Scientific Notation

Scientific (Exponential) Notation A number is written as the product of two numbers, a coefficient and 10 raised to a power 36,000 = 3.6 x x 10 x 10 x 10 x 10 Which number is the coefficient? The coefficient is 3.6. Which number is the exponent? The exponent is 4.

Converting Measurements For numbers greater than ten, the exponent is positive and equals the number of places the original decimal point has been moved to the left (coefficient indicates multiplication) For numbers less than ten, the exponent is negative and equals the number of places the original decimal point has been moved to the right (exponent indicates division)

Practice Examples The mass of an atom of gold is gram. Write this in scientific notation. Answer is 3.27 x A gram of hydrogen contains hydrogen atoms. Write this in scientific notation. Answer is 6.02 x 10 23

Multiplication and Division To multiply, multiply the coefficients and add the exponents To divide, divide the coefficients and then subtract the exponent in the denominator (bottom) from the exponent in the numerator (top)

Practice Problems Multiply: (3.0 x 10 4 ) x (2.0 x 10 2 ) Answer is 6 x 10 6 Divide: (3.0 x 10 4 ) ÷ (2.0 x 10 2 ) Answer is1.5 x 10 2

Addition and Subtraction Must make exponents the same Then add or subtract the coefficients Example: (5.40 x 10 3 ) + (6.0 x 10 2 ) Adjust 6.0 x 10 2 to 0.60 x 10 3 When the decimal point is moved to the left, the exponent increases Add the coefficients ( ) Answer is 6.00 x 10 3