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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
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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
5c
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Richard Goldman