Metric Prefixes - Online Tutor, Practice Problems & Exam Prep

Understanding metric prefixes is essential for scientific measurements and calculations. These prefixes represent different powers of ten, ranging from:

${10}^{12}\text{(tera, symbolized by T) to}{10}^{-12}\text{(pico, symbolized by p).}$

Familiarity with these terms and their corresponding symbols allows for the conversion and expression of various units, such as volume in liters, time in seconds, substance amount in moles, and electrical current in amperes. A helpful mnemonic to remember the order of metric prefixes is: "King Henry Died By Drinking Chocolate Milk Until Nine PM," where each initial corresponds to a metric prefix from tera to pico. Applying these prefixes to base units is crucial for accurate scientific communication and conversions between different scales. For instance, milliliters (mL) uses the milli prefix to denote:

${10}^{-3}\text{liters, while kiloamperes (kA) indicates}{10}^3\text{amperes.}$

Understanding and correctly using metric prefixes ensures precision and clarity in scientific measurements.

Metric Prefixes

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 multiplier's chart ranges from 1012 to 10-12. Now talk to 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 of course there are terms 10-15 and 1015, but those are usually reserved for higher levels of chemistry. Now 1012 is called Terra. Tera 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 going to be dealing with lower case letters, so lower case 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 Deca which is DA. Here is when we're dealing with our base unit. So our base unit like liters or seconds, we're going to say here this is not a metric prefix. This is just the base, our base unit. Then we have desi, death and Desi are pretty similar to differentiate them. Desi is D. Then we're going to have senti which is 10-2. So that's going to be C. You might have heard of centimeters.

Then we have 10-3 which is milli, milliliters. Then 10-6 is micro. Micro's an interesting symbol looks like this. 10-9 is nano which is lower case 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 these are just simple phrases sometimes or images that will 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 he they one of them can bear him a son. And with Ken Henry we have a trusty memory tool to help us memorize the order of the metric prefixes. So we're going to say the great Monarch, King Henry's daughter Barbara drinks chocolate milk until 9:00 PM.

So we can see here that each one of these highlighted letters 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 going to range from 1012 to 10-12. Consult with your professor to make sure that that's the range that 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

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 plug in front of it milli, so milliliters, milli being the metric prefix that we're placing in front of the base unit of liters. For seconds, we could do nanoseconds. For moles, we could do gigamoles, and for amperes, we could do 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 do we go from one metric prefix to a new one.

Metric Prefixes Example 1

So here. If we take a look at this example, it says convert the following value to the desired units. We need to convert 694 kilograms to micrograms. All right. So step one, 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 the unit after you've removed the metric prefix O. The base unit here will just be grants.

All right. So we're going to have 694K is our metric prefix grams. We're going to 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 going to 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 one on the side with the metric prefix. Our metric prefix here is Kilo, so we're going to say here 1K. And remember that comes from what we saw U 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 going to say, if necessary, convert the metric, 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 one is associated with the metric prefixes on the same side with it. So one micro is. According to the metric prefix multiplier's 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 * 103 / 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 10n to a power, 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 ( 103 divided by in ( 10-6. If you do that correctly, you should get back in your calculator 6.94 * 1011 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 refix. 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?

• A. 155 pm
• B. 7.8 x 10^–9 cm

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

a) 32 x 10-13 L

b) 7.3 x 106 g 

c) 18.5 x 1011 s

So here, if we take a look at this practice question, it says, use the prefix multipliers to express each measurement without any exponents. So, this question is a combination of changing scientific notation to standard notation and also metric prefix conversions. Alright. So, basically, we're going to have to change all these base units into some type of metric prefix and, in the process, get rid of these exponents. Alright. So, for the first one, we have 32 times 10-13 liters. If we think back to the metric prefix multipliers chart, we know that the only metric prefix that's close enough to 10-13 is pico because pico is 10-12. This means that we're going to have to convert liters to picoliters. We have 32 times 10-13 liters. I want to get rid of liters, so I put liters on the bottom and picoliters on the top. Remember, the coefficient of 1 is associated on the same side with the metric prefix, meaning 1 picoliter is 10-12. Make sure you put these in parentheses since there's times 10 to a power. Liters here cancel out. Now, if you plug this correctly into your calculator, you should get back as your answer 3.2 picoliters. So we're able to change it to one of our prefix multipliers and in the process, we removed the exponent. So we've gone from scientific notation to standard notation. For the next one, we have 7.3 times 106 grams. The metric prefix that's 106 is mega. So here, we just have to convert grams to megagrams. You want to get rid of grams, so put them on the bottom, and we're converting to megagrams, so that goes on the top. The coefficient of 1 is on the same side with the metric prefix. So, 1 megagram is 106. Make sure that these are in parentheses, so when grams cancel out and you plug this correctly into your calculator, you should get back 7.3 megagrams. Finally, we have 18.5 times 1011 seconds. The metric prefix that's closest to 1011 is tera because tera is 1012. So we're going to change seconds to teraseconds. We have 18.5 times 1011 seconds, seconds go here on the bottom, and we're trying to convert to teraseconds, so they go on the top. One tera is 1012. Make sure this is in parentheses. Seconds cancel out, and at the end, we'll have teraseconds as our answer. If you plug it in correctly, you'll get 1.85 teraseconds as our final answer. So just remember, the question here was a little bit tricky, but read through it and realize they wanted you to change all these base units into metric prefixes, and in doing so, allow you to drop the exponent that's involved. So really, we're going from scientific notation to standard notation by incorporating the metric prefixes. Now that we've done this practice question, let's click on the next one and continue.

