The Metric System - Basic Introduction

Summary

This educational video script delves into the metric system's prefixes and their corresponding symbols and multipliers. It explains the conversion process between units like kilo, mega, giga, and tera, emphasizing the importance of attaching multipliers to base units for easy conversion. The script provides examples of converting units such as from meters to kilometers and liters to milliliters, illustrating step-by-step calculations. It also touches on less common prefixes and their multipliers, offering a comprehensive guide to mastering unit conversions in the metric system.

Takeaways

• 🔢 The metric system uses prefixes to denote multiples and submultiples of units, with each prefix representing a power of 10.
• 📐 Prefixes like 'deca' (da), 'hecto' (h), 'kilo' (k), 'mega' (M), 'giga' (G), 'tera' (T), 'peta' (P), 'exa' (E), 'zetta' (Z), and 'yotta' (Y) represent increasing powers of 10 from 10^1 to 10^24.
• 🔠 The symbols for these prefixes are mostly lowercase, except for 'mega' and above, which are capitalized.
• 🔄 Conversion factors are essential for unit conversions, attaching a '1' to the prefix and the multiplier to the base unit.
• 🔄 Negative exponents are used for smaller units, with prefixes like 'deci' (d), 'centi' (c), 'milli' (m), 'micro' (µ), 'nano' (n), 'pico' (p), 'femto' (f), 'atto' (a), 'zepto' (z), and 'yocto' (y).
• 📉 To convert units, write conversion factors that cancel out the original unit and leave the desired unit.
• 📖 For one-step conversions, use a single conversion factor; for two-step conversions, use a sequence of conversion factors.
• 🧮 Scientific notation is commonly used for expressing large or small numbers, with the format being a number between 1 and 10 multiplied by 10 raised to a power.
• 📚 Understanding and practicing unit conversions is crucial for success in scientific studies and exams.
• 🔍 For more challenging unit conversion problems, resources like 'unit conversion organic chemistry tutor' on YouTube can provide additional practice.

Q & A

What is the symbol and multiplier for the 'deca' prefix in the metric system?

The symbol for 'deca' is 'da' and the multiplier is 10 to the power of 1, or simply 10.

What does the prefix 'kilo' represent in the metric system, and what is its symbol?

The prefix 'kilo' represents 10 to the power of 3, or a thousand, and its symbol is 'k'.

How is 'mega' used in the metric system, and what is its multiplier?

'Mega' in the metric system is used to represent 10 to the power of 6, which is a million, and its symbol is 'M'.

What is the conversion factor for converting grams to kilograms?

One kilogram is equal to 1000 grams, so the conversion factor is 1 kilogram = 10^3 grams.

What is the prefix for 10 to the power of 9 in the metric system?

The prefix for 10 to the power of 9 is 'giga', represented by the symbol 'G'.

How do you write a conversion factor when converting units in the metric system?

A conversion factor is written by attaching a '1' to the prefix and then the multiplier to the base unit, such as 1 kilometer = 10^3 meters.

What is the symbol for the 'milli' prefix and what does it represent?

The symbol for 'milli' is 'm' and it represents 10 to the power of negative 3, or one-thousandth.

How can you convert 478 meters to kilometers using the metric system prefixes?

To convert 478 meters to kilometers, you would divide 478 by 1000 (since 'kilo' means 10^3), resulting in 0.478 kilometers.

What is the process for converting 0.236 liters to milliliters?

To convert 0.236 liters to milliliters, you multiply by 1000 (because 'milli' means 10^-3), resulting in 236 milliliters.

How do you perform a two-step conversion from picometers to micrometers?

First, convert picometers to meters using the conversion factor 1 picometer = 10^-12 meters. Then, convert meters to micrometers using the factor 1 micrometer = 10^-6 meters. For 496 picometers, this would result in 4.96 × 10^-4 micrometers.

Outlines

00:00

📏 Introduction to Metric Prefixes and Conversion Factors

This paragraph introduces the metric system's prefixes and their corresponding symbols and multipliers. It starts with 'deca' (symbol 'da', multiplier 10^1), 'hecto' (symbol 'h', multiplier 10^2), 'kilo' (symbol 'k', multiplier 10^3), and progresses to 'mega' (symbol 'M', multiplier 10^6), 'giga' (symbol 'G', multiplier 10^9), and 'tera' (symbol 'T', multiplier 10^12). The concept of conversion factors is explained, emphasizing the importance of attaching a '1' to the prefix and the multiplier to the base unit for easy conversion between units like joules, watts, and grams. The paragraph also mentions higher prefixes like 'peta' and 'exa', but notes that for most exams, knowledge up to 'tera' is sufficient.

