Question

Let x=11/500 be a rational number. Then x has a decimal expansion which terminates after​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

TO CALCULATE

$\sf{The \: number \: of \: terms \: after \: which \: decimal}$

$\displaystyle \sf{ expansion \: terminates \: for \: the \: rational \: number \: \: \: \frac{11}{500} }$

PROCESS ( Without actual division )

STEP : 1

Write the rational number

STEP : 2

Write the denominator

STEP : 3

Factorise the denominator by Prime factorisation

STEP : 4

Write the denominator in exponent form of the prime numbers

STEP : 5

Calculate the maximum value of the powers ( say n )

STEP : 6 ( Conclusion)

Decimal expansion of the given rational number terminates after n digits

CALCULATION

$\displaystyle \sf{ The \: given \: rational \: number \: \: is \: \: \: \frac{11}{500} }$

Denominator = 500

Now

$\sf{500 = 2 \times 2 \times 5 \times 5 \times 5 \: }$

$\implies \sf{500 = {2}^{2} \times {5}^{3} \: }$

So the prime factorisation of 500 consists of two prime numbers 2 and 5

Now the power of 2 is 2 and the power of 5 is 3

Since the highest power of 5 is 3

Hence the decimal expansion of the given rational number terminates after 3 digits

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LEARN MORE FROM BRAINLY

Out of the following which are proper fractional numbers

(i)3/2 (ii)2/5 (iii)1/7 (iv)8/3

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