The metric system is a complete system of measurements that is currently used throughout the world. One of the main advantages that the metric system offers is that the conversion between its units is simple and logical, since they are on a scale of powers of 10. Because of this, converting within metric measurements is generally as easy as multiplying or dividing a given measurement by a power of 10 to find the new value, or as a shortcut, simply moving the decimal point. Below you will find detailed instructions.
Method 1 of 2: Converting through Multiplication and Division
Step 1. Learn the most common metric prefixes
The metric system has several units of measurement and you have probably heard of meters (which measure distance) and grams (which measure mass), etc. These base units are sometimes too small or too large for practical measurements. In these cases, it is 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. In these cases, prefixes are added to the unit name to represent how larger or smaller it is than the base unit. The most common prefixes, from "1000 times bigger" to "1000 times smaller" are:
- Kilo - 1000 times larger
- Hecto - 100 times bigger
- Deca - 10 times larger
- Deci - 10 times smaller
- Centi - 100 times smaller
- Milli - 1000 times smaller
- A simple trick for remembering basic metric prefixes is the mnemonic "Kelly wanted two more houses." The first letter of each word corresponds to a basic metric prefix, from highest to lowest, except for metric units (meter, liter, etc.).
Step 2. List the prefixes on one line
If you are unfamiliar with metric units, it can be helpful if you list the metric prefixes on a line in descending order. Put "kilo" on the left side of the line and "milli" on the far right. In the center of the scale, between "deca" and "deci", place the base unit of the dimension you are measuring. In other words, if you are measuring distance, write "meter", if you are measuring volume write "liter", and so on. This line gives you a simple visual reference about how your units are related; that is, if the units you want are bigger or smaller than the units you have and how big or small they are.
Step 3. Determine if the units you want are larger or smaller than the units you have
Look at your prefix line. Find the prefix that corresponds to the units you took in your initial measurement. Then find the units you want. Are they to the right or left of your starting units? If they are on the right, you are converting from a larger unit to a smaller unit. If they are to the left, you are converting from a minor unit to a major unit.
For example, let's say you want to know how many centimeters there are in a 10-kilometer race. In the prefix line, it is noted that "centi" is to the right of "kilo". So since the desired units are to the right of the initial units, you know that you are going to convert from a large unit to a smaller unit
Step 4. Determine the numerical relationship between the units you have and the ones you want
Metric units of measurement are differentiated by powers of 10 (10, 100, 1000, and so on). Therefore, converting from one metric unit to another is always achieved by multiplying or dividing the initial measurement by the appropriate power of 10. Check the arrow you drew in the units you have (the units in which your measurements are expressed) until the units you want to convert them to. The number of spaces under the arrow determines the power of 10 by which your two units are related.
- For example, in the 10-kilometer run, the arrow is seen to jump five spaces from "kilo" to "centi." This means that kilometers and centimeters are differentiated by a conversion factor of five powers of ten, which is also written as ten to the fifth power, 105, or 10 × 10 × 10 × 10 × 10 = 100,000. In other words, centimeters are 100,000 times (or 105, etc.) smaller than kilometers. Therefore, it is known that there are 100,000 centimeters in 1 kilometer.
Step 5. For "large to small" conversions, multiply by the appropriate power of 10
Converting a large unit to a small one means that you must multiply your original measurement by the amount that its unit differs from the final desired unit. Remember that this number must be a power of ten determined by the number of spaces under the arrow you drew in the previous steps.
- Sometimes, especially in school assignments, it is not enough to get the number correct. They will also ask you to demonstrate how you convert your starting unit to its final form. In simple conversions like the ones in this article, simply label the units of your initial measurement as you normally would, then label your conversion factor with the fraction (desired units) / (units of your initial measurement). The units in the denominator will cancel out with the units of your initial measurement and your answer will remain in the form of your desired units.
In the example of the 10-kilometer race, you would simply have to multiply 10 (the initial measurement in kilometers) by 105 (or 100,000: the number of centimeters in a kilometer). See below:
- 10 km × 105 cm / km =
- 10 km × 100,000 cm / km =
- = 1,000,000 cm. There are 1 000 000 centimeters in the 10-kilometer race.
