Chapter 6 Lesson 1
Scientific Notation
Name 2 steps to
make scientific notation.
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Adjust your screen
for correct lettering.
Boy, if I see one more exponent
I will go extreme on my own.
Ooooh, how extreme?
You aren't going to like this.
I don't know but I'll find
something extremely bad.
Last time you went extreme
you gave cooties to the girls.
That was 5th grade. One of
the girls really thought she got it.
Besides, I think you'll like
Scientific Notation.
Scientific Notation
Science? Notes?
This isn't science class.
First, scientific notation is not
about you taking science notes.
So, why do I need to know
science stuff in math class?
I'll show you why we need
scientific notation with just 1 card.
Watch this.
1,000,000,000,000
That is one really big number.
1,000,000,000,000
Use the Rule of 3s.
What place value is this?
1,000,000,000,000
12 zeros, that's trillions,
but that is one huge number.
That's ok. I'll use
a quick way to write it.
10
12
We already did this
when we did exponents.
Now I'll change it a little.
2,000,000,000,000
Now we have to
use scientific notation.
2,000,000,000,000
Why is it different?
2 x 10
12
It multiplies by 2 to get 2 in front.
You can write it another way.
2 x 1,000,000,000,000
It's the same number.
Choose what you want to write.
2 x 1,000,000,000,000
Too much writing is bad for you.
I'll keep scientific notation.
2 x 10
4
I'll go over what each part does.
2 x 10
First Digit
4
Place Value
Multiply a number x base 10.
We'll do a few problems.
700
There's 2 steps to write this
number with scientific notation.
What does the 1st one multiply?
7 x 100
Multiply 7 times 100.
I'm pretty sure the
2nd step has an exponent.
7 x 10
2
Yup, I knew it.
The exponent for 100 is 2.
7 x 10
2
Just 2 easy steps.
Think about what they are.
1. 1st digit and multiply
2. Use the Exponent
I've got a problem for it.
8,000
We'll solve it in 2 steps.
What's the 1st step to write 8,000?
8 x 1,000
1st digit is 8. Multiply 1000.
8 x 1,000
What's the 2nd step?
8,000
8 x 10
3
Exponent. 1000 has 3 places.
8,000
8 x 10
3
That's how it works. We use
scientific notation alot with science.
Scientific Notation
Is there a good reason they
made the name so long?
I know. It's the longest
name. Even longer than the
Pythagorean Theorem.
Are you sure? Pythagorean
Theorem is pretty long.
I counted. Scientific
Notation is 1 letter longer.
Qs
8,000
What's the 1st step to make
scientific notation from a number?
8,000 = 8 x 10
1. Find the first digit x 10.
What happens next?
8,000 = 8 x 10
3
2. Count the exponent places.
2 x 10
4
What are the 2 steps for
scientific notation?
2 x 10
First Digit
4
Place Value
First digit x base 10.
The exponent counts the places.
3,000,000
What's the 1st step to write this?
3,000,000
3 x 1,000,000
1st digit and multiply.
Finish the problem.
3,000,000
3 x 10
6
Million has 6 digits.
40,000
Now altogether in 1 step.
What's the scientific notation?
40,000
4 x 10
4
40,000 has 4 places.
90,000,000
This number's alittle bigger.
What's the scientific notation?
90,000,000
9 x 10
7
10 million is 7 digits.
We'll try a really big number.
20,000,000,000
Find the scientific notation.
20,000,000,000
2 x 10
10
10 billion has 10 digits.
900,000
Last problem. What's
the scientific notation?
900,000
9 x 10
5
100,000 is 5 digits.
Chapter 6 Lesson 1a
Scientific Notation
2 Steps to
Make Scientific Notation
Backwards
How do we go backwards?
You said go forwards, then
you decide to go backwards.
Make up your mind.
You are so funny.
It just means we'll change
scientific notation into a number.
No, I meant backwards flips.
What do you think I meant?
60,000
I think somebody needs a nap.
What are the
2 parts to scientific notation?
60,000
1. Find the first digit.
2. Count the places after.
60,000
What is this scientific notation?
60,000
6 x 10
4
No big surprises.
6 x 10 to the 4th.
60,000
6 x 10
4
Now we'll go backwards.
You'll need 3s rule for this.
8 x 10
5
What's the first digit
for the number?
8 x 10
5
8
First Digit
Looks like it starts with an 8.
8 x 10
5
8
First Digit
Next, count 5 more zeros.
What number is that?
8 x 10
5
800,000
5 places
5 places makes it 100 thousands.
Oooh, that is alittle tricky.
8 x 10
5
800,000
Why is that so tricky?
8 x 10
5
800,000
It's 5 places plus the 1st digit.
That makes it 100 thousands.
2 x 10
4
Good point. So, add the
exponent to more place.
