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Express 0. 99999 in the form p/q , wher...

Express `0. 99999 ` in the form `p/q ,` where `p` and `q` are integers and `q!=0.`

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Verified by Experts

Let `x=0.9999...-(1)`
Multiplying both sides by10
`10x=9.999...-(2)`
subtracting equation 1 from 2
`9x=9`
`x=1`.
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RD SHARMA ENGLISH-NUMBER SYSTEM-All Questions
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  2. Show that 1. 272727=1. 27 can be expressed in the form p/q , where p...

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  3. Express 0. 99999 in the form p/q , where p and q are integers and q!=...

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  4. Find three different irrational numbers between the rational numbers...

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  5. Find two irrational numbers between 2 and 2. 5.

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  7. Find five rational numbers between 3/5a n d4/5dot

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  8. Express (2157)/(625) in the decimal form.

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  9. Convert (35)/(16) into decimal form by long division method.

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  10. Find the rational number between -2/3a n d1/4dot

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  11. Insert 10 rational numbers between -3/(13)a n d9/(13)dot

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  12. Find 10 rational numbers between (-3)/11 and 8/11 by mean method.

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  14. If 1/7=0. 142857 , write the decimal expression of 2/7,3/7,4/7,5/7a ...

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  15. Convert the following decimal number in the form p/qdot 5. bar2 (...

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  16. Express 0. 0bar01 as a fraction in the simplest form.

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  17. Find the decimal representation of 8/3dot

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  18. Express -(17)/8 in decimal form by long division method.

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  19. Prove that sqrt(n) is not a rational number. if n is not a perfect squ...

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  20. Show that 0. 2353535. . .=0. 2 bar 35can be expressed in the form p/q...

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