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What is the greatest integer k for which 32.45 × 10^k is less than 1 ?

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What is the greatest integer k for which 32.45 × 10^k is less than 1 ?  [#permalink]

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New post Updated on: 12 Jul 2018, 12:06
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Can someone help me out with this?

What is the greatest integer k for which \(32.45 × 10^k\) is less than 1 ?


a. –2

b. –1

c. 0

d. 1

e. 2

Originally posted by Lisapizzola on 12 Jul 2018, 10:37.
Last edited by Lisapizzola on 12 Jul 2018, 12:06, edited 1 time in total.
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Re: What is the greatest integer k for which 32.45 × 10^k is less than 1 ?  [#permalink]

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New post 12 Jul 2018, 11:43
2
Lisapizzola wrote:
Can someone help me out with this?

What is the greatest integer k for which \(32.45 × 10^k\) is less than 1 ?


a. –2

b. –1

c. 0

d. 1

e. 2


You know when we multiply \(10^k\) with any decimal number, the decimal point in the number moves k decimal places to the left(subject to k is a negative integer).
Since we need the product:- \(32.45 × 10^k <1\), we have to move the decimal point 2 places to the left so that we would get \(0.3245<1\).
Therefore, k=-2 .

Ans. (A)

P.S:- Kindly add OA.
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What is the greatest integer k for which 32.45 × 10^k is less than 1 ?  [#permalink]

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New post 12 Jul 2018, 16:09
Lisapizzola wrote:
Can someone help me out with this?

What is the greatest integer k for which \(32.45 × 10^k\) is less than 1 ?


a. –2

b. –1

c. 0

d. 1

e. 2



First of all, understand that the result has to be less than 1.

Given,

32.45 x \(10^k\). we are asked to find out the greatest integer k.

Note :

Scientific Notation is involved here in this question . To make a fraction integer we multiply and to make integer fraction we divide by \(10^x\).

In this question we are asked to make the result less than 1 means fraction . Thus we have to divide.

So only negative value will work here.

32.45 * 10^{-2}

0.3245 < 1.

Thus , A is the best answer. No other options meet our condition.
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What is the greatest integer k for which 32.45 × 10^k is less than 1 ?  [#permalink]

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New post 12 Jul 2018, 21:26
Lisapizzola wrote:
Can someone help me out with this?

What is the greatest integer k for which \(32.45 × 10^k\) is less than 1 ?

a. –2

b. –1

c. 0

d. 1

e. 2


Rule in exponents - \(10^x = \frac{1}{10^{-x}}\)

We need to find the greatest integer k such that \(32.45 × 10^k < 1\) -> \(\frac{32.45}{10^{-k}} < 1\)

This inequality becomes \(32.45 < 10^{-k}\) - Lowest value for inequality to hold good is k = -2

Therefore, the lower possible value for k such that \(32.45 × 10^k < 1\) is when k = -2(Option A)
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What is the greatest integer k for which 32.45 × 10^k is less than 1 ?  [#permalink]

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New post 12 Jul 2018, 21:41

Solution



Approach and Working:
• \(32.45*10^k<1\)
• \(32.45<\frac{1}{10^k}\)
• \(32.45<10^{-k}\)
o Since 32.45 is less than 100, \(10^{-k}= 10^2\)
o k=-2


Hence, the correct answer is option A.

Answer: A
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