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# If the units digit of 5,610.37/10^k is 6, what is the value of k?

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Re: If the units digit of 5,610.37/10^k is 6, what is the value of k? [#permalink]
Since the Denominator is 10 raised to power k
From identity of exponents number raised to power of 10 in denominator , the decimal points shifted towards left of the numerator
Similarly, if multiplied by 10 raised to some number, the decimal point shifted towards right.
So answer is (B)=2
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Re: If the units digit of 5,610.37/10^k is 6, what is the value of k? [#permalink]
gmatt1476 wrote:
If the units digit of $$\frac{5,610.37}{10^k}$$ is 6, what is the value of k?

(A) 3
(B) 2
(C) 1
(D) -1
(E) -2

PS81711.02

Without doing any math, since we are told of unit digit which we will get if the decimal point was moved 2 spaces to the left. Thus the answer should be B - 2 .
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If the units digit of 5,610.37/10^k is 6, what is the value of k? [#permalink]
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gmatt1476 wrote:
If the units digit of $$\frac{5,610.37}{10^k}$$ is 6, what is the value of k?

(A) 3
(B) 2
(C) 1
(D) -1
(E) -2

PS81711.02

we can re write the expression $$\frac{5,610.37}{10^k}$$
$$\frac{5,61037}{10^ (k+2)}$$
since unit digit we get is 6 ; so k has to be 2
OPTION B ; 2
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Re: If the units digit of 5,610.37/10^k is 6, what is the value of k? [#permalink]
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gmatt1476 wrote:
If the units digit of $$\frac{5,610.37}{10^k}$$ is 6, what is the value of k?

(A) 3
(B) 2
(C) 1
(D) -1
(E) -2

If we move the decimal point of 5610.37 two places to the left, then the resulting number will be 56.1037, which has a units digit of 6.

We see that if k = 2, then 5610.37 / 10^2 = 56.1037 has a units digit of 6. So k must be 2.

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Re: If the units digit of 5,610.37/10^k is 6, what is the value of k? [#permalink]
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This is a simple question.

If the decimal has to be right next to 6. Then the decimal has to shift left. If the decimal has to shift left then the value of k has to be negative.

In this option D and option E are eliminated.

If you observe the decimal has to shift left twice, in that case the value of k has to be negative 2.

OR

If we have to solve mathematically

5610.37 x $$10^{-k}$$ = 56.1037

$$\frac{561037}{100}$$ x $$10^{-k}$$ = $$\frac{561037}{10000}$$

$$10^{-k}$$ = $$\frac{1}{100}$$

$$10^{-k}$$ = $$10^{-2}$$

therefore -k = -2 => k = 2
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Re: If the units digit of 5,610.37/10^k is 6, what is the value of k? [#permalink]
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gmatt1476 wrote:
If the units digit of $$\frac{5,610.37}{10^k}$$ is 6, what is the value of k?

(A) 3
(B) 2
(C) 1
(D) -1
(E) -2

PS81711.02

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Re: If the units digit of 5,610.37/10^k is 6, what is the value of k? [#permalink]
Hi Experts, sorry to ask, but is there an article where I can learn/cram everything related to powers of 10? I always find it confusing while dealing with powers 10. For example: When moving decimal to right or left, power of 10 should be + or -. Similarly, while writing 1000000 into powers of 10, is 1 counted in the integer number of power of 10.

I know this is basic but I always get confused and writing down everything always take sometime. I know the logic but it takes me time to think and apply.

Bunuel GMATinsight ScottTargetTestPrep
Re: If the units digit of 5,610.37/10^k is 6, what is the value of k? [#permalink]
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