scientific notation

Question

The speed of light is 300,000,000 meters per second. The sun is approximately 1.5x10^11 meters from the earth. How many seconds dos it take for the sunlight to reach the earth.

Answer 1

Given: Speed of Light = 300,000,000 m/s

          Distance from Sun to Earth = 1.5 x 10^11 m

 

Question: How many seconds does it take for sunlight to reach Earth? 

In other words, you are looking for Time.

 

Use the following Equation from Physics:

Speed = Distance/Time

 

Manipulate the above eqn to solve for Time:

Time = Distance/Speed

 

Time (s) = (1.5 x10^11 m) / (300,000,000 m/s)

 

First, we need to change Speed of Light into scientific notation:

300,000,000 m/s = 3 x 100,000,000 m/s

                         = 3.0 x 10^(# of decimal places you moves to get 3.0)

                         = 3.0 x 10^8 m/s

 

scientific notation = coefficient x base ^ exponent

                             3.0 x 10^8

                             1.5 x 10^11

 

Return to our problem:

 

Time ( in seconds) = (1.5 x 10^11 m) / (3.0 x 10^8)

(you can divide the coefficients together and the base/exponents together)

(when you have same base of 10 and you are dividing numbers, you can subtract the exponents)

 

= (1.5/3.0) (10^11/10^8)

= (1/2) (10^ (11-8))

= 0.5 x 10^3 

(Recall, 0.5 = 5/10 = 5.0 x 10^-1)

= (5.0 x 10^-1) x 10^3

(when you have same base of 10 and you are multiplying numbers, you can add the exponents)

= 5.0 x 10^(-1+3)

= 5.0 x 10^2 s

 

Answer 2

This is a classic.  I love it! 

 

The problem's question is: "how many seconds does it take..." That's "time".  How are time, speed and distance related?

 

d = r x t  distance is equal to rate of speed multiplied by time.  Thus t = d ÷ r  This is the relationship we'll use to solve this problem.  Now, let's organize our data:

 

r = 300,000,000 m/s  Let's write this using scientific notation:

 

r = 3 x 10⁸ m/s

 

d = 1.5 x 10¹¹ m

 

t = d ÷ r  ⇒  t = 1.5 x 10¹¹ ÷ 3 x 10⁸  or:

 

t = .5 x 10³  That is: 500 seconds or about 8.3 minutes

 

Answer: the sunlight takes about 8 minutes and 20 seconds to reach earth.

 

Fun. Isn't it?