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Show that 3.142678 is a rational number...

Show that 3.142678 is a rational number. In other words, express 3.142678 in the form `p/q ,`where p and q arc integers and `q!=0`.

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To show that 3.142678 is a rational number, we need to express it in the form \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \). ### Step-by-Step Solution: 1. **Identify the Decimal Number**: The given number is 3.142678. 2. **Remove the Decimal Point**: ...
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NCERT ENGLISH-NUMBER SYSTEMS-Solved Examples
  1. Show that 3.142678 is a rational number. In other words, express 3.14...

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  2. Show that 0. 3333. . . .=0. bar3can be expressed in the form p/q, wher...

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  3. Locate sqrt(3)on the number line.

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  4. Find the decimal expansions of (10)/3,7/8and 1/7.

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  5. Find five rational numbers between 1 and 2. We can approach this prob...

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  6. Locate sqrt(2)on the number line.

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  7. Are the following statements true or false? Give reasons for your ans...

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  8. Rationalise the denominator of 1/(7+3sqrt(2))

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  9. Simplify (i) 2^(2/3). 2^(1/3) (ii) (3^(1/5))^4 (iii) (7^(1/5))/(7^(1...

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  10. Show that 1. 272727. . .=1. bar 27can be expressed in the form p/q, wh...

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

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  12. Visualize the representation of 5. 3 bar7 on the number line upto 5 de...

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  13. Find the irrational number between 1/7and 2/7.

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  14. Add 2sqrt(2)+5sqrt(3) and sqrt(2)-3sqrt(3).

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  15. Check whether 7sqrt(5),7/(sqrt(5)),sqrt(2)+21 ,pi-2are irrational numb...

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  16. Divide 8sqrt(15)and 2sqrt(3).

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  17. Multiply 6sqrt(5)by 2sqrt(5).

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  18. Rationalise the denominator of 1/(sqrt(2))

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  19. Simplify the following expressions. (i) (5+sqrt(7))(2+sqrt(5)) (ii) (...

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  20. Rationalise the denominator of 5/(sqrt(3)-sqrt(5))

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