2 x 10
4
All 1 step. Start off with the
first digit and count the places.
20,000
4 zeros
3 places + 1 makes it 20,000.
Yawn. Tell me when it gets real.
20,000
4 zeros
Yeah, a bit too simple.
Time to amp it up abit.
5 x 10
9
Woe. 0 to 60 in 1 card.
5 x 10
9
All 1 step. Same deal.
I'll get the rule of 3s out.
In front.
thousands
3 places
millions
6 places
billions
9 places
trillions
12 places
Where does 9 fall in?
In front.
thousands
3 places
millions
6 places
billions
9 places
trillions
12 places
It's in the billions group.
Ok, I know the number.
5 x 10
9
5,000,000,000
9 places
9 places makes billions.
Wow. That's a big number.
5 x 10
9
5,000,000,000
9 places
That's what it's good at.
Back to normal numbers.
4 million
So, what's the scientific
notation for 4 million?
4 million
You mean you want me to know
the exponent for a million?
4 million
Well, yeah. We did study that.
4 million
It's just easier counting zeros.
Now I have to think about it.
1,000,000,000,000
billions
millions
thousands
It helps if you use Rule of 3s.
Each set of 3s is a group.
4,000,000
4 x 10
6
Ok, 4 times 10 to the 6th.
4,000,000
4 x 10
6
Took you long enough.
Well, here's a good one.
70 billion
I'll step it up. "What's the
scientific notation for 70 billion?"
70 billion
Ok, now I'm really complaining.
7 x 10
?
You know it starts with a 7.
What's the exponent?
7 x 10
?
Thanks alot. Ok, millions is
6, billions is 9, so just 1 more.
70,000,000,000
7 x 10
10
9 + 1 is 10, so the exponent's 10.
70,000,000,000
7 x 10
10
The rule of 3s really works.
This is the absolute last one.
50 thousand
Then we'll do the next place.
Scientific notation for 50 thousand.
50 thousand
Not any worse. Just add 3 + 1.
This is an easy one.
50,000
5 x 10
4
10,000 has 4 zeros.
Ok, that was pretty easy.
Ooops, I shouldn't say that.
Why shouldn't you say it's easy?
You know, then you just make it
alot tougher and I don't want that.
But, that's what makes math
so great. Kind of like crossword
puzzles. Sunday's the toughest.
I read the comics on Sunday.
That's enough for me.
Qs
9 x 10
3
What's the 1st step to
make Scientific Notation?
3
9 x 10 = 9_____
1. Find the first digit.
What's the 2nd step to
make a number?
3
9 x 10 = 9,000
2. Count the exponent places.
Chapter 6 Lesson 1
Scientific Notation
Short Lesson
Name 2 steps to
make scientific notation.
Scientific Notation
One way to use exponents
is scientific notation.
No, this isn't science, but science
does write numbers using it.
1,000,000
Use the Rule of 3s.
What place value is this?
1,000,000
10
6
Use an exponent to write 10s.
Now we'll change the number.
2,000,000
Now we have to
use scientific notation.
How is it different?
2,000,000
2 x 10
6
Scientific Notation
Multiply by 2 to get the number.
Think about what happened.
2 x 10
6
2 x 1,000,000
It's the same number, but it's
faster writing it with exponents.
700
The 1st part of scientific notation
has a name we'll use alot.
700
First Digit
First digit starts it all off.
Start with 7. What does it multiply?
700
7 x 100
First, write it with multiplication.
How does it use an exponent?
700
7 x 10
2
Exponent: count places
after the 1st digit.
What are the steps?
7 x 100
1. 1st digit and multiply
7 x 10
2
2. Use the Exponent
We'll try another one.
600 million
What's the scientific
notation for 600 million?
You know the 6 part.
What's the rest of it?
6 million is 600,000,000
6 x 10
8
Million has an exponent of 8.
It's 6 x 10 to the 8th power.
Here's what you need.
1,000,000,000,000
billions
millions
thousands
It helps if you use Rule of 3s.
Each set of 3s is a group.
60,000
We'll go backwards.
What are the
2 parts to scientific notation?
60,000
1. Find the first digit.
2. Count the places after.
What is 60,000 as scientific notation?
60,000
6 x 10
4
Now we'll go backwards.
8 x 10
3
As long as you know
the rule of 3s, it goes quick.
What is this number?
Start with the 1st digit.
8 x 10
3
8
First Digit
Next, what's the place
value for 3rd power?
8 x 10
3
8000
3 places
3 places makes thousands.
There's 1 thing to remember.
Questions
8,000
What do you multiply
to get scientific notation?
8 x 10
3
8000
3 zeros
This is thousands place.
Add 3 places + 1 more to get 1000s.
8,000 = 8 x 10
First digit x 10
What makes the exponent?
?
8,000 = 8 x 10
3
The exponent counts the places.
