Question

express the following in the form of p/q where p and q are integers and q≠ 0
,,,,,_
0.47​

Answer 1

Answer:

0.47( ke upar baar)

Let be,

x= 0.4777777

10x= 0.477

43

both side multiple by 100

100x = 43+10

100x-10 = 43

90x= 43

x= 43/90

Answer 2

Question:-

Express the following in the form of p/q where p and q are integers and q≠ 0

$\sf{\bold{0.4\bar{7}}}$

Required Answer:-

Given Decimal:-

$\\ \sf{\rightarrow{0.4\bar{7}}}$

To Do:-

• Express the following in the form of p/q where p and q are integers and q ≠ 0

Solution:-

Let,

$\sf{x= 0.47 = 0.47777... - - - - - - - - - - - (1)}$

Here, 1 digit is not repeating so multiply eq. 1 by 10

$\\ \sf{10 \times x = 10 \times 0.47777...}$

$\sf{\implies{10x= 4.7777... - - - - - - - - - - (2)}}$

Now only 1 digit is repeating so multiply eq 2 by 10 we get

$\\ \sf{10 \times 10x = 10 \times 4.7777...}$

$\sf{\implies{100 x = 47.777… - - - - - - - - - - - (3)}}$

On subtracting equation 2 from equation 3 we get

$\\ \sf{100x - 10 x = 47.777… - 4.777...}$

$\sf{\implies{90 x = 43}}$

$\sf{\implies{x= \frac{43}{90} }}$

$\\\underline{\boxed{\rm{Hence, \: the \: answer \: is \: \bold{ \frac{43}{90}}}}}$

More Information:-

Steps to convert a decimal number into p/q form:

• Check whether the decimal number is non terminating non-recurring decimal or non terminating recurring decimal or terminating decimal.

• If it is a terminating decimal, Find the number of decimal places in the given decimal number.

• Take 1 annexed with as many zeroes as the number of decimal places given in the decimal.

• Multiply and divide the given decimal with this number.

• Reduce the above rational number to simplest form.