Hindi, asked by palakparidubey, 1 month ago

6. The simplest form of the rational number 0. 196 is
a) 1/6
b) 3/6
c)13/66
d) 2/5​

Answers

Answered by r4728207anRashmi
3

Answer:

196/1000=98/500=49/250

Explanation:

I hope it's help you

Answered by pulakmath007
1

\displaystyle \bf   0. 1\overline{96}   =  \frac{13}{66}

Which is the required simplest form of the rational number [ The correct option is c) 13/66 ]

Correct question : The simplest form of the rational number \displaystyle \sf{ 0. 1\overline{96} } is

a) 1/6

b) 3/6

c) 13/66

d) 2/5

Given :

The number \displaystyle \sf{ 0. 1\overline{96} }

To find :

The simplest form of the rational number \displaystyle \sf{ 0. 1\overline{96} } is

a) 1/6

b) 3/6

c) 13/66

d) 2/5

Solution :

Step 1 of 2 :

Write down the given number

The given number is \displaystyle \sf{ 0. 1\overline{96} }

Step 2 of 2 :

Find the simplest form of the rational number

\displaystyle \sf{ Let  \:  \: x = 0. 1\overline{96}  }

Then x = 0.196969696..... - - - - - - - (1)

Multiplying both sides by 10 we get

10x = 1.96969696..... - - - - - - (2)

Again multiplying both sides by 100 we get

1000x = 196.96969696..... - - - - - - (3)

Equation 3 - Equation 2 gives

990x = 195

\displaystyle \sf{ \implies x =  \frac{195}{990} }

\displaystyle \sf{ \implies x =  \frac{13}{66} }

\displaystyle \sf{ \therefore \:  \:  0. 1\overline{96}  =  \frac{13}{66}}

Which is the required simplest form of the rational number

Hence the correct option is c) 13/66

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