05:03

🔍 Negative Exponents and Conversion Factors

The second paragraph delves into prefixes with negative exponents, starting with 'deci' (symbol 'd', multiplier 10^-1), 'centi' (symbol 'c', multiplier 10^-2), and 'milli' (symbol 'm', multiplier 10^-3). It explains how to write conversion factors with these prefixes, using examples like converting centimeters to meters and milliliters to liters. The paragraph also discusses how to derive common conversion factors from standard ones by adjusting the equation, such as converting 100 centimeters to a meter or a thousand milliliters to a liter. It continues with smaller prefixes like 'micro' (10^-6), 'nano' (10^-9), and 'pico' (10^-12), and briefly mentions even smaller ones like 'femto', 'atto', 'zepto', and 'yocto', noting that knowledge up to pico is typically sufficient for most classes.

10:04

🔄 Step-by-Step Conversion Examples

This paragraph provides a step-by-step guide on how to convert units using the metric system's prefixes. It begins with a simple one-step conversion from meters to kilometers, explaining the process of writing conversion factors and using them to cancel out the original unit and obtain the desired unit. The paragraph then presents a conversion from liters to milliliters, illustrating how to manipulate the conversion factor to achieve the desired unit. It also tackles a two-step conversion problem from picometers to micrometers, demonstrating the process of converting to the base unit (meters) first and then to the final unit. The paragraph emphasizes the importance of understanding how to move and change the sign of exponents when converting units.

15:05

🧮 Advanced Conversion Techniques and Resources

The final paragraph discusses advanced unit conversion techniques, particularly focusing on converting between very large and very small units. It provides an example of converting nanometers to kilometers, detailing the process of converting to the base unit (meters) and then to the final desired unit. The paragraph explains how to handle scientific notation and manipulate exponents during the conversion process. It also suggests a resource for more challenging problems, directing viewers to search for 'unit conversion' on YouTube, specifically recommending a video by 'organic chemistry tutor' for additional practice.

Keywords

💡Metric System

The metric system is a decimal-based system of measurement used worldwide for the measurement of length, mass, and capacity. In the video, the metric system serves as the foundational framework for discussing various prefixes and their corresponding multipliers, which are essential for understanding the conversion between different units of measurement. The script explains how these prefixes are used to denote different magnitudes, from kilo (thousand) to yocto (ten to the negative twenty-fourth), and how they relate to scientific and everyday measurements.

💡Prefixes

In the metric system, prefixes are used to denote specific multiples of a base unit. The video script discusses several prefixes such as kilo, mega, giga, and others, each with its own symbol and multiplier. For instance, 'kilo' stands for 10 to the power of 3, and 'mega' for 10 to the power of 6. These prefixes are crucial for expressing large or small quantities in a more manageable form and are used throughout the script to demonstrate how to convert between different units.

💡Multipliers

Multipliers in the metric system are powers of ten that are associated with each prefix. The script explains how multipliers like '10 to the power of 1' for deca or '10 to the power of 6' for mega are used to scale the base units. Understanding multipliers is key to converting between different units effectively, as demonstrated in the video through various conversion examples.

💡Conversion Factors

Conversion factors are ratios that relate different units of measurement. The video emphasizes the importance of writing conversion factors correctly by attaching the multiplier to the base unit. These factors are essential for converting from one unit to another, as shown in the script where the conversion from meters to kilometers or liters to milliliters is explained using these factors.

💡Base Units

Base units are the fundamental units of measurement in the metric system, such as meters for length, grams for mass, and liters for volume. The script mentions that when writing conversion factors, the multiplier should be attached to the base unit. This is illustrated in the video with examples like one kilogram being a thousand grams, emphasizing the relationship between prefixes, multipliers, and base units.

💡Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. The video script uses scientific notation to express very large or very small quantities, such as '3.54 times 10 to the power of 7 nanometers'. This notation is particularly useful in scientific contexts where measurements can span many orders of magnitude.

💡Negative Exponents

Negative exponents are used in the metric system to denote fractions of a base unit. The script explains prefixes like deci, centi, and milli, which correspond to 10 to the power of negative one, negative two, and negative three, respectively. Understanding negative exponents is crucial for converting between smaller units, such as from meters to centimeters or liters to milliliters.

