3 – 6 Scientific Notation
Scientific Notation
Scientific Notation- A number written as the product of a number between 1 and 10 and
a power of 10.
Any number written in scientific notation is:
1  x  1010 
a number greater than or equal to one and less
than 10 multiplied by 10 to some exponent.
n
Exponent
The Earth’s weight is about
Number from 1 to 10
6.6 x 10
21
power of 10
Scientific Notation
Lets look at the number 43,000,000. This is a big number so it might be
easier to express it in scientific notation.
We need to come up with a number between 1 and 10 using numbers from
43,000,000.
What will our number be?
Scientific Notation
Lets look at the number 43,000,000. This is a big number so it might be
easier to express it in scientific notation.
We need to come up with a number between 1 and 10 using numbers from
43,000,000.
What will our number be?
Every whole number has a decimal at the end of it. Usually it is not written it is
just understood to be there.
Scientific Notation
Lets look at the number 43,000,000. This is a big number so it might be
easier to express it in scientific notation.
We need to come up with a number between 1 and 10 using numbers from
43,000,000.
What will our number be?
4.3
Every whole number has a decimal at the end of it. Usually it is not written it is
just understood to be there.
43,000,000.
We now that we will have 4.3 x 10 to some exponent.
Scientific Notation
Every whole number has a decimal at the end of it. Usually it is not written it is
just understood to be there.
43,000,000.
We now that we will have 4.3 x 10 to some exponent.
To figure out the exponent we have to count how many times we moved the
decimal to get it in the right spot
4.3,000,000
1
Scientific Notation
Every whole number has a decimal at the end of it. Usually it is not written it is
just understood to be there.
43,000,000.
We now that we will have 4.3 x 10 to some exponent.
To figure out the exponent we have to count how many times we moved the
decimal to get it in the right spot
4.3,000,000
2
Scientific Notation
Every whole number has a decimal at the end of it. Usually it is not written it is
just understood to be there.
43,000,000.
We now that we will have 4.3 x 10 to some exponent.
To figure out the exponent we have to count how many times we moved the
decimal to get it in the right spot
4.3,000,000
3
Scientific Notation
Every whole number has a decimal at the end of it. Usually it is not written it is
just understood to be there.
43,000,000.
We now that we will have 4.3 x 10 to some exponent.
To figure out the exponent we have to count how many times we moved the
decimal to get it in the right spot
4.3,000,000
4
Scientific Notation
Every whole number has a decimal at the end of it. Usually it is not written it is
just understood to be there.
43,000,000.
We now that we will have 4.3 x 10 to some exponent.
To figure out the exponent we have to count how many times we moved the
decimal to get it in the right spot
4.3,000,000
5
Scientific Notation
Every whole number has a decimal at the end of it. Usually it is not written it is
just understood to be there.
43,000,000.
We now that we will have 4.3 x 10 to some exponent.
To figure out the exponent we have to count how many times we moved the
decimal to get it in the right spot
4.3,000,000
6
Scientific Notation
Every whole number has a decimal at the end of it. Usually it is not written it is
just understood to be there.
43,000,000.
We now that we will have 4.3 x 10 to some exponent.
To figure out the exponent we have to count how many times we moved the
decimal to get it in the right spot
4.3,000,000
7
Scientific Notation
Every whole number has a decimal at the end of it. Usually it is not written it is
just understood to be there.
43,000,000.
We now that we will have 4.3 x 10 to some exponent.
To figure out the exponent we have to count how many times we moved the
decimal to get it in the right spot
4.3,000,000
7
7
Now the decimal is in the right place so our scientific notation is 4.3 x 10
Scientific Notation
Example 2: Write 234,000,000,000 in scientific Notation
What number can we come up with that is greater than or equal to one but less
than 10??
Scientific Notation
Example 2: Write 234,000,000,000 in scientific Notation
What number can we come up with that is greater than or equal to one but less
than 10??
2.34
So right now we know that we will have 2.34 x 10….. What’s the exponent?
Scientific Notation
234,000,000,000 is my original number.
2.34, 000,000,000
2.34,000,000,000
We know that it needs to be 2.34
how many places did I have to move the decimal
place back in order to get the decimal in the right
spot?
1
Scientific Notation
234,000,000,000 is my original number.
2.34, 000,000,000
2.34,000,000,000
We know that it needs to be 2.34
how many places did I have to move the decimal
place back in order to get the decimal in the right
spot?
2
Scientific Notation
234,000,000,000 is my original number.
2.34, 000,000,000
2.34,000,000,000
We know that it needs to be 2.34
how many places did I have to move the decimal
place back in order to get the decimal in the right
spot?
3
Scientific Notation
234,000,000,000 is my original number.
2.34, 000,000,000
2.34,000,000,000
We know that it needs to be 2.34
how many places did I have to move the decimal
place back in order to get the decimal in the right
spot?
4
Scientific Notation
234,000,000,000 is my original number.
2.34, 000,000,000
2.34,000,000,000
We know that it needs to be 2.34
how many places did I have to move the decimal
place back in order to get the decimal in the right
spot?
5
Scientific Notation
234,000,000,000 is my original number.
2.34, 000,000,000
2.34,000,000,000
We know that it needs to be 2.34
how many places did I have to move the decimal
place back in order to get the decimal in the right
spot?
6
Scientific Notation
234,000,000,000 is my original number.
2.34, 000,000,000
2.34,000,000,000
We know that it needs to be 2.34
how many places did I have to move the decimal
place back in order to get the decimal in the right
spot?
7
Scientific Notation
234,000,000,000 is my original number.
2.34, 000,000,000
2.34,000,000,000
We know that it needs to be 2.34
how many places did I have to move the decimal
place back in order to get the decimal in the right
spot?
8
Scientific Notation
234,000,000,000 is my original number.
2.34, 000,000,000
2.34,000,000,000
We know that it needs to be 2.34
how many places did I have to move the decimal
place back in order to get the decimal in the right
spot?
9
Scientific Notation
234,000,000,000 is my original number.
2.34, 000,000,000
2.34,000,000,000
We know that it needs to be 2.34
how many places did I have to move the decimal
place back in order to get the decimal in the right
spot?
10
Scientific Notation
234,000,000,000 is my original number.
2.34, 000,000,000
2.34,000,000,000
We know that it needs to be 2.34
how many places did I have to move the decimal
place back in order to get the decimal in the right
spot?
11
Scientific Notation
234,000,000,000 is my original number.
2.34, 000,000,000
2.34,000,000,000
We know that it needs to be 2.34
how many places did I have to move the decimal
place back in order to get the decimal in the right
spot?
11
11
So now the decimal is in the right place. So our scientific notation is 2.34 x 10
Scientific Notation
We can also write decimals in scientific notation.
Example 3: write the number 0.643 in scientific notation
What number can we find that is greater than or equal to 1 and less than 10?
Scientific Notation
We can also write decimals in scientific notation.
Example 3: write the number 0.643 in scientific notation
What number can we find that is greater than or equal to 1 and less than 10?
6.43
So we know that we have 6.43 x 10…. What’s the exponent
Scientific Notation
0.634 is my original equation
I need to make my number 6. 43
How many places do I need to move the decimal
0.634
1
We only moved one place, however because we moved 1 place to the right
instead of to the left our exponent is negative.
Scientific Notation
So our scientific notation is
-1
6.34 x 10
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