Science Investigations
Measures of Science
Scientific Notation
Why do we use it?Expresses decimal places as
powers of 10Written in the form M x 10n
M (mantissa): numerical part of the value written as a
number between 1 and 9
Only write one digit to the left of the decimal point
n (exponent): a power of 10
Example: Which of the following is expressed correctly?
55.92 x 106 or 5.592 x 107
0.33 x 104 or 3.3 x 103
55 x 10 or 55 x 102
Rules
Numbers GREATER than ten have POSITIVE exponents that represent the number of places the decimal point was moved 450, ooo 4.5 x 105
Numbers LESS than ten have NEGATIVE exponents that represent the number of places the decimal point was moved 0.0081 8.1 x 10-3
Practice on Sheet
Conventional vs. Scientific notation
Using Calculator to type exponents
Scientific Calculator9.2 x 10-4 9.2 EE/EXP -4
Graphing CalculatorAlso type in EE/EXP in place of x10
Practice
Practice adding , subtracting, multiplying, and dividing on sheet
Metric System
Decimal system based on powers of 10
Uses prefixes (milli, centi, hecto, ect.) to change amount of SI units (g, L, m)
SI: International System – used worldwide
SI Base Units
Length: meter (m)Time: second (s)Mass: gram (g)Volume: Liter (L)
Derived Units
Combination of base unitsm/sm/s2
SI Prefixes
Abbreviation Relationship to base
Written Name
(smallest) micro 1,000,000 µm = 1 m
millionth
milli 1,000 mm = 1 m
thousandth
centi 100 cm = 1 m hundredth
deci 10 dm = 1m tenth
Base m, L, s, g
Hecto 1 hm = 100 m hundred
Kilo 1 km = 1,000 m thousand
(largest) Mega 1 Mm = 1,000,000 m
million
StopPractice converting between base units and prefixes
Significant Digits
The valid digits in a measurement Includes all the digits that you are
certain about, plus one estimated digit
Sig. Digit Rules
1)Every nonzero digit is significantEx. 24.7, 237 (3 sig. figs.)
2)Zeros between nonzeros are significantEx. 7003, 40.07 (4 sig. figs)
Sig. Digit Rules
3) Zeros appearing in front of nonzero digits are not significant-act as placeholders, show
magnitudeEx. 0.000042, 0.34 (2 sig. figs.)
4) Zeros at the end of a number and to the right of a decimal point are significantEx. 43.60, 1.010 (4 sig. figs.)
Sig. Digit Rules
5) Zeros at the end of the number without a decimal point aren’t significantEx. 300 (1 sig. fig.), 27,300
(3 sig. figs.)
Sig. Digit Short Cut
23.50
23,400
0.00560
Multiplication and Division w/ Sig. Digits
Your answer can’t have more sig. digits than the number in the calculation with the least amount of sig. digits
Ex. Finding Area Length = 60.564278 m Width = 35.25 m Answer = 2135 m2, not 2134.8908
m2
Addition and Subtraction w/ Sig. Digits
Answers can’t have more numbers to the right of the decimal point than the number with the least amount of numbers to the right of the decimal point
Ex. 22.03 + 23.1 = 45.1
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