💡One-Step Conversion

A one-step conversion is a process where a quantity is converted from one unit to another using a single conversion factor. The video script demonstrates one-step conversions, such as converting 478 meters to kilometers, by using the appropriate conversion factor. This straightforward approach is fundamental to solving problems involving unit conversions.

💡Two-Step Conversion

A two-step conversion involves converting a quantity from one unit to another through an intermediate unit. The script provides an example of converting 496 picometers to micrometers, which requires first converting picometers to meters and then meters to micrometers. This method is useful when direct conversion factors are not available.

💡Unit Cancellation

Unit cancellation is a technique used in unit conversions where units are 'cancelled out' or 'crossed out' to simplify the expression and obtain the desired unit. The video script illustrates this by showing how to set up conversion factors so that the unit to be converted disappears, leaving the desired unit. This technique is essential for solving multi-step unit conversion problems.

Highlights

Introduction to metric system prefixes and their corresponding symbols and multipliers.

Deca prefix stands for 10 to the power of 1, symbolized by 'da'.

Hecto prefix is represented by 'h' and signifies 10 squared or 100.

Kilo prefix, denoted by 'k', is equivalent to 10 to the third power or 1000.

Mega prefix, symbolized by 'M', stands for 10 to the sixth power, or one million.

Giga prefix, with the symbol 'G', represents 10 to the ninth power, or one billion.

Terra prefix, symbolized by 'T', is 10 to the twelfth power, equating to one trillion.

Peta prefix is for 10 to the fifteenth power, representing a quadrillion.

Exa prefix, denoted by 'E', signifies 10 to the eighteenth power, a quintillion.

Zeta prefix is 10 to the twenty-first power, representing a sextillion.

Yotta prefix, symbolized by 'Y', is 10 to the twenty-fourth power, a septillion.

Explanation of negative exponent prefixes such as deci, centi, and milli.

Deci prefix is 10 to the minus first power, symbolized by 'd'.

Centi prefix is represented by 'c' and is 10 to the minus second power.

Milli prefix, denoted by 'm', stands for 10 to the minus third power.

Micro prefix is 10 to the minus sixth power, symbolized by 'µ'.

Nano prefix, with the symbol 'n', is 10 to the minus ninth power.

Pico prefix is for 10 to the minus twelfth power, represented by 'p'.

Methodology for writing conversion factors in unit conversion.

How to convert units using one-step conversion problems with examples.

Process of converting units in two-step conversion problems with detailed examples.

Mental math techniques for unit conversion without using a calculator.

Practical application of unit conversion in the metric system with various examples.

Transcripts

now we're going to talk about the prefix

of the metric system the symbols

that correspond to it

and the multiplier

so first

we're going to start with deca

the symbol for deca

is d a the multiplier is 10 to the 1

or just 10.

hecto

has a symbol

lowercase h the multiplier is 10 squared

or 100

kilo

kilo is lower case k

and it's

10 to the third

or a thousand

so what this means is that

one kilogram

is a thousand grams or one times ten to

the third

grams

next up we have mega

now it's not going to be a lower case

but this is a capital case capital m

and this is 10 to the sixth

mega is basically a million

so a megawatt

a megawatt power plant

produces one times 10 to the six watts

or a million watts

next up we have giga represented by the

symbol capital g

giga is 10 to 9 which is equivalent to a

billion

so a giga joule

is 1 times 10 to the 9

joules

so what i have here are called

conversion factors notice how

i'm writing all of my conversion factors

this is going to be important when we're

solving problems

so what you always want to do is you

always want to attach a 1 to the prefix

and then the multiplier goes with the

base unit whether it's joules for energy

watts for power

grams for mass

so you always attach the multiplier to

the base unit and it makes it easy to

write the conversion factors once you

have the conversion factors down

then it's gonna be easy to convert from

one unit to another

after giga what we have next

is terra capital t

terra is 10 to 12 which is equivalent to

a trillion

so one terawatt is 1 times 10 to the 12.

watts

after tara

the next one in the list is peda

in most cases if you're studying for an

exam

typically you need to know up to tara so

going past 10 to 12

you usually don't need to know these

unless

your professor gives you you know these

notes

but usually up to 12 is you know the

limit but there's some other ones beyond

12 and i'm going to give it to you

beta

is 10 to the 15.

