**ACTIVITY 1-1 Scientific Notation and The Speed of Light**

Radio waves, like all electromagnetic waves, travel at the speed of
light -- 300 000 000 meters per second (3 hundred million meters per
second). The speed of light is obviously a large number. In working with
this number, and other large numbers, it is convenient to express it in
**scientific notation**. In scientific notation, powers of ten are used
to represent the zeroes in large numbers. The following table shows how
this is done.

  ------------------- --------------------------- -----------------------
  Number              Name                        Power of ten

  1                   one                         10^0^

  10                  ten                         10^1^

  100                 hundred                     10^2^

  1000                thousand                    10^3^

  10000               ten thousand                10^4^

  100000              hundred thousand            10^5^

  1000000             million                     10^6^

  10000000            ten million                 10^7^

  100000000           hundred million             10^8^

  1000000000          billion                     10^9^
  ------------------- --------------------------- -----------------------

If you examine the first and last columns, you can see that the power of
ten is the same as the number of zeroes in the number. So the speed of
light, which is 3 followed by 8 zeroes, becomes 3 x 10^8^ meters per
second. The standard symbol for the speed of light is **c**, so we can
write:

c = 3 x 10^8^ m/s

Since radio waves travel at a constant speed, the distance traveled is
given by:

distance = speed times time

or d = c t

where d = distance in meters

t = time in seconds

c = 3 x 10^8^ meters per second

Example Problem: How far does a radio wave travel in 5 minutes?

t = 5 min = 5(60) = 300 s = 3 x 10^2^ s

c = 3 x 10^8^ m/s

d = ? m

d = c t

d = (3 x 10^8^) (3 x 10^2^)

d = (3 x 3) x 10^8+2^

d = 9 x 10^10^ m

Problems:

1.  How far does light travel in 20 seconds?

2.  How far does light travel in 30 minutes?

3.  How far does light travel in 4 hours?

4.  How far does light travel in 2 days?

If you know the distance and the speed (c), you can find the time it
takes for radio waves to travel that distance using:

d = c t

where d = distance in meters (m)

c = speed of light (3 x 10^8^ m/s)

t = time in seconds (s)

Example Problem: How long does it take radio waves to travel from Earth
to the moon, a

> distance of 400 000 kilometers?

d = 400 000 km = 400 000 000 m = 4 x 10^8^ m

c = 3 x 10^8^ m/s

t = ?

t = 1.33 x 10^0^ (NOTE: 10^0^ = 1)

t = 1.33 s

Example Problem: How long does it take radio waves to travel Mars to
Earth when Earth

> and Mars are on the same side of the sun?

For this problem, we will be working with large numbers that have
several non-zero digits. In this case, the power of ten indicates how
many places to move the decimal to the right rather than the number of
zeroes to add. We will also round off the values so that there are only
three nonzero digits with one digit to the left of the decimal. This is
called **standard form**.

radius of Mars' orbit R~M~ = 227, 940,000 km = 2.28 x 10^8^ km = 2.28 x
10^11^ m

radius of Earth's orbit R~E~ = 149,600,000 km = 1.50 x 10^8^ km = 1.50 x
10^11^ m

d = R~M~ - R~E~

d = 2.28 x 10^11^ - 1.50 x 10^11^

d = 2.28 -- 1.50 x 10^11^

d = .78 x 10^11^

d = 7.8 x 10^10^ m (NOTE: standard form)

t = 2.6 x 10^10-8^ = 2.6 x 10^2^

t = 260 s (4 minutes 20 seconds)

Use the following table for Problems 5-8.

  ---------------------------- ------------------------------------------
  Planet                       Radius of orbit

  Mercury                      57,910,000 km

  Venus                        108,200,000 km

  Earth                        149,600,000 km

  Mars                         227,940,000 km

  Jupiter                      778,330,000 km

  Saturn                       1,429,400,000 km
  ---------------------------- ------------------------------------------

In the following problems, assume that the planets are on the same side
of the sun (as close to one another as possible).

Problems:

5.  How long would it take radio waves to travel from Jupiter to Mars?

6.  How long would it take radio waves to travel from Jupiter to Venus?

On these last two problems, be careful when you subtract the distances
that they have the same power of ten. (HINT: one distance will not be in
standard form.)

7.  How long would it take radio waves to travel from Jupiter to Saturn?

8.  How long would it take radio waves to travel from Mercury to Mars?

Answer key for Activity 1.

1\. 6 x 10^9^ m

2\. 5.4 x 10^11^ m

3\. 4.32 x 10^12^ m

4\. 5.18 x 10^13^ m

5\. 1.83 x 10^3^ s (30.6 minutes)

6\. 2.23 x 10^3^ s (37 minutes)

7\. 2.17 x 10^3^ s (36 minutes)

8\. 5.6 x 10^2^ s (9.4 minutes)