MATH BASICS REVIEW

Exponents

Common Ones

Mega- 106- 1 million

Kilo- 103- 1 thousand (example: 1 kilometer = 1000 meters)

Deci- 10-1- 1 tenth (example: 1 decimeter = 0.1 meter)

Centi- 10-2- 1 hundreth (example: 1 centimeter = 0.01 meter)

Milli- 10-3- 1 thousandth (example: 1 millimeter = 0.001 meter)

Micro- 10-6- 1 millionth (example: 1 micrometer = 0.

How do you convert something to scientific notation?

EX 1] 600

First, count the number of places (include zeroes) until there is a number that is greater than 1 and smaller than 10, and put the decimal there.

For example:

6.00 (the decimal would be placed between the 6 and 0, because 6 is greater than 1, but less than 10. 60 is greater than 10, and so would not be appropriate.)

Second, count the zeroes that follow. This will be the exponent.

For example:

There are 2 zeroes that follow after the decimal. Therefore, to convert to scientific notation, the answer would be 6.00 x 102. You can see that this makes sense because 10 squared is 100, multiplied by 6 is 600, which is the original number we were trying to convert.

EX 2] 525,000,000

The decimal would be 5.25000000

There are 8 numbers following the end of the decimal so the exponent is 8

Scientific notation would therefore be 5.25 x 108

How do you work with exponents?

Just a few simple rules:

If you are multiplying two numbers, the exponents get added.

EX] 104 x 107 = 1011

If you are dividing two numbers, the exponents get subtracted.

EX] 104 ÷ 107 = 103

If you are adding or subtracting two numbers, the exponents must be the same.

EX] 6.0 x 103 must be transformed to 60 x 102 in order to add it to 2.0 x 102, giving you 62 x 102. Then you should covert the number so that there is only one digit preceding the decimal point: 6.2 x 103.

Conversions

A few things to remember that help with conversions:

  • Write out units whenever applicable
  • Take note of whatever is given and whatever you know
  • Always keep in mind the units that are asked for and you are ultimately trying to get to
  • As you work from left to right, make sure the same units are on the top and bottom of consecutive fractions (so they cancel)

EX] How many hours are in a calendar year?

24 hours x 365 days = 8,760 hours/year

1 day year

Because the units of days cancel, the units that you get are hours/year, which is what the question is asking. This is a simplified example, but the principle is the same.