Metric Prefixes - Online Tutor, Practice Problems & Exam Prep

Understanding metric prefixes is essential for scientific calculations, as they represent multiples of ten. Key prefixes include tera (10¹²), giga (10⁹), mega (10⁶), kilo (10³), and milli (10^-3). These prefixes can be applied to base units like liters, seconds, and amperes, facilitating conversions such as milliliters and nanoseconds. A mnemonic, "King Henry's Daughter Barbara Drinks Chocolate Milk Until 9 PM," aids in memorizing the order of these prefixes, enhancing comprehension and application in chemistry.

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 multipliers chart ranges from 10 to the 12 to 10 to the negative 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 to the negative 15, 10 to the positive 15. Well, those are usually reserved for higher levels of chemistry. Now 10 to the 12 is called terra. Terra uses the variable of t, capital T. 10 to the 9 is giga, which is capital G. Mega is capital M, and it's 10 to the 6. 10 to the 3 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. 10 to the 2 is hecto, which is H. Now 10 to the 1 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 to the negative 2. So that's gonna be C. You might have heard of centimeters. Then we have 10 to the negative 3 which is milli, milliliters. Then 10 to the negative 6 is micro. Micro is an interesting symbol, looks like μ. 10 to the negative 9 is nano, which is lowercase n, and then 10 to the negative 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 help 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 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 we 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 10 to the 12, and it decreases all the way down to 10 to the negative 12 over here. So just remember, your metric prefixes for us, we're gonna range from 10 to 12 to 10 to the negative 12. Consult with your professor to make sure that that's the range all you that 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 are 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 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 desired units. We need to convert 694 kilograms to micrograms. Alright. 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. We're going to have 694 kilo 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. 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 1 on the side with the metric prefix. Our metric prefix here is kilo, so we're going to say 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 10 to the 3, 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 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 10 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 parentheses, 103, divided by, in parentheses, 10-6. If you do that correctly, you should get back in your calculator 6.941011 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?

• 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 32×10-13 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 32×10-13 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 or on the same side with the metric prefix, meaning 1 pico 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 106. The metric prefix that's 106 is mega. So here, we just have to convert grams to megagrams. We have 7.3×106 grams. 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 mega is 106. Make sure that these are in parentheses, so when grams cancel out and you plug this correctly in your calculator, you should get back 7.3 megagrams. And then finally, we have 18.5×1011 seconds. The metric prefix that's closest to 1011 is tera because tera is 1012. So we're going to change seconds to teraseconds. So we have 18.5×1011 seconds, seconds go here on the bottom, and we're trying to find 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. So 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 micrograms or micrometers actually to just meters. Okay. So 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 8.3×10−5m. For the next one, we have to go from kilograms to the base unit of grams. So we have 193 kilograms, so kilograms. We need to get rid of kilograms, so we have to put it on the bottom and grams on the top. Coefficient of 1 goes on the same side with the Kilo with the metric prefix, so 1 kilo is 103. So remember to place this in parenthesis. Kilograms here cancel out and we'll be left with grams at the end. So here you'll get 1.93×105g. 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. So 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 2.7×10−3mol. So remember, this is just a simple metrics 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:

What are the metric prefixes and their corresponding powers of ten?

Metric prefixes are modifiers that represent multiples of ten. Key prefixes include:

• Tera (T): 10¹²
• Giga (G): 10⁹
• Mega (M): 10⁶
• Kilo (k): 10³
• Hecto (h): 10²
• Deka (da): 10¹
• Base unit: 10⁰
• Deci (d): 10^-1
• Centi (c): 10^-2
• Milli (m): 10^-3
• Micro (μ): 10^-6
• Nano (n): 10^-9
• Pico (p): 10^-12

These prefixes are used to simplify the expression of large or small quantities in scientific calculations.

How can I memorize the order of metric prefixes?

A useful mnemonic to memorize the order of metric prefixes is: "King Henry's Daughter Barbara Drinks Chocolate Milk Until 9 PM." Each highlighted letter corresponds to a metric prefix:

• K: Kilo (10³)
• H: Hecto (10²)
• D: Deka (10¹)
• B: Base unit (10⁰)
• D: Deci (10^-1)
• C: Centi (10^-2)
• M: Milli (10^-3)
• U: Micro (10^-6)
• N: Nano (10^-9)
• P: Pico (10^-12)

This mnemonic helps in remembering the sequence from larger to smaller prefixes.

How do metric prefixes apply to base units?

Metric prefixes are placed in front of base units to indicate multiples or fractions of those units. For example:

• Milliliters (mL): Milli (10^-3) + Liters (L)
• Nanoseconds (ns): Nano (10^-9) + Seconds (s)
• Gigamoles (Gmol): Giga (10⁹) + Moles (mol)
• Kiloamperes (kA): Kilo (10³) + Amperes (A)

This system simplifies the expression and conversion of large and small quantities in scientific measurements.

What is the significance of metric prefixes in scientific calculations?

Metric prefixes are crucial in scientific calculations as they provide a standardized way to express large and small quantities. They simplify the notation and conversion of units, making it easier to perform calculations and communicate measurements. For example, instead of writing 0.000001 meters, you can write 1 micrometer (μm). This standardization is essential for accuracy and consistency in scientific research and education.

Can you provide examples of metric prefix conversions?

Sure! Here are some examples of metric prefix conversions:

• 1 kilometer (km) = 1,000 meters (m)
• 1 milligram (mg) = 0.001 grams (g)
• 1 gigabyte (GB) = 1,000,000,000 bytes (B)
• 1 nanosecond (ns) = 0.000000001 seconds (s)

These conversions are based on the powers of ten associated with each metric prefix, making it straightforward to switch between different units.