6.22

1. 6.22 positive exponents, perfect squares, square roots, and for numbers greater than 10, scientific notation. Calculators will be used.

2. Ppg 53 • EXPONENTS- • • Any real number other than zero raised to the zero power is 1. Ex-50=1 100=12370=1 • Directions for Scientific Notation • Step 1 • Example 1: 3.2 × 103 is scientific notation for 3,200 • REMEMBER: The decimal in a whole number is at the end of the number • 31, 2 0 0 . ( x 10 ) set up • Step 2 • The whole number must be between 1 and 10 ex. 3 1200. Basically, draw a line after the first number. • Write as a decimal 3.12 • Count out digits behind line. There are 4. This is your power. 104 • Write 3.12 x 104 • Directions- rewriting a scientific notation • Example 4.2 x 105 • Write whole or decimal number w/o the decimal point. 42 • Add zeros according to number of power 4200000 • Count spaces behind decimal point and add decimal to number 4200000 rewrite 420,000 • PRACTICE- • Write in Scientific Notation problems 1-4 • 2, 430, 000 2. 445 3. 75, 030 4. 80,000 • Write in Standard Notation problems 5-8 6.05 x 104 . 6. 1.6 x 1087. 9 x 103 8. 9.45 x 104 • 9. 80 =______ 10. Which number is the base in 74 ? 6.22 Vocabulary pg 54 Exponent- A numerical value composed of a power and a base. EX- 53 means 5x5x5= 125 Exponential Notation- In exponential notation, the base is the number that is multiplied, and the exponent represents the number of times the base is used as a factor. EX- 53 5 is the base and 3 is the number of times you multiply 5 times itself. Power- The power, written as a superscript number, symbolizes how many times the base number must be multiplied to find the numerical value of the exponent. EX- 53 3 is the power. Base- The base is the factor that will be multiplied in an exponent. The power tells how many times the base will be multiplied to find the numerical value of the exponent. EX- 53 5 is the base. Power of Ten- A power of ten is an exponent composed of the number ten (10) raised to a power. The power tells how many zeroes will be in the standard form of the exponent. EX- 10³ will have three zeroes in the answer, making it 1,000. If 10³ was written as a product of its factors, it would read 10×10×10=1,000. Square root- A square root of a number is a number which, when multiplied by itself, produces the given number. EX- the square root of 49 is 7 since 7  7 = 49. Squared- A number multiplied by itself; symbolized by a superscript 2 written above and to the right of a number. EX- 5 squared (5²) would be solved by multiplying 5×5=25. Perfect square- Perfect squares are the numbers that result from multiplying any whole number by itself Ex- 36 = 6  6. Scientific notation- Scientific notation for a number is expressed by writing the number as a number greater than or equal to 1 but less than 10 times a power of 10. EX- 3.2  103 is scientific notation for 3,200. Cubed- A number, multiplied by itself and then multiplied again by itself. It is symbolized by a superscript 3 written above and to the right of a number. EX- 4 cubed (4³) would be solved by multiplying 4×4×4=64.