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

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Intern
Joined: 01 Jul 2017
Posts: 3
What is the greatest integer k for which 32.45 × 10^k is less than 1 ?  [#permalink]

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Updated on: 12 Jul 2018, 13:06
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Question Stats:

92% (00:35) correct 8% (00:40) wrong based on 53 sessions

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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, 11:37.
Last edited by Lisapizzola on 12 Jul 2018, 13:06, 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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12 Jul 2018, 12:43
1
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)

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Joined: 31 Oct 2013
Posts: 571
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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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12 Jul 2018, 17:09
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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12 Jul 2018, 22:26
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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Joined: 04 Jan 2015
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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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12 Jul 2018, 22:41

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.

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What is the greatest integer k for which 32.45 × 10^k is less than 1 ? &nbs [#permalink] 12 Jul 2018, 22:41
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