Transcript Scientific Notation

Scientific Notation
A short-hand way of writing
large numbers without
writing all of the zeros.
Scientific Notation Video
How many protons are in the Sun if
it’s made up entirely of protons?
Mass of the sun = 2 x 1030 kg
Mass of a proton = 1.673 x 10-27 kg
Video Answer
Scientific Notation
A number is expressed in
scientific notation when it is in
the form
a x 10n
where a is between 1 and 10
and n is an integer
The Distance From the
Sun to the Earth
150,000,000 km
Step 1
Move decimal left
Leave only one number in front of
decimal
Step 2
Write number without zeros
Step 3
Count how many places you moved
decimal
Make that your power of ten
The power of
ten is 8 because
the decimal
moved 8 places.
150,000,000 --Standard Form
1.5 x 108 --Scientific Notation
Practice Problem
Write in scientific notation.
Decide the power of ten.
1) 98,500,000 = 9.85 x 10?
3) 279,000,000 = 2.79 x 10?
9.85 x 107
6.41 x 1010
2.79 x 108
4) 4,200,000 = 4.2 x 10?
4.2 x 106
2) 64,100,000,000 = 6.41 x 10?
1) Express 0.000 000 0902 in
scientific notation.
Where would the decimal go to make the
number be between 1 and 10?
9.02
The decimal was moved how many places?
8
When the original number is less than 1, the
exponent is negative.
9.02 x 10-8
2) Express 1.8 x 10-4 in standard notation.
0.00018
3) Express 4.58 x 106 in standard notation.
4,580,000
On the graphing calculator, scientific
notation is done with the
button.
4.58 x 106 is typed 4.58
6
More Practice Problems
Convert to Scientific Notation
1) 734,000,000 = ______
2) 870,000,000,000 = ______
3) 90,000,000,000 = _______
1) 7.34 x
108
2) 8.7 x
1011
3) 9 x 1010
More Practice Problems
Convert to Scientific Notation
1) 0.0734 = ______
2) 0.870 = ______
3) 0.009 = _______
1) 7.34 x
10-2
2) 8.70 x
10-1
3) 9 x 10-3
Scientific Notation to
Standard Form
Multiply by the power of ten
3.4 x 105 in scientific notation
3.4 x 100 000 (or 3.4 [exp] 5)
340,000 in standard form
Write in Standard Form
6.27 x 106
9.01 x 104
6,270,000
90,100
Converting Units
Use the given conversions and set up an
equation
Convert 1500 m to km
We know 1km = 1000m, so set up the equation:
1km = __?_km__  0.001x1500 = 1.5 km
1000m
1500m
Converting Lightyears
1 light year = 9.5 x 1012 km
Use the following equation to convert ly to km
and km to ly
1ly
=
ly__
9.5 x 1012 km
km
or
9.5 x 1012 km = ____km __
1ly
ly