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The average distance between the Sun and a certain planet is approximately 2.3 x 10^14 inches. Which of the following is closest to the average distance between the Sun and the planet, in kilometers? (1 kilometer is approximately 3.9 x 10^4 inches.)

(A) 7.1 x 10^8 (B) 5.9 x 10^9 (C) 1.6 x 10^10 (D) 1.6 x 10^11 (E) 5.9 x 10^11

Practice Questions Question: 65 Page: 161 Difficulty: 650

The average distance between the Sun and a certain planet is approximately 2.3 x 10^14 inches. Which of the following is closest to the average distance between the Sun and the planet, in kilometers? (1 kilometer is approximately 3.9 x 10^4 inches.)

(A) 7.1 x 10^8 (B) 5.9 x 10^9 (C) 1.6 x 10^10 (D) 1.6 x 10^11 (E) 5.9 x 10^11

The distance in kilometers would be: \(\frac{2.3*10^{14}}{3.9*10^4}\approx{\frac{23*10^{13}}{4*10^4}}\approx{6*10^9}\).

Re: The average distance between the Sun and a certain planet is [#permalink]

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15 Oct 2012, 04:42

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Distance between the Sun and a certain planet in Inches = 2.3 x 10^14 1 kilometer = 3.9 x 10^4 inches Distance between the Sun and a certain planet in Km = (2.3 x 10^14)/ (3.9 x 10^4) = \((23/39) * 10^10\) = \((230/39) * 10^9\) = \(5.9 * 10^9\)

Answer B
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Re: The average distance between the Sun and a certain planet is [#permalink]

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15 Oct 2012, 05:04

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Good question.

I took \(2.3 x 10^14\)and rounded down to \(2*10^14\), and took \(3.9*10^4\) and rounded up to \(4*10^4\).

Then, I did a unit conversion from Inches to Kilometers: \((2*10^14 Inches) * (\frac{1 Kilometer}{(4*10^4 Inches)})\)

Canceling out, we get \(\frac{(2*10^14 Inches)}{(4*10^4 Inches)}*1 Kilometer = 0.5*10^10 Kilometer\) or \(5*10^9 Kilometers\)

Since we rounded to begin with, we have to look for the solution that is both closest to our answer AND makes the most sense. In this case, the answer is

The average distance between the Sun and a certain planet is approximately 2.3 x 10^14 inches. Which of the following is closest to the average distance between the Sun and the planet, in kilometers? (1 kilometer is approximately 3.9 x 10^4 inches.)

(A) 7.1 x 10^8 (B) 5.9 x 10^9 (e) 1.6 x 10^10 (0) 1.6 x 10^11 (E) 5.9 x 10^11

Practice Questions Question: 65 Page: 161 Difficulty: 650

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Re: The average distance between the Sun and a certain planet is [#permalink]

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22 Oct 2012, 09:04

Bro Bunuel, I wonder who you are and BB also declared you as the mystery man.. but you are doing an awesome job out here! thank you for all your help. My Question is

what if 6.1 x 10^9 is also one of the answer choices? what will your approach be in this case?
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Re: The average distance between the Sun and a certain planet is [#permalink]

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11 Sep 2014, 01:27

Bunuel wrote:

The average distance between the Sun and a certain planet is approximately 2.3 x 10^14 inches. Which of the following is closest to the average distance between the Sun and the planet, in kilometers? (1 kilometer is approximately 3.9 x 10^4 inches.)

(A) 7.1 x 10^8 (B) 5.9 x 10^9 (C) 1.6 x 10^10 (D) 1.6 x 10^11 (E) 5.9 x 10^11

Practice Questions Question: 65 Page: 161 Difficulty: 650

The average distance between the Sun and a certain planet is [#permalink]

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25 Oct 2015, 18:02

schelljo wrote:

Will someone please help me explain how you get from \(\frac{6}{10}*10^9\) to the answer.

Thanks!

You are given that the distance is \(2.3*10^{14}\) inches. You need to convert this into equivalent distance in kilometers with the relation given as 1 km = \(3.9*10^4\) inches

Thus, by unitary method, if \(3.9*10^4\) inches equals 1 km, then \(2.3*10^{14}\) inches will equal = \(\frac{2.3*10^{14}}{3.9*10^4}\)

You can now assume \(2.3 \approx 2.4\) and \(3.9 \approx 4.0\) to make both the numbers divisible by a common factor (4 in this case).

