = 1128/9
x = 376/3
Hence, 125.3 (bar on 3) is 376/3
(vi) Given : 4.7 (bar on 7)
Let x = 4.7777…. ………..(1)
Here one digit is repeating so we multiply by 10 on both sides :
10x = 47.7777…. ……….(2)
On subtracting eq (1) from eq (2) :
10x – x = 47.7777…. – 4.7777….
9x = 43
x = 43/9
Hence , 4.7 (bar on 7) is 43/9.
(vii) Given : 0.47 (bar on 7)
Let x = 0.47777….
Here one digit is repeating so we multiply by 10 on both sides :
10x = 4.7777…. ……… (1)
On Multiplying both sides by 100 :
100x = 47.7777…. ……….. (2)
On subtracting eq (1) from eq (2) :
100x – 10x = 47.7777…. – 4.7777…
90x = 43
x = 43/90
Hence, 0.47 (bar on 7) is 43/90.
HOPE THIS ANSWER WILL HELP YOU…..
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Answer:
Answer is in the attachments.