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

a) 83 µm

b) 193 kg

c) 2.7 mmol

So here in this practice question, it says, use scientific notation to express each quantity with only the base unit. So remember, our metric prefix is what goes in front of our base unit. For example, in micrometers, the metric prefix is micro, so the base unit is meters. In kilograms, kilo is our metric prefix, and the base unit is grams. And in millimoles, milli is our metric prefix, so moles is our base unit. So, if we take a look at the first one, we have to go from micrometers to just meters. Remember micro is our metric prefix. To get rid of it, to cancel out the units, it has to go here on the bottom. Remember, 1 micro is 10-6. We put this in parentheses, micrometers cancel out, so you should get as your answer here 8.3×10-5 meters. For the next one, we have to go from kilograms to the base unit of grams. So, we have 193 kilograms. We need to get rid of kilograms, so we have to put it on the bottom and grams on the top. The coefficient of 1 goes on the same side with the kilo with the metric prefix, so 1 kilo is 103. Remember to place this in parentheses. Kilograms here cancel out and we'll be left with grams at the end. So, here you'll get 1.93×105 grams. Then finally, we have millimoles, so we have 2.7 millimoles. We want to get rid of millimoles, so it goes on the bottom, and then we have moles on the top. Remember from your metric prefix multipliers chart, 1 milli is 10-3. Put this in parentheses. Here, we're going to see that millimoles cancel out. So at the end, we get 2.7×10-3 moles. So remember, this is just a simple metric conversion question. We're going from a metric prefix to just the base units. So just remove the metric prefix and you'll have your answer. Doing so in this particular question allowed us to go from standard notation to scientific notation.

If a room has a volume of 1.15 x 10⁸ cm³, what is the volume in km³?

• A. 1150 km³
• B. 115 km³
• C. 1.15 x 10^-7 km³
• D. 1.15 x 10⁵ km³

Here’s what students ask on this topic:

How do the prefixes in the metric system relate to the basic units?

The prefixes in the metric system, also known as the International System of Units (SI), serve to denote multiples or fractions of the basic units. Each prefix represents a specific factor by which the base unit is multiplied or divided, making it easier to express very large or very small quantities. For example:

• Kilo- (k) multiplies the unit by 1,000. So, a kilometer (km) is 1,000 meters.
• Mega- (M) multiplies the unit by 1,000,000. A megagram (Mg) is 1,000,000 grams.
• Giga- (G) multiplies the unit by 1,000,000,000. A gigawatt (GW) is 1,000,000,000 watts.

Conversely, for smaller quantities:

• Milli- (m) divides the unit by 1,000. A millimeter (mm) is 0.001 meters.
• Micro- (µ) divides the unit by 1,000,000. A microliter (µL) is 0.000001 liters.
• Nano- (n) divides the unit by 1,000,000,000. A nanometer (nm) is 0.000000001 meters.

How can I remember metric prefixes?

Remembering metric prefixes can be easier if you use mnemonic devices. One common mnemonic for the metric prefixes from largest to smallest is "King Henry Died By Drinking Chocolate Milk." This stands for kilo-, hecto-, deka-, base unit (meter, liter, gram), deci-, centi-, and milli-. Each prefix corresponds to a factor of ten, with kilo- being a thousand times the base unit and milli- being one-thousandth of the base unit.

Here's a breakdown:

• Kilo- (k) = 1,000
• Hecto- (h) = 100
• Deka- (da) = 10
• (Base unit: meters, liters, grams)
• Deci- (d) = 0.1
• Centi- (c) = 0.01
• Milli- (m) = 0.001

For smaller or larger units, you can extend the mnemonic or create a new one. For example, "Mighty King Henry Died By Drinking Chocolate Milk Monday Night" adds micro- (µ) for one-millionth and nano- (n) for one-billionth. Creating a visual chart or flashcards can also reinforce your memory. Practice converting between units using these prefixes to become more familiar with them.

How to do metric conversion?

Metric conversion involves changing a measurement from one unit to another within the metric system. To do this, you need to understand the base units for different types of measurements, such as meters for length, liters for volume, and grams for mass. The metric system is based on multiples of ten, which makes conversion simpler. Here's a basic guide:

1. Identify the current unit and the unit you want to convert to.
2. Determine the conversion factor. For example, 1 kilometer (km) is 1000 meters (m), so the conversion factor from km to m is 1000.
3. Multiply or divide the number you are converting by the conversion factor. If you are converting to a larger unit (e.g. m to km), you divide. If you are converting to a smaller unit (e.g. km to m), you multiply.
4. Ensure your answer is in the correct unit.

Remember the prefixes: kilo- (1000), hecto- (100), deka- (10), deci- (0.1), centi- (0.01), and milli- (0.001). These prefixes help you move the decimal point to the right or left to make the conversion.