University:
Eastern Kentucky University
Course:
MAT 112 | Algebra with Applications
Academic year:

2020
Views:

125

Pages:

1
Author:

Dominick Dickson

Physics and Math 10: Mathematics Arithmetic and Sig Figs Exponents, Log and Ln Scientific Notation: Improves the ease of calculation. It is usually helpful to convert a number to scientific notation (3# ×# 10' ) − (9# ×#10+ ) = (3# ×# 10' ) − (0.9# ×#10' ) =#2.1# ×# 10' (1.5# ×#10' )(3# ×#10+ ) =#4.5# × #101 2#×#3456 +#×#347 =4# ×# 1081 8+ )' (2# ×# 10 =8# ×# 10 √9# ×#102 (9# × #102 )3/+ = Common 1++ =1 Squares: 2+ =4 - Divide the exponent by 2 - Left Add - Right Subtract Significant Figures: Include all nonzero digits and any trailing zeroes in a number with a decimal point. Estimation: Multiplication: If one number is rounded up, the other should be rounded down in proportion. 16+ 17+ 18+ 19+ 20+ = 256 = 289 = 324 = 361 = 400 𝒆=𝟐. 𝟕 log R (1)=0 log R (greater#than#1) = Positive log R (𝐴)=1 log R (less#than#1) = Negative ) = log#(𝐴) + log#(𝐵) log ( 𝐴# × #𝐵 𝐴 log a b=#log#(𝐴) − log#(𝐵) 𝐵 log(𝐴c )=𝐵#log#(𝐴) 1 log#( )= # −log#(𝐴) 𝐴 Division: If one number is rounded up, the other should also be rounded up in proportion. Estimating Log: log (𝐴# ×# 10c) = log( 𝐴) + log ( 10c ) = # log(𝐴) + 𝐵 Trigonometry log (𝐴# ×# 10c) ≈𝐵+ 0. 𝐴 SOH CAH TOAsin ( ∅ ) = # e f Common Values: 11+ = 121 12+ = 144 13+ = 169 14+ = 196 15+ = 225 𝐥𝐧(𝑨) =#𝑩 𝐞𝑩 =𝑨 Log and Ln: 𝐥𝐨𝐠( 𝑨 ) =#𝑩 𝟏𝟎𝑩 =𝑨 LARS mnemonic when moving the decimal within scientific notation. Left Þ Add, Right Þ Subtract 481.2# ×# 10> =4.812 × 10? 0.00314# × 108'=3.13 × 108: 6+ = 36 7+ = 49 8+ = 64 9+ = 81 10+ = 100 3 =9 4+ = 16 5+ = 25 - Multiply exponents =3# ×#10= falls between. For example, √180 is between 13 and 14. √180= # √4 # × # √9 # × #√5= 2# × #3# × # √5=6√5 √5 # ≈2.2 so 6√5 # ≈13.2. - Add exponents - Subtract exponents 8: Estimating To calculate the square root of any number less than 400, you can Square Roots: approximate its value by determining which two perfect squares it q R cos( ∅) = # f e hij#(∅) tan ( ∅) = #R = #klh#(∅) cos( q) sin(q ) tan( q ) 0° 1 0 0 30° √3 2 1 2 √3 3 45° √2 2 √2 2 1 60° 1 √3 √3 2 2 90° 0 1 undefined 180° -1 0 0 The Unit Circle x=cos(q) tan(q) 45-45-90 triangle 30-60-90 triangle 𝑦=sin(q) o =# p =# hij#( q) klh( q)

Physics and Math 10 Mathematics

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