Review for Test #2• Rational Numbers and Irrational Numbers

• Real Numbers• Powers and Exponents • Scientific Notation

Rational Numbers: Are numbers that can be written as fractions.Whole number PercentIntegers Perfect Square Decimal

Repeating decimal Terminating decimal

Irrational Numbers: A number that CAN NOT be written as a fraction. Decimals that are non-terminating Non repeating

How to identify between Rational and Irrational

1. Divide to form a fraction

2. Decimal must be repeating or termination

“Real Numbers”Whole Numbers: All positive number including

(0,1,2,3..)IT CAN’T BE: Negative, Fraction, Decimals

Integers: All positive and negative number (-2,-1,0,1,2) IT CAN’T BE: Fraction and Decimals

Natural Number: All positive number NOT including 0IT CAN’T BE: Zero, Negative, Fraction, Decimals

Name ALL sets to which the number belongs :

7: Whole, Integer, natural, rational

-4: Rational, Integers

Square root of 4: Whole, Integer, Natural, Rational

2/5: Rational

0.12369: Irrational

6%: Rational

-2 1/4: Rational

Powers and Exponents: An exponent tells you HOW

many times the base is being used as a factor. The common factor is called a base . Numbers expressed using exponents are called factors.

Write each expression using Exponents:

9x9x9x9x9x9x9

97

(-6)(-6)(-6)(-6) 3

(3/4)(3/4)(3/4)(3/4) (3/4) 4

Evaluate: (Solve)

(-3)5

(-3)(-3)(-3)(-3)(-3) = -243

(-1/3) 4

(-1/3)(1/3)(1/3)(1/3) = (1/81)

Count Negative: Even number of negative = POSTIVEOdd number of negative = NEGATIVE

Powers of Powers Rule: To MULTIPLY powers with the SAME base, keep

the base and ADD the exponents.

a5 x a5 = a10

Rule: To MULTIPLY powers with the DIFFERENT base, multiply the base and ADD the exponents.

105 x 505 = 5010

Diving Powers or Quotient Rule: To DIVIDE powers with the same base,

keep the base and SUBTRACT exponents.

b10 ÷ b5 = b5

Rule: To DIVIDE powers with different base, divide the base and SUBRACT the exponents.

1010 ÷ 55 = 25

Power of a Product:Rule: Multiply ALL the exponents on the inside

times the exponents on the outside.

(ab) m = am x bm

Negative Exponents: 4-2 = 1/42

Why?? Because when making a fraction you put a one under the whole number then you find the reciprocal.

REMEMBER: You can NOT leave an exponent negative because there is no way to express its meaning. You must make it a POSITIVE!

Zero Exponents:Rule: Anything to the power of zero = ONE!

a0 = 1

Scientific Notation: Standard Form to Scientific Notation

If my number is a WHOLE number, my EXPONENT is going to be POSTIVE!

250000 = 2.5 X 105

If my number is a DECIMAL number, my EXPONENT is going to be NEGATIVE!

0.0057 = 5.7 X 10-3

Scientific Notation to Standard Form:

If my EXPONENT is a NEGATIVE , my answer is going to be a DECIMAL!

5.7 X 10-3 = 0.0057

If my EXPONENT is a POSITIVE, my answer is going to be a WHOLE number!

2.5 X 105 = 250000

Compute (evaluate) with Scientific Notation

Divide: Divide the coefficient Subtract the exponents

Multiply:Multiply the coefficientAdd the exponents

Compute (evaluate) with Scientific Notation

Addition: If your EXPONENTS are different you must make

them the SAME. You pick the smallest exponent and make it equal to the

biggest exponent. Once the exponents are the SAME, then ADD the

coefficients.

GOOD LUCK!