NS 1.1­ Scientific Notation.notebook
September 09, 2015
Expanded Form and Scientific Notation
Get out your calculator and type in the following multiplication question:
12 3456 x 12 3456 = What do you notice? NS 1.1­ Scientific Notation.notebook
September 09, 2015
What your calculator will display will vary based on the type of calculator you have but, chances are, you will have a decimal number displayed in some way.
­My calculator displays the product as 1.524138e+10. ­Other displays probably give you 1.5 x 1010
The product (answer to a multiplication question) of 12 3456 x 12 3456 is 15 241 383 936
So....
­Why wouldn't your calculator give you the answer in that form?
­How does 1.524138e+10 = 15 241 383 936?
NS 1.1­ Scientific Notation.notebook
September 09, 2015
Scientific Notation
Both forms of the answer a calculator will give you are
represented in scientific notation.
-Scientific notation is a way to represent really big or really small
numbers in a condensed form
-Scientific notation is the product of a decimal number and an
exponent
NS 1.1­ Scientific Notation.notebook
September 09, 2015
Decimals
Ones
.
Tenths
Hundredths
Thousandths
.
**When numbers are expressed in scientific notation, the
decimal is always between the first and second digit
NS 1.1­ Scientific Notation.notebook
September 09, 2015
Exponents
Remember that when we use exponents, there are two parts to the number:
54 5 is the base (the "big" number) and 4 is the exponent/power (the "little" raised number)
-when we see 54, it means the base (5) multiplied by itself 4 times (the value of the exponent)
54 (exponent form) = 5 x 5 x 5 x 5 (expanded form) = 625 (standard form)
What would 32 be in standard form?
**When numbers are expressed in scientific notation, the base is always 10
NS 1.1­ Scientific Notation.notebook
September 09, 2015
Let's put it all together
Pluto is approximately 7.5 billion km from earth
*How do we write 7.5 billion in standard form?
7 500 000 000
Remember that scientific notation involves a decimal number
(value between 1 and 10) and a number expressed in exponent
form with a base of 10
-what would the decimal number be?
7.5
-how would we figure out what the exponent would be?
7 500 000 000 = 7.5 x 10?
7 500 000 000 = 7.5 x 109 (put the decimal between the 7 and the
5, then count how many times you would need to move the decimal
to the right to get the "end" of the number
NS 1.1­ Scientific Notation.notebook
September 09, 2015
Sometimes numbers are a little bit messier....
On August 1, 2015, the estimated world population was:
7 259 479 658
How would we write that in scientific notation?
NS 1.1­ Scientific Notation.notebook
September 09, 2015
We can also write numbers in expanded form
Let's take that super-specific world population estimate
(7 259 479 658) and use it to practise doing so.
First off, who can read me that number?
hundred
ten
millions
millions
2
5
billions
7
millions
9
hundred
ten
thousands thousands
4
7
thousands hundreds
9
6
tens
ones
5
8
Expanded form breaks the number down into scientific notation
for each digit
Example: 7 in the billions column would be written as 7 x 109
*What number is in the "hundred millions" column? How would we express that in scientific notation?
NS 1.1­ Scientific Notation.notebook
hundred
ten
millions
millions
2
5
billions
7
millions
9
hundred
September 09, 2015
ten
thousands thousands
4
7
thousands hundreds
9
6
tens
ones
5
8
In your groups, finish writing the number in expanded form
7 259 479 658 = 7 x 109 + 2 x 108 +
NS 1.1­ Scientific Notation.notebook
September 09, 2015
Reminders about Homework...
-After each lesson, there will be approximately 15 questions
provided to practise the skills in focus (paper copies and digital
copies will be provided)
-You will find 3 questions with stars beside them. These will be
the questions that we will take up the following day (along with any
other questions you would like to ask about)
-Please keep your homework questions in your duotang and answer
the questions in your notebook (date and title your work)
**You do not need to do all 15 questions every night. Do as many
as you feel you need to do to master the skills in focus.
NS 1.1­ Scientific Notation.notebook
September 09, 2015