Measures of Science

 Why do we use it?  Expresses decimal places as powers of 10  Written in the form M x 10 n  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? x 10 6 or x x 10 4 or 3.3 x x 10 or 55 x 10 2

 Numbers GREATER than ten have POSITIVE exponents that represent the number of places the decimal point was moved  450, ooo  4.5 x 10 5  Numbers LESS than ten have NEGATIVE exponents that represent the number of places the decimal point was moved   8.1 x 10 -3

 Conventional vs. Scientific notation

 Scientific Calculator  9.2 x  9.2 EE/EXP -4  Graphing Calculator  Also type in EE/EXP in place of x10

 Practice adding, subtracting, multiplying, and dividing on sheet

 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

 Length: meter (m)  Time: second (s)  Mass: gram (g)  Volume: Liter (L)

 Combination of base units  m/s  m/s 2

AbbreviationRelationship to base Written Name (smallest) micro1,000,000 µm = 1 mmillionth milli1,000 mm = 1 mthousandth centi100 cm = 1 mhundredth deci10 dm = 1mtenth Basem, L, s, g Hecto1 hm = 100 mhundred Kilo1 km = 1,000 mthousand (largest) Mega1 Mm = 1,000,000 mmillion

 Stop  Practice converting between base units and prefixes

 The valid digits in a measurement  Includes all the digits that you are certain about, plus one estimated digit

1) Every nonzero digit is significant Ex. 24.7, 237 (3 sig. figs.) 2) Zeros between nonzeros are significant Ex. 7003, (4 sig. figs)

3) Zeros appearing in front of nonzero digits are not significant -act as placeholders, show magnitude Ex , 0.34 (2 sig. figs.) 4) Zeros at the end of a number and to the right of a decimal point are significant Ex , (4 sig. figs.)

5) Zeros at the end of the number without a decimal point aren’t significant Ex. 300 (1 sig. fig.), 27,300 (3 sig. figs.)

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 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 = m  Width = m  Answer = 2135 m 2, not m 2

 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 = 45.1