The nearest star outside our solar system is approximately 4 x 10^13

We can approximate 380,000 km as 400,000 km.

\(4*10^5\) km is represented by \(1\)cm

\(4 * 10^{13}\) km is represented by \(\frac{1}{4*10^{5}} * 4*10^{13}\)

\(\frac{1}{4*10{5}} * 4*10^{13}\)

= \(10^{8}\) cms

We have to find the value in km

100 cm = 1m
1000 m = 1km

1km = 100 * 1000 cm

= \(\frac{10^{8}}{100 * 1000} = 10^{3}\) kms

Option C
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380000=\(3.8*10^5\)
All the choices are in power of 10, so 3.8 has been approximated as 4.

So \(4*10^5=1cm\)

Therefore, \(4*10^{13} \ \ or \ \ 4*10^5*10^8=10^8*(4*10^5)=10^8*(1cm)=10^8cm \)

But the answer is asked in km, so \(10^8cm = \frac{10^8}{10^2}m=10^6m=\frac{10^6}{10^3}km=10^3km\)

C
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The nearest star outside our solar system is approximately 4 x 10^13 kilometers (km) from Earth and our moon is approximately 380,000 km from Earth. If these distances were scaled down so that the distance from Earth to our moon was represented by 1 centimeter, then which of the following is closest to the scaled down distance, in kilometers, from Earth to the nearest star outside our solar system?

Given, 1 cm = 380,000 km as Representative Factor
Therefore The nearest star outside our solar system = (4 x 10^13/380,000) cm
= (4 x 10^13/380,000) cm
= (4 x 10^5 x 10^8/380,000) cm (Because 4 x 10^5/380,000 = 1 )
= (1 x 10^8) cm
= (1 x 10^8 x 10^-5) km (Because 1cm = 10^-5 km)
= 1000 Km

Hence C

If we denote the scaled down distance from Earth to Moon by 1 cm’, then we have the following unit conversion equation:

1 cm’ = 3.8 × 10⁵ km

In addition, we need to consider the following unit conversion equations as well:

1 m’ = 100 cm’
1 km’ = 1,000 m’

Now, we simply multiply 4 × 10¹³ km by the corresponding unit conversion factors until all unnecessary units of measurement cancel out.

(4 × 10¹³ km)(1 cm’/3.8 × 10⁵ km)(1 m’/10² cm’)(1 km’/10³ m’) =

= 4/3.8 × 10³ km’ ≈ 1 × 10³ km’ = 1,000 km’

Answer: C
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­Video solution here:

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Given: The nearest star outside our solar system is approximately 4 x 10^13 kilometers (km) from Earth and our moon is approximately 380,000 km from Earth.

Asked: If these distances were scaled down so that the distance from Earth to our moon was represented by 1 centimeter, then which of the following is closest to the scaled down distance, in kilometers, from Earth to the nearest star outside our solar system?

The ratio of 4 x 10^13 kilometers to 380,000 km = 4*10^13/380,000 = 4/3.8 * 10^8 = 10^8 approx
Centimeters in 1 km = 100000 = 10^5 cms

The scaled down distance, in kilometers, from Earth to the nearest star outside our solar system = 10^8/10^5 =  10^3 = 1000 km

IMO C­

­Hey JeffTargetTestPrep KarishmaB GMATCoachBen avigutman chetan2u manasp35 !

I found the same value but in a different /I think/ way and I'd like your opinion whether my method is valid.

We are told that we want to represent the distance between Earth and moon in 1cm=1/10^5 km which means that we have to adjust the current distance to satisfy this condition. That's why I went on " 4*(10^5) = x/(10^5) " which resulted in x = 4*(10^10). I plugged this into " 4*(10^13) = 4*(10^10)*y " and I found that y = the scaled down distance in km from Earth to star = 10^3 = 1.000

­Completely valid