Can someone help me with this math problem? related to scientific notations.

Question

Write each answer in scientific notation.

1. A light year is the distance light travels in one year. If the speed of light is about 3 x 10^5 km/s, how long is a light-year in kilometers? (Use 365 days for the length of a year.)

2. A spherical cell has a radius of 2.75 x 10^ -6 m. Use the formula for the surface area of a sphere SA = 4πR^2 (four pi radius squared) to find the surface area of a cell.

thank you.

Answer 1

1. There are 365*24*60*60 = 31,536,000 seconds/year

   = 3.1536x10^7 seconds/year

So: a light-year light travels would be:

(3.1536x10^7s/yr)(3x10^5km/s)= 9.4608x10^12 km/yr

2. Since R = 2.75 x 10^-6 m, then

The surface area is

  SA = 4πR^2

  SA = 4(3.1416)(2.75 x 10^-6)^2 m^2     (use π = 3.1416)

  SA = 12.5664 x (2.75)^2 x (10^-6)^2 m^2

  SA =  12.5664 x 7.5625 x 10^-12 m^2

  SA = 95.0334 x 10^-12 m^2  

  SA = 9.50334 x 10^+1 x 10^-12 m^2

  SA = 9.50334 x 10^-11 m^2

Answer 2

first, find the number of seconds in one years:

365 days = 24(365) hours = 60(24)(365) minutes = 60(60)(24)(365) seconds

this gets multiplied by the speed of light (remember, rate x time = distance)

(3)(10^5)(60)(60)(24)(365) = 94608000x10^5 = 9.4608 x 10^12

that's it for #1.

for #2,

SA = 4πr² = 4π(2.75)²(10^-6)²= 4π(7.5625)(10^-12)

= approximately 95.0332(10^-12) = 9.50332 x 10^-11

that's it! ;)

Answer 3

I need to know EXACTLY how "about 3 x 10^5 km/s" is written. It pertains to the number of significant figures in the answer. Scientific notation is the easy part.

Anyway it is easiest to do by dimensional analysis.

3.0 x 10^5 km / 1 sec. x 60 sec. / 1 min. x 60 min / 1 hr. x

24 hrs. / 1 day x 365 days / 1 yr.

It is not possible to write it the way I would by hand, but if you do it yourself by the numerator directly over the denominator and putting the "fraction" line between them the it will be more clear. Multiply all of the top numbers and put them on the top. If any of the numbers on the bottom were something other than 1 you would multiply them as well, but you know 1x1x1x1x1=1 already.

I am not sure how familiar with dimensional analysis you are, but when there is a unit of measurement in the denominator, for example "sec.", and also in the numerator in the following fraction, you cancel that unit on measurement. In this case you will cancel sec.,min., hr.,, and day. This will leave km / yr, which is the units of measurement you need your answer in.

If you are unsure how to write out 3 x 10^5, you simply move the decimal point five places to the left, but since you didn't put one in you can assume it is right next to the three.

You should be able to figure out the rest.

2) In this problem since the radius is 2.75 x 10^-6 or

0.00000275 m, the equation you will start with is:

surface area = 4(pie)r^2

All you need to do is substitute 0.00000275 into the equation and you are done: 4 x pie x (0.00000275)^2