Transcript Scientific Notation

Units and Standards
Units and Standards
• In science, numbers aren’t just numbers.
• They need a unit. We use standards for this unit.
• A standard is:
•a basis for comparison
•a reference point against which other things can
be evaluated
• Ex. Meter, second, degree
Units and Standards
• The unit of a #, tells us what standard to use.
• Two most common system:
•English system
•Metric system
•The science world agreed to use the International
System (SI)
•Based upon the metric system.
Units and Standards
Units and Standards
• Conversions in the SI are easy because everything
is based on powers of 10
Units and Standards
• Ex. Length.
• Base unit is meter.
Common conversions
2.54 cm = 1 in
5280 ft = 1 mile
2000 lb = 1 ton
1 kg = 2.205 lb
1 lb = 453.6 g
1 lb = 16 oz
1 L = 1.06 qt
4 qt = 1 gallon
4 cups = 48 tsp
Scientific
Notation
Scientific Notation
A short-hand way of writing
large numbers without
writing all of the zeros.
Scientific notation
consists of two parts:
A number between 1 and 10
A power of 10
Nx
x
10
The Distance From the
Sun to the Earth
149,000,000km
Step 1
Move the decimal to the left
Leave only one number in front of
decimal
Step 2
Write the number without zeros
Step 3
Count how many places you moved
decimal
Make that your power of ten
The power of
ten is 7 because
the decimal
moved 7 places.
93,000,000 --Standard Form
9.3 x 107 --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?
More Practice Problems
On these, decide where the decimal will be moved.
1) 734,000,000 = ______ x 108
2) 870,000,000,000 = ______x 1011
3) 90,000,000,000 = _____ x 1010
1) 7.34 x
108
2) 8.7 x
1011
3) 9 x 1010
Complete Practice Problems
Write in scientific notation.
1) 50,000
2) 7,200,000
3) 802,000,000,000
1) 5 x 104
2) 7.2 x 106
3) 8.02 x 1011
Scientific Notation to
Standard Form
Move the decimal to the right
3.4 x 105 in scientific notation
3.40000 --- move the decimal
340,000 in standard form
Practice:
Write in Standard Form
6.27 x 106
9.01 x 104
6,270,000
90,100
Accuracy, Precision and
Significant Figures
Accuracy & Precision
Accuracy:
 How
close a measurement is to the true
value of the quantity that was measured.
 Think: How close to the real value is it?
Accuracy & Precision
Precision:
 How
closely two or more measurements
of the same quantity agree with one
another.
 Think: Can the measurement be
consistently reproduced?
Significant Figures
The numbers reported in a
measurement are limited by the
measuring tool
Significant figures in a
measurement include the known
digits plus one estimated digit
Three Basic Rules
Non-zero digits are always significant.
 523.7
has ____ significant figures
Any zeros between two significant digits
are significant.

23.07 has ____ significant figures
A final zero or trailing zeros if it has a
decimal, ONLY, are significant.


3.200 has ____ significant figures
200 has ____ significant figures
Practice
How many sig. fig’s do the following
numbers have?








38.15 cm _________
5.6 ft ____________
2001 min ________
50.8 mm _________
25,000 in ________
200. yr __________
0.008 mm ________
0.0156 oz ________
Exact Numbers
Can be thought of as having an infinite
number of significant figures
An exact number won’t limit the math.
 1.
12 items in a dozen
 2. 12 inches in a foot
 3. 60 seconds in a minute
Adding and Subtracting
The answer has the same number of
decimal places as the measurement with
the fewest decimal places.
25.2 one decimal place
+ 1.34 two decimal places
26.54 answer
26.5 one decimal place
Practice:
Adding and Subtracting
In each calculation, round the answer to the correct
number of significant figures.
A. 235.05 + 19.6 + 2.1 =
1) 256.75 2) 256.8 3) 257
B. 58.925 - 18.2 =
1) 40.725 2) 40.73 3) 40.7
Multiplying and Dividing
Round to so that you have the same
number of significant figures as the
measurement with the fewest
significant figures.
42
x 10.8
453.6
two sig figs
three sig figs
answer
450 two sig figs
Practice:
Multiplying and Dividing
In each calculation, round the answer to the correct
number of significant figures.
A. 2.19 X 4.2 =
1) 9 2) 9.2 3) 9.198
B. 4.311 ÷ 0.07 =
1) 61.58 2) 62 3) 60
Practice work
How many sig figs are in each number listed?



A) 10.47020
B) 1.4030
C) 1000
D) 0.060
E) 90210
F) 0.03020
Calculate, giving the answer with the correct number
of sig figs.



12.6 x 0.53
(12.6 x 0.53) – 4.59
(25.36 – 4.1) ÷ 2.317