Math, asked by divishagora7091, 9 months ago

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

Answered by nikitasingh79
35

(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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Answered by laxmigupta373
4

Answer:

Answer is in the attachments.

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