Scientific Notation is based on powers of the base number 10.
The number 123,000,000,000 in scientific notation is written as :
The second number is called the base . It must always be 10 in scientific notation. The base number 10 is always written in exponent form. In the number 1.23 x 1011 the number 11 is referred to as the exponent or power of ten.
Rules for Division in Scientific Notation:
1) Divide the coefficients
2) Subtract the exponents (base 10 remains)
Example 1: (6 x 106) / (2 x 103) = 3 x 103
What happens if the coefficient is less than 10?
Example 2: (2 x 10 7) / (8 x 103) = 0.25 x 104
While the value is correct it is not correctly written in scientific notation since the coefficient is not between 1 and 10. We must move the decimal point over to the right until the coefficient is between 1 and 10. For each place we move the decimal over the exponent will be lowered 1 power of ten.
0.25x10 4 = 2.5 x 103 in scientific notation.Now Try these:
(write your answers in the form of coefficientx10^exponent) If your answer is 3.5 x 10 3 you should type 3.5x10^3 in the box then click the submit button).
What happens when the exponent(s) are negative?
We still subtract the exponents (apply the rules for subtracting signed numbers)
Example 5: (9 x 10 -6) / (3x 10-3) = 3. x 10-3
Example 6: (2 x 10 3) / (4 x 10-8) = 0.5 x 1011 = 5 x 10 10
Now Try these:
(write your answers in the form of coefficientx10^exponent) If your answer is 3.5 x 10 3 you should type 3.5x10^3 in the box then click the submit button). Divide the following numbers using Scientific Notation.
Introduction to Scientiic Notation: Learn the basic principles of scientific notation. Convert standard numbers to scientific notation.
Multiplication with Scientific Notation: Learn multiplication using scientific notation, with positive and negative exponents.
Division with Scientific Notation: Learn division using scientific notation with positive and negative exponents.
Word Problems using Scientific Notation: Mixed multiplication/division problems, word problems using scientific notation.
An Integrated Math Science and Art (STEAM) Activity- Mass, Volume Density Activity using the Gates Project from Central Park NYC.