so remember mega is a million giga is a

billion

tera is a trillion

beta

represents

a quadrillion

exa

capital e

that's 10 to the 18

which is

a quench quintillion

after exa you have

zeta

and that's not a lower kc but this is a

capital z but i am running out of space

zeta is 10 to the 21st or 10 to the 21.

and that is a sextillion

after that we have yoda

represented by the symbol capital y

and that's 10 to the 24th which is

a septillion

so if you know up to 10 to 12

should be okay for your exam now let's

go over the

multipliers that have a negative

exponent

this is the other half

so let's start with the prefix

deci

represented by the symbol lowercase d

deci is 10 to the minus one

next we have centi

lowercase c that's ten to negative two

and then milli

lowercase m is ten to the minus three

the only time you have a capital symbol

is mega and above like mega giga terra

and anything above that everything else

dissembles our lower case

so think about what this means

think about how we can write a

conversion factor with this information

one centimeter always put a prefix in

front of put a one in front of the

prefix

one centimeter is one times ten to the

minus two meters

so always attach the multiplier to the

base unit

one milliliter

is one times ten to the minus three

liters

now once you write this conversion

factor

what you can do is you can alter it if

we multiply both sides by a hundred

we get that a hundred centimeters

is equal to one meter

ten to negative two

times a hundred is simply one

if we multiply this by a thousand

we get this common conversion factor

a thousand milliliters

is equal to one liter

so if you can write the standard

conversion factors you can get

the common ones

as well

simply by adjusting the equation

now after melee the next one

is micro

micro is ten to the minus six

so one micrometer

is one times ten to negative six

meters

after micro

we have a nano

lower case n nano is 10 to the minus

nine

so think of ten to nine which was giga

that represents one billion nano ten to

negative nine is the billionth

omega 10 to the six was a million

micro ten to the minus six is a

millionth

with a th at the end

so one nanometer

is one times ten to the negative nine

meters

after nano its pico lower case p

ten to negative twelve

one picometer

is one times ten to negative twelve

meters

now there's some other ones below this

so i'm going to run through the list

quickly

next we have femto the lowercase f

that's 10 to the negative 15.

after femto is ato

with the symbol lowercase a

and this is 10 to negative 18.

after ato it's

zepto

lowercase z

10 to negative 21. and after zepto is

yakdo

lowercase y

10 to negative 24.

but for the smaller

units

typically you need to know up to pico

so you need to know from pico 10 to

negative 12 to tara 10 to the positive

12.

