the number systems: nested...
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Unit 1:
Roots and Powers
1.1: Number Sets
Every number that we work with in high school is classified as a Real Number ( ). Within the Real Number System there are a variety of number sets:
- Natural Numbers: They are our countable numbers. = {1, 2, 3, 4, ...}
- Whole Numbers: Countable numbers and zero.W = {0, 1, 2, 3, ...}
- Integers: All positive and negative whole numbers. = { ..., -3, -2, -1, 0, 1, 2, 3, ...}
- Rational Numbers: Decimal numbers which repeat or terminate. These can all be written as a fraction.
= {..., -3.33..., -1.5, - , 0, √.16, 5.9, .....}
**N, W, and I are all sets within the Rational Numbers.
- Irrational Numbers: A decimal number which does not terminate or repeat. It cannot be written as a fraction.
= {...., 1.67983456...., , √12, ...}
The Number Systems: Nested Diagram
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a) 9
c) 7/11
2. Math3. Frac (1)4. Enter
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1.2 Prime Numbers, GCF, LCM
Unit 1:
Roots and Powers
Classify as prime or composite.
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State the following:
a) Factors of 12.
Factor
2 x 2 x 2 x 2 x 3 = 48x 3 = 48
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The greatest common factor (GCF) of a set of numbers is the largest whole number which divides exactly into each term.
Ex. GCF of 8, 16 is _____.
Enter Numbers (#,#)
* to find the GCF of 3 numbers, find the gcf of the first two, then use the answer and the last number
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The LCM of 6 and 8 is ____.
Ti-NSpire TI-83/841. Menu 1. Math2. 2: Number 2. Num3. 4: Least Common Multiple 3. 8: lcm(4. Enter Numbers (#,#) 4. Enter Numbers (#,#)
Determine the LCM of 126 and 441.
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Unit 1:
Roots and Powers
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You will be using the Perfect Square/Perfect Cube chart in the classroom, but on the final exam you will need to make your own. Try to do the following in your head:
Perfect Squares Perfect Cubes
* think repeated multiplication
Sometimes you will need to use larger powers. The nice thing about exponents is the larger they get, the shorter your list needs to be. Try these:
Powers of Four Powers of Five
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.
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Unit 1:
Roots and Powers
Ex. √16 x 9 is equal to √16 x √9 because:
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So, how do we convert entire radicals to mixed radical form?
1. Find the largest perfect square that the radicand is divisible by (without making a decimal answer.) Use the chart.
3. The number / factor left over is the new radicand that stays under the radical sign.
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Ex. Convert the following to Mixed Radicals in simplest form.
So, how do we convert mixed radicals to entire radicals?
multiply Note:
is a fraction
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identify ...
Index:
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