Transcript scientific notation significant digits

Scientific Notation & Significant Figures
Scientific Notation
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Scientific Notation (also called Standard Form) is a
special way of writing numbers that makes it easier to
use big and small numbers.
You write the number in two parts:
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Just the digits (with the decimal point placed after the first
digit), followed by
× 10 to a power that would put the decimal point back
where it should be (i.e. it shows how many places to move
the decimal point).
Scientific Notation
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If the number is 10 or greater, the decimal place has to
move to the left, and the power of 10 will be positive.
If the number is smaller than 1, then decimal place has
to move to the right, so the power of 10 will be
negative.
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Example: 0.0055 would be written as 5.5 × 10-3
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Because 0.0055 = 5.5 × 0.001 = 5.5 × 10-3
Scientific notation
Decimal notation
127
0.0907
0.000506
2 300 000 000 000
Scientific notation
1.27 x 102
9.07 x 10 –2
5.06 x 10 –4
2.3 x 1012
What is a significant figure?
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There are 2 kinds of numbers:
 Exact: the amount of money in your
account. Known with certainty.
 Approximate: weight, height—anything
MEASURED. No measurement is perfect.
Measuring and recording
 If you
measured the
length of a pen
with your
ruler you
might record
4.72cm.
 To a
mathematician
4.72, or 4.720
is the same.
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But, to a scientist
4.72cm and 4.720cm is
NOT the same
4.720cm to a scientist
means the
measurement is
accurate to within one
thousandth of a cm.
We know that the
length of the pen is
between 4.7 and 4.8
because these are our
smallest markings. The
last digit recorded is a
guess.
Rules for Significant Digits
1. Numbers
•All digits from 1 to 9 (nonzero digits) are
significant.
5.87 = 3 significant digits
8981 = 4 significant digits
Zeroes
2. All zeros which are between non-zero digits are
always significant.
Ex. 901 (3), 321.09 (5), 1011(4)
3. Zeroes to the left are NOT significant, and serve only
to locate the decimal point.
Ex. 0.0987(3), 0.00001(1)
4. Zeros to the right MAY be significant, if it is also to
the right of the decimal place. To be significant, the
zero must follow a non-zero number.
Ex. 23400 (no, 3), 0.0670 (yes,3)
Counted Numbers
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5. Because counted numbers are not measured, they
have an infinite number of significant figures.
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i.e. 3 test tubes, 5 pennies, 10 beakers.
How many significant figures?
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1.2
2100
56.76
4.00
0.0792
7,083,000,000
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•
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2
2
4
3
3
4
Significant Digits Tips
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It is better to represent 100 as 1.00 x 102
Alternatively you can underline the position of the last
significant digit. E.g. 100.
This is especially useful when doing a long calculation or
for recording experimental results
Don’t round your answer until the last step in a calculation.
Adding with Significant Digits
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When adding or subtracting, the answer can have no
more places after the decimal than the LEAST of the
measured numbers
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E.g. a) 13.64 + 0.075 + 67 b) 267.8 – 9.36
13.64
+ 0.075
+ 67.
81
80.715
267.8
– 9.36
258.44
Multiplication and Division
Use the same number of significant digits as the value
with the fewest number of significant digits.
 E.g. a) 608.3 x 3.45 b) 4.8  392
a) 3.45 has 3 sig. digits, so the answer will as well
608.3 x 3.45 = 2098.635 = 2.10 x 103
b) 4.8 has 2 sig. digits, so the answer will as well
4.8  392 = 0.012245 = 0.012 or 1.2 x 10 – 2
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Review
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Scientific Notation
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Know the 2 parts to writing scientific notation:
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The digits
10 to a power
Know how to convert between scientific notation and
decimal form (on your formulas handout).
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If the power of 10 is positive, the decimal place moves to the right
that many times.
If the power of 10 is negative, the decimal place moves to the left
that many times.
Review
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Significant Digits
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Know the 5 rules for determining significant digits
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1. Digits 1-9 are always significant.
2. Zeroes between non-zero digits are significant.
3. Zeroes to the left of non-zero digits are not significant. They
only serve as placeholders.
4. Zeroes to the right of non-zero digits are significant if they are
also to the right of the decimal place.
5. Counted numbers have an infinite number of significant figures.
Physics formula sheet
Review
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Adding and Subtracting
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Your answer can only have as many decimal places as the
measured number with the fewest decimal places.
Multiplying and Dividing
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Your answer can only have as many significant figures as the
measured number with the fewest significant figures.