# National Aeronautics and Space Administration

## Black Holes - Page 17

SCIENTIFIC NOTABLES - LEVEL 2

The following activity is designed as practice with the use of scientific notation.

Working with large numbers such as galactic distances can be very time consuming. It is often more useful to express large numbers in terms of powers of 10 known as scientific notation.

Example: 1,000,000 = 1.0x106 (106 means 10x10x10x10x10x10 =1,000,000)

Notice that the decimal place has been moved 6 places to the left leaving only 1 number in front of the decimal.

1. The Sun is 150,000,000 kilometers from Earth. Convert 150,000,000 into scientific notation.

2. One light-year equals 9,500,000,000,000 kilometers. Convert 9,500,000,000,000 into scientific notation.

Any number less than 1 can also be converted into scientific notation. This time the decimal is moved to the right and the exponent becomes negative.

Example: .053 = 5.3x10-2 (10-2 means .1x.1 = .01, .01x5.3 = .053)

Notice the decimal was moved two places to the right.

1. The diameter of a singularity is .000000000000000000000000000000001 centimeters. Convert this value into scientific notation.

2. The average wavelength of an ultraviolet ray is 600 nanometers. Convert this to millimeters and then place the value in scientific notation. (1 nanometer = .000001 millimeters)

To add or subtract numbers in scientific notation, the numbers must all be written to the same power of 10.

 Example: 2.6x103 is the same as 2.6x103 +0.2x104-------- +2.0x103-------- 4.6x103
1. Jupiter is 778.3 million kilometers from the Sun. Saturn is 1.429 billion kilometers from the Sun. Place these numbers in scientific notation and determine the minimum distance from Jupiter to Saturn.

2. Billions of years ago, colliding or merging stars may have resulted in the formation of supermassive black holes. If a star with a mass of 65 million Suns merged with a star that had a mass of 1.5 billion Suns, what would be the combined mass involved in the merger? Place all numbers in scientific notation prior to performing the necessary operation.

When multiplying, the powers of 10 are added together.

Example: (3x103)(2x104) = 6x107