Step 6. For "small to large" conversions, divide by the appropriate power of ten
Converting from a small unit to a larger one is essentially the opposite process: instead of multiplying, you must divide. Take your initial measurements and divide them by the amount by which its units differ from the final desired units; again, this must be a power of ten.
- Alternatively, instead of dividing your measure by 103, you must multiply it by 10-3. Both operations are valid and will give you the same result.
Let's do an example problem. Let's say you want to convert 360 centimeters to decameters. Since "centi" and "deca" are separated by three spaces on the prefix line, you know that decameters are 103 times larger than centimeters. They would be converted by dividing as follows:
- 360 cm / (103 cm / dam) =
- 360 cm / (1000 cm / dam) =
- = 0.36 dam. 360 centimeters make 0.36 decameters
Method 2 of 2: Converting Through Decimal Movement
Step 1. Determine the direction and size of the conversion
This quick method allows you to simply and easily convert between metric units without having to perform multiplication or division. To get started, all you have to know is whether you are converting from a small unit to a larger unit or vice versa, as well as the size of the conversion you are doing; In other words, if your desired units differ from the initial units by 101, 102, etc.
- Both can be determined by counting the spaces or drawing an arrow on the metric prefix line. For example, if you want to convert from kilometers to decameters, you know that you are converting from a larger unit to a smaller one, because we have gone to the right side of the line to obtain from "kilo" to "deca", and we know that the decameters are 102 times smaller than kilometers, because "kilo" and "deca" are separated by two spaces.
Step 2. Move the decimal point in your measurement
Since two metric measurements always differ by a few multiples of ten, it is possible to perform metric conversions by moving the decimal point of your starting number. When converting from a large measure to a smaller one, move the decimal point one space to the right for each power of ten your initial unit differs. When converting from a small unit to a larger one, move the decimal point to the left. Remember that the power of ten, by which your desired units differ, is determined by the number of spaces between the two units on the prefix line.
For example, let's say you want to convert 1 kilometer to centimeters. Since thanks to the line of prefixes it is known that the centimeters are 105 times smaller than kilometers, move the decimal point 1 five spaces to the right. See below:
- 1, 0
- 10, 0
- 100, 0
- 1000, 0
- 10 000, 0
100 000, 0. There are 100 000, 0.
centimeters in 1 kilometer.
- You'll also do the opposite: move the decimal of a number to the left to make it a larger unit.
Step 3. Add zeros if necessary
When you move the decimal point of a number, be sure to add zeros for each space that moves the decimal point beyond the available digits. For example, when you convert 1 kilometer to centimeters, the decimal point at the beginning is to the right of the number 1, like this:
Step 1.. Moving the decimal to the right means that you must add a zero for the number to become e
The same principle applies when moving the decimal point to the left: start adding zeros when you move the decimal point beyond the available digits of the number. For example, let's say you want to convert 1 millimeter to meters. Since the meters are 103 times larger than millimeters, it will simply move the decimals three spaces to the left as shown below:
- 1, 0
- 0, 10
- 0, 010. Notice that a zero is added to the left side of the 1.
- 0, 0010. Another zero is added to get the final answer. There are 0, 001 meters in 1 millimeter.
- Only add zeros if you want to remove digits when you move the decimal point. Adding zeros in the middle of a number can make your answer wrong.
There are abbreviations for each prefix and unit that you can use to make typing easier.
- Meter: m
- Liter: L
- Gram: g
- Kilo: k
- Hecto: h
- Deka: Da or Dka
- I said: d
- Centi: c
- Mill: m
- There are actually more prefixes that are used in the SI system, which is very similar to the metric system.
- Practice! Finally, if you use it long enough, you will have it memorized and you will not need to draw a line.
- This can take a bit of space if you do it during an exam. Try not to use a lot of space, if you decide to do this method.
- Don't use this method if you have prefixes other than the ones mentioned in this article, for example mega or micro.
- Do not use this method, if the unit is raised to power; for example, if you want to go for a square meter (m2) to square centimeter (cm2).