Oftentimes, when dealing with calculations, we'll run into contact with the metric prefixes. Now, metric prefixes can be seen as modifiers that are multiples of 10. And we're going to say when dealing with these metric prefixes, we're going to have this chart here. This metric prefix multipliers chart ranges from 1012 to 10-12. Now talk to your professor. Make sure you don't have to know anything beyond this point. For this level of chemistry, this is a pretty thorough range to deal with. But there, of course, there are terms 10-15, 1015. Well, those are usually reserved for higher levels of chemistry. Now 1012 is called terra. Terra uses the variable of t, capital T. 109 is giga, which is capital G. Mega is capital M, and it's 106. 103 is kilo. Now, at this point we're gonna be dealing with lowercase letters, so lowercase k. You might have heard of kilometer. So kilometer has kilo in it. It's metric prefix label. 102 is hecto, which is h. Now 101 is related to deka, which is da. Here is when we're dealing with our base unit. So our base unit like liters or seconds. We're gonna say here this is not a metric prefix, this is just the base, our base unit. Then we have deci. Dep and deci are pretty similar. To differentiate them, deci is d. Then we're gonna have centi, which is 10-2. So that's gonna be c. You might have heard of centimeters. Then we have 10-3 which is milli, milliliters. Then 10-6 is micro. Micro is an interesting symbol. 10-9 is nano, which is lowercase n, and then 10-12 is pico, which is p. Now this is a lot of terms. This is a lot of symbols, but we have our first memory tool. So when we have memory tools, either just simple phrases sometimes or images that'll help us memorize a specific chemistry-related topic. Here in this case, this memory tool helps us memorize the order for the metric prefix multipliers. Now we have King Henry from history, King Henry who kept on divorcing his wives until they wanted them to compare him a son. And with King Henry, we have a trusty memory tool to help us memorize the order of the metric prefixes. So we're gonna say the great monarch, King Henry's daughter Barbara, drinks chocolate milk until 9 pm. So you can see here that each one of these highlighted letters, each one of these highlighted letters here, corresponds to these metric prefix multipliers. And this memory tool also ranges from 1012 and it decreases all the way down to 10-12 over here. So just remember, your metric prefixes for us, we're gonna range from 1012 to 10-12. Consult with your professor to make sure that that's the range all you need to know in terms of this topic. And in terms of memorizing, rely on this memory tool. It'll help you remember the order that each metric prefix multiplier comes into play when it comes to this chart. Now that we've talked about the general idea of metric prefixes and this range, move on to the next video, and let's see how we can apply them to base units.

# Metric Prefixes - Video Tutorials & Practice Problems

**Metric Prefixes** are “labels” that can be placed in front of base units.

## Metric Prefix Multipliers

### Metric Prefixes

#### Video transcript

### Metric Prefixes

#### Video transcript

The metric prefixes themselves can act as labels that can be placed in front of various base units. So here we have base units for volume in the form of liters, in terms of time we use seconds, the base units for the amount of a substance is moles, and for electrical current amperes. Notice that some of these common base units are also connected to our SI base units. Now, the metric prefixes themselves are the variables that we place in front of each of these base units. So for liters, we could use milliliters, with milli being the metric prefix that we're placing in front of the base unit of liters. For seconds, we could use nanoseconds. For moles, we could use gigamoles, and for amperes, we could use kiloamperes. Here, all that's happening is I'm taking each one of these metric prefixes and placing them in front of one of these base units. This is key when it comes to metric prefix conversions. So click on the next video, and let's take a look at how we go from one metric prefix to a new one.

### Metric Prefixes Example 1

#### Video transcript

So here if we take a look at this example, it says, convert the following value to desired units. We need to convert 694 kilograms to micrograms. Alright. So step 1, if the given value has a metric prefix, which it does because 'kilo' is our metric prefix, then convert it to the base unit. The base unit is just a unit after you've removed the metric prefix. So the base unit here would just be grams. Alright. So we're gonna have 694 kilo is our metric prefix, grams. We're gonna say in order to cancel out units, always make sure that they are on opposite levels. So, we want to cancel out these kilograms which are on the top, so we're gonna place kilograms here on the bottom. And then we need to change this into our base units of grams. Now the next part is important. Always place the coefficient of 1 on the side with the metric prefix. Our metric prefix here is 'kilo', so we're gonna put here 1 kilo, and remember that comes from what we saw up above. Based on the metric prefix multipliers chart, we saw that when it is 'kilo', it's 103, so it'd be 103. Now because the kilograms are on opposite levels, they can cancel out. Next, we're gonna say, if necessary, convert the base unit to a new metric prefix. Now we didn't ask to find our answer in grams. We're asked to find it in micrograms. So we must continue onward. Grams are here on the top. In order to cancel them out, I put them here on the bottom, And then we need to get to micrograms, micro is our metric prefix, and then micrograms. Again, the coefficient of 1 is associated with the metric prefix, it's on the same side with it. So 1 micro is, according to the metric prefix multipliers chart above, it's 10-6. So now grams cancel out and we'll have at the end our value. So here that would be 694 times 103 divided by 10-6. Now, some of you, depending on your calculator, if you plug it in as you see it, you might get the wrong answer. So anytime you have 103, it's always best to put it in parentheses in your calculator. Otherwise, you may get the incorrect answer. So it'd be 694 times, in parentheses, 103, divided by, in parentheses, 10-6. If you do that correctly, you should get back in your calculator 6.9411 micrograms as your answer. And this represents our metric prefix conversions. We're just going from a metric prefix to either the base unit or a new metric prefix. Take to heart the steps that we've outlined here to approach any problem like this. Now that we've done this example question, move on to some practice questions.

Which quantity in the following pair is smaller?

^{–9}cm

Use the prefix multipliers to express each measurement without any exponents.

a) 32 x 10^{-13} L

b) 7.3 x 10^{6} g

c) 18.5 x 10^{11} s

#### Problem Transcript

Use scientific notation to express each quantity with only the base unit.

a) 83 µm

b) 193 kg

c) 2.7 mmol

#### Problem Transcript

If a room has a volume of 1.15 x 10^{8} cm^{3}, what is the volume in km^{3}?

^{3}

^{3}

^{-7}km

^{3}

^{5}km

^{3}

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- Write the abbreviation for each of the following units: c. kilometer
- Write the abbreviation for each of the following units: b. deciliter
- Write the abbreviation for each of the following units: a. milligram
- Write the complete name for each of the following units: a. cL
- Write the complete name for each of the following units: b. kg
- Write the complete name for each of the following units: c. ms
- Write the numerical value for each of the following prefixes: c. milli
- Write the numerical value for each of the following prefixes: b. tera
- Write the numerical value for each of the following prefixes: a. centi
- Use a prefix to write the name for each of the following: b. 10⁶ m
- Use a prefix to write the name for each of the following: c. 0.001 m
- Use a prefix to write the name for each of the following: d. 10⁻¹² m
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- For each of the following pairs, which is the larger unit? b. milliliter or microliter
- For each of the following pairs, which is the larger unit? a. milligram or kilogram
- Give the full name of the following units: a. cc b. dm c. mm d. nL e. mg f. m³
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