Algebra Ch. 1

Question 1

What are natural numbers?

Answer 1

a set of numbers that are used to count objects. Also known as “counting numbers”.

Question 2

What are whole numbers?

Answer 2

a set of numbers containing the natural numbers AND zero.

Question 3

What are integers?

Answer 3

a set of numbers containing the natural numbers, zero, and negative numbers.

Question 4

What are rational numbers?

Answer 4

numbers that can be expressed in the form a/b where “a” and “b” are integers and “b” does not equal 0.

Question 5

What are real numbers?

Answer 5

all irrational and rational numbers.

Question 6

What is a finite set?

Answer 6

a set whose elements can be counted. Ex. {0,1,2,3,5,11}

Question 7

What is an infinite set?

Answer 7

a set whose elements cannot be counted because there is no end to the set. Ex. {6,7,4,0…}

Question 8

What is an empty set?

Answer 8

a set that contains no elements. Written as { }

Question 9

What are opposites?

Answer 9

a number that is the same distance away from zero but on the other side of zero. (Either positive or negative. Both numbers cannot be negative or positive.)

Question 10

What is a subset?

Answer 10

a set in which all its elements are contained in another set of equal or greater size.
Ex. A={1,2,3,4,5,6,7} B={3,6,7} B is a subset of A.

Question 11

What is a number line?

Answer 11

a line that is used to show the numbers of a set in their relationship to each other.

Question 12

What is a graph?

Answer 12

a point on the number line that represents each number.

Question 13

What is a standard number line?

Answer 13

a number line that has positive numbers appearing to the right of zero, and negative numbers appearing to the left of zero.

Question 14

What is a unit measure?

Answer 14

the distance between points on a number line.

Question 15

What is absolute value?

Answer 15

the distance a number is away from zero on the number line. (distance is always positive.) Ex. l5l=5, l-3l=3

Question 16

What is inequality?

Answer 16

a comparison between two numbers that are not equal.

Question 17

What is an irrational number?

Answer 17

an infinite, non-repeating decimal.

Question 18

What is to square?

Answer 18

to multiply a number by itself.

Question 19

What is a square root?

Answer 19

the opposite of squaring a number.

Question 20

What is the radical sign?

Answer 20

the symbol means to take the square root of the number underneath the sign.

Question 21

What is rational approximation?

Answer 21

a rational number that is close to but not equal to the value of an irrational number.

Question 22

What is a real number line?

Answer 22

all the points on a number line represented by all the irrational and rational numbers

Question 23

What is the completeness property of real numbers?

Answer 23

every point on the real number line corresponds to a real number, and every real number corresponds to a point on the real number line.

Question 24

What is GPE?

Answer 24

the amount of inaccuracy in a measurement that is figured out by multiplying 1/2 times the value of the last significant digit.

Question 25

What are significant digits?

Answer 25

digits that are used to determine a measure, excluding zeros that used as place holders in the beginning of a decimal fraction and at the end of an integer.

Question 26

What is precision?

Answer 26

the place value of the last significant digit in a number.

Question 27

What is accuracy?

Answer 27

the number of significant digits in a measure.

Question 28

Give an example of an irrational number:

Answer 28

Pi, √2, √5, √8, 0.01001000100001...

Question 29

Give an example of a square number:

Answer 29

3^2=3x3=9. 9 is a square number.

Question 30

What is the square root of 9?

Answer 30

3

Question 31

What is the square root of 36?

Answer 31

6

Question 32

What are the rules for determining significant digits?

Answer 32

1. All nonzero digits are significant. Ex. 45.67 has four significant digits. 2. All zeros between significant digits are significant. Ex. 204.65 has five significant digits. 3. All zeros at the end of a decimal fraction are significant. Ex. 67.0000 has six significant digits. 4. Zeros that come before the first nonzero digit in a decimal fraction are NOT significant. Ex. 0.00098 has two significant digits. 5. Zeros at the end of an integer may or may not be significant. Sometimes a dot is placed over a zero if it is significant. Ex. 3,200 has two significant digits.

Question 33

Multiplication and division have to do with accuracy or precision?

Answer 33

(fill in)

Question 34

Addition and subtraction have to do with accuracy or precision?

Answer 34

(fill in)

Question 35

What is a common fraction?

Answer 35

a fraction with a numerator and denominator.

Question 36

What is the meaning of everywhere dense?

Answer 36

between any two rational numbers there exist another rational number.

Question 37

What is a decimal fraction?

Answer 37

a fraction in which the numerator is written after the decimal point and the denominator is indicated by the place value of the last digit.

Question 38

What is a numeral?

Answer 38

symbols that are used to represent numbers like 1,2,3,4, etc.

Question 39

What is a successor?

Answer 39

the counting number that is one more than another counting number.