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If 0.018*10^r/0.0003*10^w=6*10^7, the r-w=

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Carcass
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If 0.018*10^r/0.0003*10^w=6*10^7, the r-w= [#permalink] New post   02 Sep 2021, 09:50
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If \(\frac{0.018*10^r}{0.0003*10^w}=6*10^7\), the \(r-w=
\)

(A) 6
(B) 7
(C) 8
(D) 9
(E) 15
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A
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GreenlightTestPrep
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Re: If 0.018*10^r/0.0003*10^w=6*10^7, the r-w= [#permalink] New post   02 Sep 2021, 10:11
Carcass wrote:
If \(\frac{0.018*10^r}{0.0003*10^w}=6*10^7\), the \(r-w=
\)

(A) 6
(B) 7
(C) 8
(D) 9
(E) 15


Useful property: \(\frac{AB}{CD}=(\frac{A}{C})(\frac{B}{D})\)

Given: \(\frac{0.018*10^r}{0.0003*10^w}=6*10^7\)

Apply the above property to get: \((\frac{0.018}{0.0003})(\frac{10^r}{10^w})=6*10^7\)

Simplify both fractions: \((60)(10^{r-w})=6*10^7\)

Divide both sides of the equation by \(6\) to get: \((10)(10^{r-w})=10^7\)

Divide both sides of the equation by \(10\) to get: \(10^{r-w}=10^6\)

Since both sides of the equation have the same base, the exponents must be equal: \(r-w=6\)

Answer: A
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godxyz
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Re: If 0.018*10^r/0.0003*10^w=6*10^7, the r-w= [#permalink] New post   03 Sep 2021, 23:18
GreenlightTestPrep wrote:
Carcass wrote:
If \(\frac{0.018*10^r}{0.0003*10^w}=6*10^7\), the \(r-w=
\)

(A) 6
(B) 7
(C) 8
(D) 9
(E) 15


Useful property: \(\frac{AB}{CD}=(\frac{A}{C})(\frac{B}{D})\)

Given: \(\frac{0.018*10^r}{0.0003*10^w}=6*10^7\)

Apply the above property to get: \((\frac{0.018}{0.0003})(\frac{10^r}{10^w})=6*10^7\)

Simplify both fractions: \((60)(10^{r-w})=6*10^7\)

Divide both sides of the equation by \(6\) to get: \((10)(10^{r-w})=10^7\)

Divide both sides of the equation by \(10\) to get: \(10^{r-w}=10^6\)

Since both sides of the equation have the same base, the exponents must be equal: \(r-w=6\)

Answer: A


GreenlightTestPrep
Hi sir,

In the Simplify both fractions step, shouldn't it be 0.6 instead of 60. I'm getting the answer as 8.

Thanks in advance!
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GreenlightTestPrep
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If 0.018*10^r/0.0003*10^w=6*10^7, the r-w= [#permalink] New post   04 Sep 2021, 06:33
1
godxyz wrote:
GreenlightTestPrep
Hi sir,

In the Simplify both fractions step, shouldn't it be 0.6 instead of 60. I'm getting the answer as 8.

Thanks in advance!


In that part, I'm saying that \(\frac{0.018}{0.0003} = 60\)
One option is to use your on-screen calculator to verify.

Another option is to create an equivalent (and easier to evaluate) fraction and multiplying numerator and denominator by the same value.
Notice that, if we multiply the numerator and denominator by 10,000, we get integer values for the numerator and denominator.
Let's see what happens....

\(\frac{0.018(10,000)}{0.0003(10,000)} = \frac{180}{3}=60\)

Does that help?
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godxyz
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Re: If 0.018*10^r/0.0003*10^w=6*10^7, the r-w= [#permalink] New post   04 Sep 2021, 06:42
1
GreenlightTestPrep wrote:
godxyz wrote:
GreenlightTestPrep
Hi sir,

In the Simplify both fractions step, shouldn't it be 0.6 instead of 60. I'm getting the answer as 8.

Thanks in advance!


In that part, I'm saying that \(\frac{0.018}{0.0003} = 60\)
One option is to use your on-screen calculator to verify.

Another option is to create an equivalent (and easier to evaluate) fraction and multiplying numerator and denominator by the same value.
Notice that, if we multiply the numerator and denominator by 10,000, we get integer values for the numerator and denominator.
Let's see what happens....

\(\frac{0.018(10,000)}{0.0003(10,000)} = \frac{180}{3}=60\)

Does that help?


Ah, yes sir. Sorry my bad!

Thank you for your response!
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Re: If 0.018*10^r/0.0003*10^w=6*10^7, the r-w= [#permalink]
04 Sep 2021, 06:42
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