and those are the common prefixes that

you're going to encounter in class

the other ones they're optional

typically

they're not commonly used

now let's talk about how we can convert

from one unit to another

so for instance let's say

if we have

478 meters

and we wish to convert it to kilometers

how can we do that

well this is a one-step conversion

problem

so we just need to know

the conversion factor between kilometers

and meters

we know that kilo represents

10 to the third or a thousand

so we can write the conversion factor

one kilometer always put a one in front

in front of the prefix

one kilometer is one times ten to the

third meters

so step one write a one

write the prefix with the base unit

write the multiplier

and then the base unit without the

prefix

and that's how you can write your

conversion factor

now to convert it

start with what you're given we're given

478 meters we'll put it over one

in the next fraction we're going to put

our conversion factor

notice that we have the unit meters on

top

so to cancel meters we need to put this

part of the equation in the bottom

this is going to be 1 times 10 to the 3

meters

and then the other part is going to go

on top

so we need to set the fractions in such

a way that

the unit we want to convert from

disappears and the unit that we want to

get to remains

so this becomes 478

divided by a thousand

and that gives us the answer

0.478 kilometers

so that's how you can do a one-step

conversion problem

let's try another one

let's say we have

400

actually

let's say

0.236 liters and we want to convert that

to milliliters

feel free to pause the video and try

that example

so first let's write the conversion

factor one milliliter

is equal to remember milli is 10 to the

minus three so it's going to be one

and then we're going to put the

multiplier 10 to negative three and then

the base unit liters

so that's our conversion factor

now let's start with what we're given

we're given .236 liters we'll put that

over one

now we got to find out what goes on the

top and the bottom

of

the next fraction since we have liters

on top of the first fraction we want

liters to be on the bottom of the second

which means milliliters have to go on

top

so this number attached to liters has to

go on the bottom

so we'll put 1 times 10 to the minus 3

liters on the bottom

and then this will by default go on top

so this tells us that we need to divide

by a thousand to convert liters into

milliliters

actually not by a thousand we need to

divide by

ten to the minus three

which is point zero zero one

that has the equivalent effect of

multiplying by a thousand

so it's 0.236

you can divide it by .01

or if you multiply by a thousand you're

going to get

236

milliliters

by the way when dividing this

put this in parentheses because

your calculator may divide by one and

then multiply by ten to negative three

now let's try a two-step conversion

problem

let's say

we have

hmm

496

micrometers

and we want to convert that

to

actually let's say this is in

picometers 496 picometers

and we want to convert that to

micrometers

try that problem

now even though there are shortcut

methods available that you can use

what i'm going to do is i'm going to do

this one step at a time

i'm going to convert picometers

into the base unit meters and then

meters to micrometers

so let's write the conversion factor

from pico to meters

pico is ten to the minus twelve so one

picometer

is one times ten to negative twelve

meters

we'll use that in the first step

for the second step we'll convert meters

to micrometers one micrometer

we know it's

micro is ten to the minus six so it's

one times

ten to negative six and then the base

unit meters

so let's start with what we're given 496

picometers over one

let's use the first conversion factor

to go from picometers to meters

so because we have the unit picometers

on the top left we're going to put it on

the bottom right of the second fraction

meters is going to go on top

so we have one picometer

is equal to

10 to negative 12 meters

so now the unit picometers will cancel

and now let's use the second conversion

factor to go from meters to micrometers

since we have meters here we're going to

put meters on the bottom

micrometers on top

so it's one micrometer

and the number that's attached to meters

is

10 to negative six

so now we can cross out the unit meters

so when we do the math we're going to

get the answer

so you can plug this in your calculator

or you can do it mentally

let's talk about how we can do this

mentally

so we have 496.

we can ignore the one

what's important here is the 10 to

negative 12.

now notice that we have a tens of

negative six on the bottom

what we can do is take this

and move it to the top

if you have let's say

x to the negative three this is one over

x cubed if you move it from the bot from

the top to the bottom

the exponent changes sign it goes from

negative three to positive three

likewise if you have a negative exponent

on the bottom and you decide to move it

to the top

it'll go from negative to positive

so if you flip it or if you move it from

one side to the other side of the

fraction

it's going to change side so it's 10 to

negative 6 on the bottom but when we

move it to the top it's going to be

10 to the positive 6.

now when multiplying common bases

we can add the exponents

negative 6 i mean negative 12 plus 6

that's going to be negative 6. so we

have 496

times ten to negative six

and the unit

is the unit that's left over micrometers

now we need to move the decimal

two units to the left

496 is the same as 4.96

times 10 to the second power

10 squared is 100 so 4.96 times 100 is

496.

and then we still have 10 to negative 6

as well so adding these two will give us

negative 4. the final answer is going to

be 4.96

times 10 to the negative 4

micrometers so that's how you can do a

problem like that without the use of a

calculator

we typically leave our answer in

scientific notation

so you want the decimal point to be

between

the first two non-zero numbers

now let's try another example

let's say

we have 3.54

times 10 to the

negative

actually let's say positive

10 to the positive 7

nanometers

and let's convert that to

kilometers

go ahead and try that problem

by the way for those of you who want

harder problems to work on

go to the youtube search bar type in

unit conversion

organic chemistry tutor

and a video that i've created it's a

very long video

will show up and you'll get more harder

problems that involve unit conversion

now for this problem what i'm going to

do is i'm going to convert nanometers to

meters

and then meters to kilometers so because

it's a two-step problem

i need two conversion factors the first

one

one nanometer is one times ten to the

negative nine meters

the second one one kilometer

kilometer is ten to the three so it's

one times ten to the three meters

so those are our two

conversion factors that we're going to

use

now let's start with

what we're given 3.54

times 10 to the 7 nanometers

now i want nanometers on the bottom

and meters on top

so that these will cancel

and then i want meters on the bottom

and my final unit kilometers on top

so that these will cancel

so now i just got to fill it in

so we have a one in front of the

nanometer we'll put that here and then

it's 10 to negative 9 meters

so this will go here

for the second one we have a 1 in front

of kilometers

and 10 to the 3 in front of meters

so now let's do the math

it's three point five four

times ten to the seven

and then we have ten to negative nine

and we're going to move this to the top

that's gonna be ten to the minus three

so now let's add

7 plus negative 9 is negative 2

negative 2 plus negative 3 is negative

5. so the final answer is going to be

3.54

times 10 to negative 5 kilometers

so that's how you can do a two-step

conversion problem

when dealing with units in the metric

system

thanks for watching