Welcome to a quick and simple method for converting from one metric prefix to another, such as kilo to centi. First, a brief introduction to what metric prefixes are, and then onward to converting. We will work from a horizontal chart showing the name of each prefix, the symbol for each, and the exponent of 10 that the prefix represents. And note that this chart is available via the link in the description below.
So all prefixes are used with a base unit, such as gram, meter, or liter, and there are many other base units. All prefixes are used with a base unit, and since each prefix represents a number, it is a shorthand for verbalizing a specific amount of that base unit. For example, in 1 kilogram, kilo is the prefix and gram is the base.
It can be abbreviated with their symbols, kg for kilogram, And its meaning comes from the exponent. Kilo is 10 to the third, so kilogram is 10 to the third grams, or 1000 grams. Let's try centimeter with centi as prefix, meter as base.
Its abbreviation is cm, which represents 10 to the negative 2 meters, or 0.01 meters. Lastly, it is very important to note that any number can be expressed using prefixes. Putting an 8 in front of mm gives us 8 mm, or 8 ml, which represents 8 times 10 to the negative 3 liters, or 0.008 liters.
Now let's get to converting from one prefix to another. The chart is laid out in this manner specifically to give easier access to the exponent represented by each prefix. Note that the base unit is just 1, or 10 to the 0. Our first example is converting 0.150 meters to centimeters.
Note that when a symbol is by itself, it is always a base unit, in this case meter. The conversion follows two simple rules. First is to subtract exponents. So we have meter with an exponent of 0, and we want to get to centi with an exponent of negative 2. Write down the exponents and subtract, giving a difference of 2. Now we will move the decimal that amount in the direction of the wanted unit.
Centi is wanted, so move the decimal two places to the right, which is toward centi. Beginning with 0.150, the decimal is moved two places to the right, giving 15.0 centimeters. 0.150 meters is equal to 15.0 centimeters.
We have moved the decimal two places to the right. Next problem. 0.150 kilometers is equal to how many centimeters? Using the same two steps, we see that we are starting with kilo and want to get to centi. Exponent for kilo is 3 and for centi is negative 2. We subtract and get a difference of 5, so the decimal is moved 5 places to the right, towards centi, the wanted unit.
0.150 moving the decimal 5 places to the right. Note there are now blank spaces. Always fill in the blanks with zeros.
So we now have 15,000. There are 15,000 centimeters and 0.150 kilometers. For the first two examples, we went from a larger unit to a smaller unit.
Let's see how to convert from a smaller unit to a larger unit. 384.0 milligrams is how many decigrams? We use the same steps as before. We are starting with milli and want to get to deci. The exponent for milli is negative 3 and for deci it is negative 1. We subtract and the difference is 2. Deci is the wanted unit, so move the decimal two places to the left toward deci.
Starting with 384.0, the decimal is moved two places to the left, which gives 3.840. 384.0 milligrams is equal to 3.840 decigrams. Let's try one more problem.
Stop the video, see if you can work out problem number four, and then start the video to check your answer. Notice that the first symbol is by itself, so it is a base unit. So we want to start with the base unit liter, and want to get to Mega.
Base units have an exponent of 0. Mega is 6. The difference is 6. Mega is the wanted unit, so the decimal is moved 6 places to the left toward Mega. The decimal is moved 6 places to the left. Blanks are filled with 0s.
By convention we add 0 before the decimal. 8,432.0 liters is equal to 0.0084320 megaliters. All you need is this chart and the two rules.
Subtract exponents and move the decimal that amount in the direction of the wanted unit. If you want the chart, it is linked in the description below. That's it for another Mad Scientist production. See ya!