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POWER OF TEN CONVERTER HOW TO

Remember that this number should be a power of ten given by the number of spaces under the arrow you drew in the steps above. Converting from a large unit to a smaller unit means you should multiply your original measurement by the amount that its units differ from the desired final units. Thus, you know that there are 100,000 centimeters in 1 kilometer.įor "large to small" conversions, multiply by the appropriate power of ten. In other words, centimeters are 100,000 times (or 10 5, etc.) times smaller than kilometers. This means that kilometers and centimeters differ by a conversion factor of five powers of ten, also written as ten to the fifth power, 10 5, or 10 × 10 × 10 × 10 × 10 = 100,000.

For instance, in our 10-kilometer race example, we see that our arrow from "kilo" to "centi" jumps over five spaces.

The number of spaces under your arrow gives the power of ten by which your two units are related. Look at the arrow you've drawn from the units you have - the units your measurement has been taken in - to the units you want to convert to. Thus, converting from one metric unit to another is always accomplished by multiplying or dividing your initial measurement by the appropriate power of ten. Metric units of measurement differ by powers of 10 - 10, 100, 1,000, and so on. The first letter of each word corresponds to a basic metric prefix, in order of largest to smallest, except for the "U" in "Until", which corresponds to "unit," or the metric base units (meter, liter, etc.)ĭetermine the numerical relationship between the units you have and the units you want.

A handy trick for remembering the basic metric prefixes is the mnemonic "King Henry Died Until Drinking Chocolate Milk," (or, if you prefer, "King Henry Doesn't Usually Drink Chocolate Milk").

X Research source The most common of these prefixes, from "1,000 times larger" to "1,000 times smaller," are:

In these cases, we add prefixes to the name of the unit to signify how much bigger or smaller it is than the base unit. In these cases, it's necessary to use units that differ from the base units by a power of 10 - in other words, measurements that are 10 times larger or smaller, 100 times larger or smaller, and so on. These base units are sometimes either too small or too large to make practical measurements. The metric system has a variety of units of measurement - you have probably heard of meters (which measure distance) and grams (which measure mass), etc. Any opinions expressed on this website are entirely mine, and do not necessarily reflect the views of any of my employers.Learn the most common metric prefixes. All text and images on this website not specifically attributed to another source were created by me and I reserve all rights as to their use. Jeff Cruzan is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. It was a calculator shortcut developed at a time when most calculator users were engineers. Historical note: EE stands for Engineering Exponent. That's nice, but not completely necessary. Some calculators have a mode such that when you press something like EE 4, it will print 10 4. This calculator was not set up to use scientific notation for numbers in the 1000 range. Notice that the 3 rd result was displayed as 4613.333. On this calculator it's done using the button. You can set your calculator to display results in scientific notation if you'd like. See if you can follow the rest of those calculations. On the calculator shown here, EE is the 2nd function of the comma (, ) key.įour calculations – two multiplications and two divisions – have been entered and performed on this calculator.

Both are a shorthand for " times ten to the power of."įor example, if I want to enter 2.48 x 10 19, on the calculator on the left, I enter the sequence " 2.48 EE 19". On most calculators, we enter scientific notation using a button labeled EXP or EE. To move the decimal between the 2 and the 3, we'll need to move it five places to the left: This example is similar to the first, except that there is actually a decimal in the original number. Note that the number in scientific notation is really a kind of recipe for recovering our original number: "Take 1.2 and move the decimal 7 places to the right." When we're forming the scientific notation, the move is in the opposite direction, but that's only to form 1.2 x 10 7 in the first place. It's 1.2 with 6 zeros (the 7 th place is taken up by the 2): Now it's a simple matter to form the number in scientific notation. Now we simply count how many spaces from the right (the original decimal) that is: Example 1: 12,000,000įirst, there is an implicit (not shown but there) decimal after 12,000,000, and our goal is to put it after the 1 and before the 2: This is one of the tasks you may have to do most, so it's a good one to learn.

POWER OF TEN CONVERTER HOW TO

Here are a few examples of how to convert numbers, big and small, to scientific notation.