When you are working with very large or small quantities of things, writing and saying those numbers can be tedious. Scientific notation and metric prefixes offer a convenient and shorter way of representing those numbers, and we'll be using these methods and abbreviations throughout the rest of the articles here. Don't worry - the math isn't complicated. If you can multiply and divide by ten, you'll master these important tools in no time.
The table below contains the most important prefixes and their corresponding scientific notation, along with examples of numbers and units you are likely to see on the rest of the website. We'll explain how to use them below.
|Prefix||Scientific Notation||Plain English||Regular Notation||Metric Prefix or Scientific Notation|
|Giga (G)||109||Billion||1,000,000,000 Hz||1 Gigahertz (GHz) or 1 x 109 Hz|
|Mega (M)||106||Million||3,000,000 Hz||3 Megahertz (MHz) or 3 x 106 Hz|
|Kilo (k)||103||Thousand||5,000 meters||5 kilometers (km) or 5 x 103 m|
|None||100||None||9 seconds||9 seconds|
|Milli (m)||10-3||One thousandth||0.007 Volts||7 millivolts (mV) or 7 x 10-3 Volts|
|Micro (μ)||10-6||One millionth||0.000006 meters||6 micrometers or 6 x 10-6 meters|
Here's how scientific notation works: 101 means you multiply a number by ten once. For example, 3 x 101 is just another way of writing 30. 102 means you multiply a number by ten twice: 3 x 102 is just 3 x 10 x 10, or 3 x 100, which is 300. For numbers with a negative power, like 10-1, you divide by ten instead of multiplying. The exponent (the small number written above the ten) tells you how many times you divide by ten. For example, 3 x 10-1 means 3/10, or 0.3. 3 x 10-2 means divide 3 by ten two times, so you get 0.03.
If you need to convert a number greater than one to scientific notation, just follow these steps.
- Step One - Put a decimal point immediately after the first digit.
- Step Two - Count how many digits come after the decimal point. This will be the exponent that you attach to the number 10. Then, multiply the decimal number by this power of ten.
- Step Three - Erase any zeros that come after the decimal point.
Example: Convert 3,500,000 to scientific notation.
Step One - We place a decimal after the first digit, and we get 3.500000.
Step Two - We count the number of digits after the decimal place. We get six. Next, we take this number and turn it into a power of ten - 106. Then, we multiply our decimal number and power of ten, and we get 3.500000 x 106.
Step Three - We erase all the unnecessary zeros in the decimal number. This gives us the correct answer - 3.5 x 106.
If you have a number that is less than 1, you follow the same steps, but in a slightly different order.
- Step One - First, count digits to the right of the decimal place, and stop after you reach the first non-zero digit. Remember this number - it's the exponent you will need later.
- Step Two - Move the decimal point to the right of the first non-zero digit.
- Step Three - Erase all of the zeros to the left of the decimal point, and multiply by 10 raised to the correct power. Make sure you include the negative sign in the exponent!
Example: Convert 0.0045 to scientific notation.
Step One - We start at the decimal place and count right, stopping after our first non-zero digit. We should end up with 3 (0,0,4).
Step Two - We move the decimal point between the 4 and 5, which gives us 0004.5.
Step Three - We erase all the unnecessary zeros, and multiply by 10-3. We now have the correct answer: 4.5 x 10-3.
Scientific notation makes writing numbers easier, but they can still be a mouthful - saying "3.5 times ten to the ninth" is just as hard as saying "three billion five hundred million." This is where the metric prefixes come in handy - the prefixes tell you how the number is written in scientific notation. If you say 3.5 Gigahertz (or write 3.5 GHz), it just means 3.5 x 109 Hz. Pay close attention to the difference between mega (M) and milli (m) - they mean very different things!
If this is your first time learning this material, don't be afraid to ask questions! Send us an e-mail or post on the forum and we'll be happy to help you understand.