Is this correct, please help?

Question

Alkaid, the most distant star in the Big Dipper, is 2.1 X 10^18m from the Earth. Approximately how long does it take light to travel from Alkaid to the Earth?

I took 10^18 which gave me 1,000,000,000,000,000,000... I timed this by 2.1 which gave me 2100000000000000000 Then I expressed it in scientific notation which gave me 2.1X17^18. Is this right??? The other answer that I got was 630880.79..Please help

Answer 1

Actually, you don't need to multiply out your number and then reduce it back to scientific notation. In doing so, you just made a mistake when you changed the 10^18 to be 17^18 and you end up back at the starting point (almost).

Instead, take the total distance:
You have the distance already expressed in scientific notation. 2.1 x 10^18m

Now take the distance light travels in a year:
Light travels 9.46 × 10^15m in a year (this is the length of a light year).

Divide the total distance by the length of a light year to get your answer in years.

2.1 x 10^18 ..... 2.1 x 10^3
------------------ = ---------------
9.46 x 10^15 ........ 9.46

= 2.1 / 9.46 x 1000
= 0.221987 x 1000
≈ 221.987 years

Rounding, the answer is approximately 222 years.

You could take the speed of light in meters/second, divide this into your distance to get time. But then you would have to convert seconds into a resonable number, like years. In doing so, be careful because the year has an average length of around 365.2421 rather than 365.

Answer 2

I am a math wiz... lol but im not a geek
the first one was right cuz 10^18 is 1 with 18 0's wich makes 1000000000000000000 right, then 2.1 is just 2.1instead of 1 and 1 of the 0's so it does 21 and 17 0's. And yes with the 2.1 and the 17 0's 2.1X17^18 in scientific notation with the base and the exponent is correct.

Answer 3

2.1X10^18 is right
Light travels at 186000 miles/ sec. (close enough for
government work).
Assuming your units m means miles,
2.1X10^18 /1.86 X 10^5=1.129 X 10^(18-5)
=1.129X10^13 seconds
Seconds/yr=3600/hr X 24 hr/day X 365 days /year
=3.154X10^7 seconds
1.129x10^13 / 3.154X10^7=0.358X10^6 years
=358000 years

Note: if your "m" is really meters, then
1.6093X10^3m = 1 mile
2.1X10^18 / 1.6093X10^3 = 1.3049X10^15 miles
1.3049X10^15 / 1.86X10^5=0.7016X10^10 seconds
0,7016X10^10 /3.154X10^7=0.2224X10^3 years
That's 222.4 years

Seems more realistic to me. I guess you meant
meters after all!

Answer 4

Light travels 9,460,730,472,580,800m per light year
(2.1∙10¹⁸m)(1ly/ 9,460,730,472,580,800m)
≅ (2.1∙10¹⁵∙10³m)(1ly/9.46∙10¹⁵m)
= (2.1/9.46)∙10³ly
=0.22198*10³
= 221.08 light years

Answer 5

speed of light is 299,792,458 meters/sec
take 2.1x10^18 and divide by this and get
7,004,845,999 seconds
divide by 3600 to get 1945790.555hours
divide by 24 to get 81074.60647 days
divide by 365 to get 222.1222095 years

Answer 6

yes,you are correct because all the answers i checked on the calculator.they were all correct

Answer 7

Yes it is correct