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Transcript
Lecture 9 Notes: Section 4.5 & 46 – Richard Goldman MAT116 Algebra I Basic Mathematics for College Students – 3e Review Decimal Places 0.1 1 Tenth 0.01 1 Hundredth 0.001 1 Thousandth Leading 0 0.1 = .1 (Leading zero is a general convention used to help eliminate error) Trailing 0 0.10 = 0.1 (Trailing zero is an engineering/scientific convention use to display accuracy) Rounding Round from the right just like with whole numbers. Adding & 1. Line up Decimal points Subtracting 2. Add trailing zeros to match longest decimal Decimals 3. Add or subtract as you would whole numbers Multiplying 1. Multiply as you would whole numbers Decimals 2. Count total decimal places in both factors and add to product (add leading 0’s if necessary) Dividing 1. Move the decimal place in the devisor to make it a whole number Decimals 2. Move the decimal place in the dividend the same number places 3. Divide until there is no remainder or the desired precision is reached (add trailing zeros to the dividend as necessary) Rounding Carry out division one digit past desired accuracy and then round back Multiply & Move the decimal place to the Left or Right for each 0 in the power. Divide by 10’s 4.5 Fractions and Decimals Converting Carry out the indicated division Fractions into ½ = 1 ÷ 2 = 0.5 Decimals _ Repeating 10 ÷ 3 = 3.33333333333333 or 3.3… or 3.3 (overbar) Decimal Quotients Rounding Carry out to one digit past desired precision and then round back. Repeating 1/3 ≈ 0.3333 (approximately equal to) Decimals Working Either convert to all fractions or all decimals. Problems with Examples: Fractions and 0.24 = 24/100 Decimals 0 .6 3 5 .0 3/5 = 0.6 565321555 Page 1 of 2 Richard Goldman 4.6 Square Root Radical Symbol √ Negatives Perfect Squares Pythagorean Theorem (optional) Square Root The number that must be squared to produce the number The answer is really two numbers - both a negative and a positive number We normally only deal with the positive square root Means square root Number under radical is the radicand √36 = 6, -√36 = -6, √-36 is not a real number (anything squared will always be positive) Whole number roots a2 + b2 = c2 Demo: 3, 4, 5 Rt. Triangle: a2 b2 c2 32 4 2 c 2 9 16 c 2 25 c 2 25 c 2 5c 565321555 Page 2 of 2 Richard Goldman