Why Use Scientific Notation
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Scientific Notation
• A way to express very large numbers or very small
numbers
• A number between 1 and <10 followed by “ x 10?”
• Ex:
• 602214085700000000000000 6.022 x 1023
• 0.00000000580
5.80 x 10-9
3.0 x 108
• 300000000
Scientific Notation
• Examples:
Write the following numbers in scientific notation:
7.85 x 105
=
3.0 x 10-10
a) 785000
b) 0.00000000030 =
• A positive exponent: move decimal to the right (starting with sci. not.)
• 3.65 x 104 = 36500
• A negative exponent: move decimal to the left (starting with sci. not.)
• 3.65 x 10-4 = 0.000365
• Practice on your calculator
Which is larger:
4.5 x 10-5 or 3.8 x 10-7 ? 0.000045
0.00000038
Significant
Figures
• Digits in a number which define its uncertainty
• How to count them:
1. All non-zero digits (1-9) “count”
• Example:
How many sig figs are in 4579?
Answer: 4
2. Zeroes:
1. Don’t count if they are beginning: 0.00000000007 (only 1 sig fig)
2. End zeroes only count if there is a decimal
• 30.0 (3 sig figs), 41.00 (4 sig figs)
• 150000 (2 sig figs because no decimal)
3. Zeroes BETWEEN 1-9 ALWAYS count (like 30034 sig figs)
Determine the sig figs for the following numbers:
1) 1.05
2) 0.45
3) 500
4) 500.
5) 450.3
6) 3.40 x 10-5
7) 0.60
8) 0.0070
9) 2.30
10)1.008
11)5.800
12)0.0001
Multiplying and Dividing
STEPS for sig figs:
1. Do the math.
2. Look at the numbers you just multiplied/divided.
Count their sig figs and determine which number
has the fewest sig figs.
3. Round your answer to the least sig figs (from #2).
Examples:
1) 2.450 x 0.023 = 0.05635
4
2 number of sig figs
Answer: 0.056
2) 0.004 x 23.56 = 0.09424
1
4 number of sig figs
Answer: 0.09
Try these:
1) 2.010/0.33
2) 0.990 x 4780
3) 3.4 x 10-4 x 4.568 x 10-5
Adding and Subtracting
STEPS for sig figs:
1. Do the math.
2. Look at the numbers you just added/subtracted. Determine
which number has the least number of decimal places.
3. Round your answer to the same amount of decimal places as
you found in step 2.
4. If the numbers are whole numbers, round to the least
number of sig figs.
Examples:
1) 120.0015 + 5.2
=125.2015
=125.2
2) 14.6+ 110.256
=124.9
NOTE:
Certain conversion factors have an
infinite number of sig figs.
IGNORE THESE!!!
These will not determine the number of
sig figs in your answer.
Try these:
1)575.456 + 10.5 =
2)570. cm= ________mm
(use dimensional analysis)