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

Metric Prefix Multipliers

1

concept

## Metric Prefixes

3m

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oftentimes, when dealing with calculations will run into contact with the metric prefix is now metric prefix is can be seen as modifiers that are multiples of 10. And we're gonna say when dealing with these metric prefixes and we're gonna have this chart here, this metric prefix multipliers chart ranges from 10 to to 10 to the negative 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 to the negative 15 10, the positive 15. Both those air usually reserved for higher levels of chemistry. Now 10 to the 12 is called Tara. Tara uses the variable off T capital T 10 to the nine is Giga, which is capital. Gene Mega is Capital M and it's 10 to the 6. 10 to the three is kilo. Now, at this point, we're gonna 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. 10 to the two is Hector, which is H now 10 to the one is related to Decca, which is D A. Here is when we're dealing with our base unit. So are based unit like leaders or seconds. We're gonna say here, this is not a metric prefix. This is just the base. Our base unit. Then we have Desi Death and D C are pretty similar to differentiate them. Desi is D Then we're gonna have senti, which is 10 to the negative too. So that's gonna be see you might have heard of centimeters then we have 10 to the naked through which is Milli Milliliters. Then 10 to the negative six is micro micro is an interesting symbol. Looks like this 10 to the negative nine is Nana, which is lower Case N and then 10 to the negative 12 is PICO, which is P now. This is a lot of terms. That's a lot of symbols, but we have our first memory tools. So when we have memory tools either just simple phrases sometimes or images that will help us memorize a specific chemistry related topic here in this case, this memory to will 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 they one of them compare him a son. And with Ken Henry, we have a trustee memory tool to help us memorize the order of the metric prefix is so we're gonna say the great monarch, King Henry's daughter Barbara, drinks chocolate milk until 9 p.m. So we can see here that each one of these highlighted letters Uh huh. Each one of these highlighted letters here corresponds to these metric prefix multipliers. And this memory tool also ranges from 10 to the 12th 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 need that that you need to know in terms of this topic and in terms of memorizing, rely on this memory tool. It will help you remember the order that each metric prefix multiplier comes into play when it comes to this chart. Now that we talked about the general idea of metric prefixes and this range move onto the next video and let's see how we can apply them to base units.

2

concept

## Metric Prefixes

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the metric prefixes themselves can act as labels that can be placed in front of various base units. So here we have based units for volume in the form of leaders. In terms of time we use seconds. The base units for the amount of a substance is moles and for electrical current and peers notice that some of these common base units are also connected to our sea based units. Now the metric prefix themselves are the variables that we place in front of each of these base units. So leaders, we could plug in front of it. Millie. So millie leaders, Millie being the metric prefix that were placed in front of the base unit of leaders for seconds we could do nanoseconds for moles, we could do giga moles and for amperes we could do kilo and peers 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.

3

example

## Metric Prefixes Example 1

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So here. If we take a look at this example, it says convert the following value to desired units. We need to convert 694 kg. Two micrograms. Alright, So Step one If the given value has a metric prefix which it does because kilo is our metric prefix that converted 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 grants. Right? So we're gonna have 6. 94 kilo is our metric prefix grams. We're going to say in order to cancel out Unit's, always make sure that they are on opposite levels. So we want to cancel out these kilograms which were 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 Gramps. 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 gonna say here 1 kg, 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 three. So the 10 to the three now Because the kilograms are on opposite levels, they can cancel out next. Yeah, we're gonna say if necessary, convert the metric the base unit toe a new metric prefix. Now, we didn't ask to find our answering. Grams were asked to find it in micrograms. So we must continue Onward grams air here on the top. In order to cancel him 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 prefix on the same side with it. So one micro is according to the metric prefix multipliers chart above its 10 to the negative six. So now Graham's cancel out and we'll have at the end our value. So here, that would be 6, 94 times 10 to the three divided by 10 to the negative six. Now, some of you, depending on your calculator. If you plug it in as you see it, you might get the wrong answer. So any time you have 10 toe a power It's always best to put it in parentheses in your calculator. Otherwise, you may get the incorrect answer. Should be 6 94 times in parentheses, 10 to the three divided by in parentheses, 10 to the negative. Six. If you do that correctly, you should get back in your calculator 6.94 times to the 11 micro grams as your answer, and this represents our metric prefix conversions were just going from a metric prefix toe. 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.

4

Problem

Which quantity in the following pair is smaller?

A

155 pm

B

7.8 x 10

^{–9}cm5

Problem

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

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6

Problem

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

a) 83 µm

b) 193 kg

c) 2.7 mmol

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7

Problem

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

A

1150 km

^{3}B

115 km

^{3}C

1.15 x 10

^{-7}km^{3}D

1.15 x 10

^{5}km^{3}Additional resources for Metric Prefixes

PRACTICE PROBLEMS AND ACTIVITIES (44)

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- Bottles of wine sometimes carry the notation “Volume = 75 cL. What does the unit cL mean?
- Which quantity in each of the following pairs is larger? (a) 5.63 * 106 cm or 6.02 * 101 km
- Which quantity in each of the following pairs is smaller? (c) 2.9 GA or 3.1 * 1015 mA
- How many microliters are in 1 L? In 20 mL?
- Carry out the following conversions. (c) 65.2 mg = _____ = g = _____ pg
- Carry out the following conversions. (b) 8.5 cm^3 = _____ m^3 = _____ mm^3
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- Using your knowledge of metric units, English units, and the information on the back inside cover, write down...
- Using your knowledge of metric units, English units, and the information on the back inside cover, write down...
- Use the prefix multipliers to express each measurement without exponents. a. 1.2 * 10 - 9 m b. 22 * 10 - 15 s ...
- Use the prefix multipliers to express each measurement without exponents. a. 1.2 * 10 - 9 m b. 22 * 10 - 15 s ...
- Use the prefix multipliers to express each measurement without exponents. a. 1.2 * 10 - 9 m b. 22 * 10 - 15 s ...
- Use prefix multipliers to express each measurement without exponents. a. 38.8 * 105 g b. 55.2 * 10 - 10 s c. 2...
- Use prefix multipliers to express each measurement without exponents. a. 38.8 * 105 g b. 55.2 * 10 - 10 s c. 2...
- Use scientific notation to express each quantity with only base units (no prefix multipliers). a. 35 mL b. 225...
- Complete the table. a. 1245 kg 1.245 * 106 g 1.245 * 109 mg b. 515 km _____dm _____cm c. 122.355 s _____ms ___...
- Complete the table. a. 1245 kg 1.245 * 106 g 1.245 * 109 mg b. 515 km _____dm _____cm c. 122.355 s _____ms ___...
- Complete the table. a. 1245 kg 1.245 * 106 g 1.245 * 109 mg b. 515 km _____dm _____cm c. 122.355 s _____ms ...
- Complete the table. a. 1245 kg 1.245 * 106 g 1.245 * 109 mg b. 515 km _____dm _____cm c. 122.355 s _____ms ___...
- Complete the table. a. 355 km>s _____cm>s _____m>ms b. 1228 g>l _____g>ml _____kg>ml c. 554 ...
- Express the quantity 254,998 m in each unit. a. km b. Mm c. mm d. cm
- Express the quantity 556.2 * 10 - 12 s in each unit. a. ms b. ns c. ps d. fs
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- A house has an area of 195 m2. What is its area in each unit? a. km2 b. dm2 c. cm2
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