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