Math, asked by rkdolic, 3 months ago

please if somebody know the solution of Questions number-9,11
please tell correct answer
thanks​

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Answers

Answered by tennetiraj86
4

Step-by-step explanation:

Solutions :-

9)

i)

Given decimal number = 0.130130013000...

This is non terminating and non recurring decimal.

It is an irrational number.

It is not a rational number.

_______________________________

ii) Given decimal number = 10.01456

This is a terminating decimal.

It is a rational number.

=> 10.01456

=> 1001456/10000

=> 250364/2500

=> 62591/625

It is in the form of p/q

q = 625

625 = 5×5×5×5

Prime factorization of q = 5×5×5×5

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iii) Given decimal number = 122.058 bar on 058

=>122.058058058...

It is a non terminating recurring decimal.

It is a rational number.

Let x = 122.058058058...-------(1)

Since the periodicity is 3 then multiplying (1) with 1000 then

=> 1000×x = 122.058058...×1000

=> 1000x = 122058.058058...-----(2)

On Substituting (1) from (2)

1000x = 122058.058058...

x = 122.058058...

(-)

_________________________

999x = 121936.000000...

_________________________

=> 999x = 121936

=> x = 121936/999

122.058 bar on 058 = 121936/999

This is in the form of p/q

q = 999

q = 3×3×3×37

Prime factorization of q = 3×3×3×37

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10)

Given number = 13/120

It can be written as 13/(2×2×2×3×5)

=> 13/(2³×3¹×5¹)

The denominator is in the form of 2³×3¹×5¹

We know that

X = p/q is a rational number if q is in the form of 2^m×5^n then it is a terminating decimal.

It is not in the form of 2^m×5^n

So , It is not a terminating decimal

It is non terminating recurring decimal.

______________________________

11)

Given numbers are 798 , 168 and 56

We know that

Euclid's Division Lemma:-

For two Positive integers a and b there exist two positive integers q and r satisfying a = bq+r, where 0≤r<b.

On taking 798 and 168

Let a = 798 and b = 168

on writing it a=bq+r

=> 798 = 168×4 + 126

and now a = 168 and b = 126

=> 168 = 126 × 1 + 42

and a = 126 and b = 42

126 = 42×3 + 0

HCF of 798 and 168 is 42

now

On taking 42 and 56

Let a = 56 and b = 42

On writing it a= bq +r

=> 56 = 42×1+14

and

Now a = 42 and b = 14

42 = 14×3 + 0

HCF of 56 and 42 is 14

HCF of 798 , 168 and 56 is 14

Used formulae :-

  • The decimal expansion of a rational number is either a terminating decimal or non terminating recurring decimal.

  • The decimal expansion of an irrational number is non terminating and non recurring decimal.

  • The number of digits in the recurring part of a decimal number after the decimal point is called periodicity.

  • X = p/q is a rational number if q is in the form of 2^m×5^n then it is a terminating decimal.

Euclid's Division Lemma:-

For two Positive integers a and b there exist two positive integers q and r satisfying a = bq+r, where 0≤r<b.

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