learning goals: 1. state whether or not a number is in scientific notation….and why. 2. write a...
TRANSCRIPT
Learning Goals:1. State whether or not a number is in
Scientific Notation….and why.2. Write a given number in Scientific
Notation.
Scientific Notation!
What does it mean??
Scientific Notation!
Do you know this number?
300,000,000 m/sec.
It's the speed of light !
(The speed at which light
travels.)
Do you know this number?
120,000 km
It's the diameter of
Saturn!
Scientists have developed a shorter method
to express very large or very small numbers.
This method is called scientific notation.
Scientific Notation is made of two factors:
A coefficient and a power of 10.
_____ x 10
Let’s look at some
examples!
What do all of the Scientific Notation
representations have in common?
Standard Notation
Scientific Notation
123,000,000,000 1.23 x 1011
56,000,000 5.6 x 107
387,000,000 3.87 x 108
7,000 7.0 x 103
Discuss with a partner and share out.
What do all of the coefficients
have in common?
1.23 x 1011
5.6 x 107
3.87 x 108
7.0 x 103
Discuss with a partner and share out.
What do all of the powers of 10
have in common?Discuss with a partner and share out.
1.23 x 1011
5.6 x 107
3.87 x 108
7.0 x 103
What do all of the exponents represent?
Discuss with a partner and share out.
123,000,000,000 1.23 x 1011
56,000,000 5.6 x 107
387,000,000 3.87 x 108
7,000 7.0 x 103
The number 132,400,000,000 in scientific notation is written as which of the following:
1.324 x 1011
13.24 x 1010OR
The number 89,000,000 in scientific notation is written as which of the
following:
8.9 x 106
OR8.9 x 107
The number 3,875 in scientific notation is written as which of
the following:
3.875 x 100
OR3.875 x 103
Write the number 76,000 in scientific notation:
Let’s take a look at some very
small numbers!
Do you recognize this number?
0.000000000753 kg.
It is the mass of a single dust particle!
Do you recognize this number?
0.000017 m
It is the width of a
single human hair!
Let’s look at some
examples!
What do all of the Scientific Notation
representations have in common?
Standard Notation Scientific Notation
0.000000078 7.8 x 10-8
0.0000456 4.56 x 10-5
0.0000000094 9.4 x 10-9
0.0007 7.0 x 10-4
Discuss with a partner and share out.
What do all of the coefficients
have in common?Discuss with a partner and share out.
7.8 x 10-8
4.56 x 10-5
9.4 x 10-9
7.0 x 10-4
What do all of the powers of 10
have in common?Discuss with a partner and share out.
7.8 x 10-8
4.56 x 10-5
9.4 x 10-9
7.0 x 10-4
What do all of the exponentsrepresent?
Discuss with a partner and share out.
0.000000078 7.8 x 10-8
0.0000456 4.56 x 10-5
0.0000000094 9.4 x 10-9
0.0007 7.0 x 10-4
The number 0.000000049 in scientific notation is written as which of the following:
49 x 10-8
OR4.9 x 10-8
The number 0.00003 in scientific notation is written as which of the
following:
3 x 10-5
OR0.3 x 10-4
The number 0.00000000707 in scientific notation is written as
which of the following:
7.7 x 10-10
OR7.07 x 10-9
Write the number 0.0000065 in scientific
notation:
Sarah vs. Stacy
There’s a correct way to write Scientific Notation, just like the Order of Operations. Without a set standard,
several answers could actually be correct.
Using the standards you just learned, decide which student is correctly
writing the numbers.
Sarah vs. StacyProblem #1
831,000Sarah thinks the answer is
Stacy thinks the answer is
8.31 X 105 8.31 X 10-5
Who is correct? And how do you know?
What mistake did the incorrect student make?
Sarah vs. StacyProblem #2
0.00345Sarah thinks the answer is
Stacy thinks the answer is
3.45 X 10-2 3.45 X 10-3
Who is correct? And how do you know?
What mistake did the incorrect student make?
Sarah vs. StacyProblem #3
0.0000006Sarah thinks the answer is
Stacy thinks the answer is
0.6 X 106 6.0 X 10-7
Who is correct? And how do you know?
What mistake did the incorrect student make?
On Your Own!!A.
8.24 x 3-5B.
9.71 x 108
C.
0.4 x 102D.
39.13 x 10-4
1. Which number below is written in Scientific Notation?
2. Write the following numbers in Scientific Notation:480,000 0.000734