Kilo - 1,000 times larger Hecto - 100 times larger Deca - 10 times larger Deci - 10 times smaller Centi - 100 times smaller Milli - 1,000 times smaller 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”). 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. )
For example, let’s say that we want to know how long a 10-kilometer race is in centimeters. On our line of prefixes, we would see that “centi” is to the right of “kilo”. Since our desired units are to the right of our initial units, we know we’re converting from a large unit into a smaller unit.
For instance, in our 10-kilometer race example, we see that our arrow from “kilo” to “centi” jumps over five spaces. This means that kilometers and centimeters differ by a conversion factor of five powers of ten, 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. ) times smaller than kilometers. Thus, you know that there are 100,000 centimeters in 1 kilometer.
Sometimes, especially in schoolwork, it’s not enough to simply give the correct number. You’ll also be asked to show how you converted your initial unit label to its final form. In simple conversions like we’re dealing with here, just 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 with the units of your initial measurement, leaving your answer in terms of your desired units. In our 10-kilometer race example, we would simply multiply 10 (our 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 our 10 kilometer race.
Alternatively, you can multiply by the inverse power of ten to get the same results. For example, rather than dividing your measurement by 103, you would multiply it by 10-3. Both operations are valid and will give the same answer. Let’s do an example problem. Let’s say we want to covert 360 centimeters to decameters. Since “centi” and “deca” are three spaces apart on the line of prefixes, we know that decameters are 103 times larger than centimeters. We would convert by dividing as follows: 360 cm / (103 cm/dam) = 360 cm / (1,000 cm/dam) = = 0. 36 dam. 360 centimeters make 0. 36 decameters.
Both of these can be determined by counting spaces and/or drawing an arrow on a line of the metric prefixes. For example, if we want to convert from kilometers to decameters, we know that we’re converting from a large unit to a small unit because we have to travel to the right along the line to get from “kilo” to “deca,” and we know that decameters are 102 times smaller than kilometers because “kilo” and “deca” are separated by two spaces.
For example, let’s say that we want to convert 1 kilometer into centimeters. Since we can tell from the line of prefixes that centimeters are 105 times smaller than kilometers, we move the decimal point in “1” five spaces to the right. See below: 1. 0 10. 0 100. 0 1,000. 0 10,000. 0 100,000. 0. There are 100,000. 0. centimeters in 1 kilometer. You may also do the reverse - move a number’s decimal to the left to convert to a larger unit.
For example, let’s say that we want to convert 1 kilometer into centimeters. Since we can tell from the line of prefixes that centimeters are 105 times smaller than kilometers, we move the decimal point in “1” five spaces to the right. See below: 1. 0 10. 0 100. 0 1,000. 0 10,000. 0 100,000. 0. There are 100,000. 0. centimeters in 1 kilometer. You may also do the reverse - move a number’s decimal to the left to convert to a larger unit.
For example, let’s say that we want to convert 1 kilometer into centimeters. Since we can tell from the line of prefixes that centimeters are 105 times smaller than kilometers, we move the decimal point in “1” five spaces to the right. See below: 1. 0 10. 0 100. 0 1,000. 0 10,000. 0 100,000. 0. There are 100,000. 0. centimeters in 1 kilometer. You may also do the reverse - move a number’s decimal to the left to convert to a larger unit.
The same principal applies when moving a decimal point to the left - begin inserting zeroes when you move the decimal beyond the number’s available digits. For instance, let’s say we want to convert 1 millimeter into meters. Since meters are 103 times larger than millimeters, we would simply move the decimal three spaces to the left as below: 1. 0 0. 10 0. 010. Notice that we add a zero to the left of the 1. 0. 0010. We add another zero to get our final answer. There are 0. 001 meters in 1 millimeter. Only add zeroes if you run out of digits when moving the decimal point. Inserting superfluous zeroes into the middle of a number can make your answer incorrect.
The same principal applies when moving a decimal point to the left - begin inserting zeroes when you move the decimal beyond the number’s available digits. For instance, let’s say we want to convert 1 millimeter into meters. Since meters are 103 times larger than millimeters, we would simply move the decimal three spaces to the left as below: 1. 0 0. 10 0. 010. Notice that we add a zero to the left of the 1. 0. 0010. We add another zero to get our final answer. There are 0. 001 meters in 1 millimeter. Only add zeroes if you run out of digits when moving the decimal point. Inserting superfluous zeroes into the middle of a number can make your answer incorrect.
The same principal applies when moving a decimal point to the left - begin inserting zeroes when you move the decimal beyond the number’s available digits. For instance, let’s say we want to convert 1 millimeter into meters. Since meters are 103 times larger than millimeters, we would simply move the decimal three spaces to the left as below: 1. 0 0. 10 0. 010. Notice that we add a zero to the left of the 1. 0. 0010. We add another zero to get our final answer. There are 0. 001 meters in 1 millimeter. Only add zeroes if you run out of digits when moving the decimal point. Inserting superfluous zeroes into the middle of a number can make your answer incorrect.
