Scientific Notation
Scientific Notation Represent a number as the product of a coefficient (N) and power of ten (M). N x 10M Coefficient: number with only one non- zero digit to the left of the decimal point 4.25 x 103
Scientific Notation Number Factored Number # factors of 10 1 x 100 10 1 x 101 100 10 x 10 2 1 x 102 1000 10 x 10 x 10 3 1 x 103 10000 10 x 10 x 10 x 10 4 1 x 104 100000 10 x 10 x 10 x 10 x 10 5 1 x 105 1000000 10 x 10 x 10 x 10 x 10 x 10 6 1 x 106
# factors of 10 in denominator Scientific Notation Number Factored Number # factors of 10 in denominator Scientific Notation 1 1 x 100 0.1 1 10 1 x 10-1 0.01 1 10 x 10 2 1 x 10--2 0.001 1 10𝑥10𝑥10 3 1 x 10-3 0.0001 1 10𝑥10𝑥10𝑥10 4 1 x 10-4 0.00001 1 10𝑥10𝑥10𝑥10𝑥10 5 1 x 10-5 0.000001 1 10𝑥10𝑥10𝑥10𝑥10𝑥10 6 1 x 10-6
Scientific Notation When writing a number in scientific notation: A number that is greater than ten (10) will have a positive exponent A number that is less than one (1) will have a negative exponent
Scientific Notation to Standard Form Positive exponent: multiply by the number of factors of 10 represented by the exponent. 3.6 x 105 = 3.6 x 10,000 = 360,000 number greater than one
Scientific Notation to Standard Form 1.23 x 104 = 6.57 x 102 = 4.987 x 102 = 5.9843 x 103 =
Scientific Notation to Standard Form Negative exponent: divide by the number of factors of 10 represented by the exponent 4.7 x 10-3 = 4.7/ 1000 = 0.0047 number less than one
Scientific Notation to Standard Form 1.23 x 10-4 = 6.57 x 10-2 = 4.987 x 10-5 = 5.9843 x 10-3 =
Standard Form to Scientific Notation Factoring 10’s from a number. Magnitude (size) of the number must stay the same Only changing the FORM of the number 100 = 1 x 10 x 10 = 1 x 102 5,250 = 5.25 x 10 x 10 x 10 = 5.25 x 103 0.000535 = 5.35 / (10,000) = 5.35 x 10-4
Standard Form to Scientific Notation Exponent is the number of places you move the decimal point to obtain the coefficient. If the number is >10, exponent is positive If the number is <1, exponent is negative Coefficient is a number from one to nine
Standard Form to Scientific Notation 33,000,000 = 468.9 = 954,000 = 12.5 =
Standard Form to Scientific Notation 0.000578 = 0.000000981= 0.0000492 = 0.0287 =
Scientific Notation on Calculators Use exponent key (EE or exp) 5 E 5 represents 5 x 105 OR 5 05 represents 5 x 105 Record number in proper form, not as it appears on calculator!!!