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A rational number in its decimal expansi...

A rational number in its decimal expansion is 327.7081. What can you say about the prime factors of q, when this number is expressed in the from `(p)/(q)` ? Give reason

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To solve the problem, we need to express the decimal number 327.7081 in the form of a fraction \( \frac{p}{q} \) and analyze the prime factors of \( q \). ### Step-by-Step Solution: 1. **Identify the Decimal Number**: The given decimal number is 327.7081. 2. **Convert to Fraction**: To convert the decimal to a fraction, we can express it as: \[ ...
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NCERT EXEMPLAR-REAL NUMBERS-Real Numbers
  1. Can two number have 18 as their HCF and 380 as their LCM? Give reason

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  2. Without actually performing the long divison, find if (987)/(10500) wi...

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  3. A rational number in its decimal expansion is 327.7081. What can you s...

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  4. Prove that the square of any positive integer is of the form 4q or ...

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  5. Show that cube of any positive integer is of the form 4m, 4m+1 or 4m+3...

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  6. Show that the square of any positive integer cannot of the form 5q+2 o...

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  7. Show that the square of any positive integer cannot be of the form 6m+...

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  8. Show that the square of any odd integer is of the form 4m+1, for some ...

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  9. If n is an odd positive integer, show that (n^2-1) is divisible by 8.

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  10. Prove that if xa n dy are odd positive integers, then x^2+y^2 is even ...

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  11. Use Euclid division algorithm to find the HCF of 441, 567 and 693.

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  12. Using Euclid's division algorithm, find the largest number that divide...

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  13. Prove that sqrt3+sqrt5 is irrational

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  14. Show that 12^n cannot end with the digits 0 or 5 for any natural numbe...

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  15. In a morning walk, three persons step off together and their steps mea...

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  16. Write the denominator of the rational number 257/5000 in the form 2^m ...

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  17. Prove that sqrtp+sqrtq is an irrational, where p and q are primes.

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  18. Show that the cube of a positive integer of the form 6q+r,q is an inte...

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  19. Show that one and only one out of n ,n+2or ,n+4 is divisible by 3, whe...

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  20. Prove that one of every three consecutive positive integers is divi...

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