70 thousand
What is this scientific notation?
70 thousand
7 x 10
4
You need to know
the exponents for numbers.
7 x 10
6
All in 1 step. What's
the scientific notation?
7 x 10
6
7,000,000
6 zeros
Add 6 places + 1 for millions.
Chapter 6 Lesson 1
Scientific Notation
Practice #1
Name 2 steps to
make scientific notation.
9 x 10
3
What's the 1st step to make a
number from scientific notation?
3
9 x 10 =
9
1. Find the first digit.
What's the 2nd step?
3
9 x 10 =
9
Count the places.
What number does 3 make?
3
9 x 10 =
9,000
1000 has 3 places.
8,000
What's the 1st step to change a
number into Scientific Notation?
8,000 = 8 x 10
1. Find the first digit x 10.
What happens next?
8,000 = 8 x 10
3
2. Count the exponent places.
Problems
2 x 10
4
What's the 1st step to
make a number?
2 x 10
4
2
Make a 1st Digit
What finishes the number?
2 x 10
4
20,000
Count the places.
4 zeros makes 20 thousand.
5 x 10
3
All 1 step. What
is 5 x 10 to the 3rd?
5 x 10
3
5,000
5 and 3 zeros is 5,000.
8 x 10
6
Find the number.
How many places is it?
8 x 10
6
8,000,000
8 and 6 zeros is 8 million.
4 x 10
5
What is 4 x 10 to the 5th?
4 x 10
5
400,000
4 and 5 zeros is 400 thousand.
6 x 10
4
What is 6 x 10 to the 4th?
6 x 10
4
60,000
6 and 4 zeros is 60 thousand.
Chapter 6 Lesson 1
Scientific Notation
Practice #2
Name 2 steps to
make scientific notation.
8,000
What's the 1st step to change a
number into Scientific Notation?
8,000 = 8 x 10
1. Find the first digit x 10.
What happens next?
8,000 = 8 x 10
3
2. Count the exponent places.
9 x 10
3
What's the 1st step to make a
number from scientific notation?
3
9 x 10 =
9
1. Find the first digit.
What's the 2nd step?
3
9 x 10 =
9
Count the places.
What number does 3 make?
3
9 x 10 =
9,000
1000 has 3 places.
Problems
9,000
What is the 1st step to
make scientific notation?
9,000
9 x 10
?
Find the 1st digit x 10.
What is the exponent?
9,000
9 x 10
3
9000 has 3 places.
9 x 10 to the 3rd
80,000
What is the 1st step to
make scientific notation?
80,000
8 x 10
?
Find the 1st digit x 10.
What is the exponent?
80,000
8 x 10
4
80,000 has 4 places.
8 x 10 to the 4th
200
All in 1 step.
What is the scientific notation?
200
2 x 10
2
2 x 10 to the 2nd
5,000,000
What's the scientific
notation for 5 million?
5,000,000
5 x 10
6
5 x 10 to the 6th
Chapter 6 Lesson 1
Scientific Notation
Performance #1
Name 2 steps to
make scientific notation.
600,000
800,000
Change to scientific notation.
600,000
6 x 10
5
800,000
8 x 10
5
100 thousands is 5.
2,000,000
7,000,000
Make scientific notation.
2,000,000
2 x 10
6
7,000,000
7 x 10
6
Millions is 6.
20 thousand
60 thousand
Change to scientific notation.
20 thousand
2 x 10
4
60 thousand
6 x 10
4
10 thousands is 4.
60 million
50 million
What's the scientific notation?
60 million
6 x 10
7
50 million
5 x 10
7
10 million is 7.
8 x 10
9 x 10
6
7
Find the number for each.
6
8 x 10 =
8,000,000
Millions
7
9 x 10 =
70,000,000
10 Millions
2 x 10
3
3 x 10
4
Find the number for each.
3
2 x 10 =
2,000
thousands
4
3 x 10 =
30,000
10,000s
Chapter 6 Lesson 1
Scientific Notation
Performance #2
Name 2 steps to
make scientific notation.
5000
8,000,000
Change to scientific notation.
5000 =
5 x 10
3
8,000,000 =
8 x 10
6
40,000
60,000,000
Make scientific notation.
40,000 =
4 x 10
4
60,000,000 =
6 x 10
7
2 thousand
3 hundred
Change to scientific notation.
2 thousand
2 x 10
3
3 hundred
3 x 10
2
60 million
800 thousand
What's the scientific notation?
60 million is
6 x 10
7
800 thousand is
8 x 10
5
8 x 10
7 x 10
3
2
Find the number for each.
3
8 x 10 =
8,000
Thousands
2
7 x 10 =
700
Hundreds
2 x 10
4
9 x 10
5
Find the number for each.
4
2 x 10 =
20,000
10 thousands
5
9 x 10 =
900,000
100,000s