Download Scientific Notation and The Speed of Light: Calculating Distances and Time of Radio Waves and more Lecture notes Science education in PDF only on Docsity! 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 100 10 ten 101 100 hundred 102 1000 thousand 103 10000 ten thousand 104 100000 hundred thousand 105 1000000 million 106 10000000 ten million 107 100000000 hundred million 108 1000000000 billion 109 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 108 meters per second. The standard symbol for the speed of light is c, so we can write: c = 3 x 108 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 108 meters per second Example Problem: How far does a radio wave travel in 5 minutes? t = 5 min = 5(60) = 300 s = 3 x 102 s c = 3 x 108 m/s d = ? m d = c t d = (3 x 108) (3 x 102) d = (3 x 3) x 108+2 d = 9 x 1010 m RULE: to multiply, MULTIPLY the numbers, ADD the powers of ten 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 108 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 108 m c = 3 x 108 m/s t = ? t = 1.33 x 100 (NOTE: 100 = 1) t = 1.33 s t = d c t = d c RULE: to divide, DIVIDE the numbers and SUBTRACT the powers of ten. (Subtract the bottom power from the top) t = 4 x 108 3 x 108 t = 4 3 x 108-8