The average distance between the Sun and a certain planet is approximately 2.3 x 10^14 inches. Which of the following is closest to the average distance between the Sun and the planet, in kilometers? (1 kilometer is approximately 3.9 x 10^4 inches.)

(A) 7.1 x 10^8 (B) 5.9 x 10^9 (C) 1.6 x 10^10 (D) 1.6 x 10^11 (E) 5.9 x 10^11

Practice Questions Question: 65 Page: 161 Difficulty: 650

This problem is a unit conversion with an added twist of scientific notation. We need to convert 2.3 x 10^14 inches to KILOMETERS. We are given that 1 kilometer is approximately 3.9 X 10^4 inches. We also should recognize that we are being asked which of the following is CLOSEST to the average distance between the Sun and the planet, in Kilometers. Because we are being asked for an approximation, we can use some estimation here.

To convert 2.3 x 10^14 inches to kilometers, we need to multiply 2.3 x 10^14 inches by the ratio of:

1 km/(3.9 x 10^4 inches)

However, before doing this multiplication, it will make things easier to clean up each scientific notation expression. Let’s start with 2.3 x 10^14 inches.

2.3 x 10^14 inches

is equivalent to

23 x 10^13 inches

Notice that because we turn 2.3 into 23, or move the decimal one place to the right, we have to then turn 10^14 into 10^13, or move the decimal one place to the LEFT to “counterbalance” the fact that we’ve moved the decimal one place to the right for 2.3.

Next we can adjust 3.9 x 10^4 inches. However, we can simply round this value up to 4 x 10^4 inches.

Since we’ve rounded 3.9 up to 4, let’s round 23 up to 24 also. That is, we are converting 24 x 10^13 inches into kilometers given that 1 km is approximately 4 x 10^4 inches:

(24 x 10^13 inches) x 1 km/(4 x 10^4 inches)

(24 x 10^13)/(4 x 10^4) km

We can break this work up into two separate calculations:

1) 24/4 = 6

2) 10^13/10^4 = 10^9

Thus, our answer is about 6 x 10^9 km.

We see that the closest answer is B.
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Re: The average distance between the Sun and a certain planet is [#permalink]

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25 Oct 2017, 07:56

Bunuel wrote:

The average distance between the Sun and a certain planet is approximately 2.3 x 10^14 inches. Which of the following is closest to the average distance between the Sun and the planet, in kilometers? (1 kilometer is approximately 3.9 x 10^4 inches.)

(A) 7.1 x 10^8 (B) 5.9 x 10^9 (C) 1.6 x 10^10 (D) 1.6 x 10^11 (E) 5.9 x 10^11

Practice Questions Question: 65 Page: 161 Difficulty: 650

Re: The average distance between the Sun and a certain planet is [#permalink]

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10 Nov 2017, 11:42

Bunuel wrote:

SOLUTION

The average distance between the Sun and a certain planet is approximately 2.3 x 10^14 inches. Which of the following is closest to the average distance between the Sun and the planet, in kilometers? (1 kilometer is approximately 3.9 x 10^4 inches.)

(A) 7.1 x 10^8 (B) 5.9 x 10^9 (C) 1.6 x 10^10 (D) 1.6 x 10^11 (E) 5.9 x 10^11

The distance in kilometers would be: \(\frac{2.3*10^{14}}{3.9*10^4}\approx{\frac{23*10^{13}}{4*10^4}}\approx{6*10^9}\).

Answer: B.

Bunuel hello, can you please explain how and why did you round 10^14 to 10^13 ...there no decimals to round this number ... thanks!

The average distance between the Sun and a certain planet is approximately 2.3 x 10^14 inches. Which of the following is closest to the average distance between the Sun and the planet, in kilometers? (1 kilometer is approximately 3.9 x 10^4 inches.)

(A) 7.1 x 10^8 (B) 5.9 x 10^9 (C) 1.6 x 10^10 (D) 1.6 x 10^11 (E) 5.9 x 10^11

The distance in kilometers would be: \(\frac{2.3*10^{14}}{3.9*10^4}\approx{\frac{23*10^{13}}{4*10^4}}\approx{6*10^9}\).

Answer: B.

Bunuel hello, can you please explain how and why did you round 10^14 to 10^13 ...there no decimals to round this number ... thanks!

\(2.3*10^{14}=2.3*10*10^{13}=23*10^{13}\). It's done to transform 2.3 to integer 23.
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