Scientific Notation Notes September Scientific Notation Notes

Count all the stars in this picture, be as accurate as you can.

Scientific Notation Scientific Notation- is a way to write a number multiplied by a power of ten. Makes numbers easier to work with

Scientific Notation RULE: #’s that are greater than 1 have a POSITIVE exponent EXAMPLE 300,000,000 3.0 x 10 8 = 300,000,000 it must be a number between 1 and 10 this is always there ( x 10 ) this is the number of places the decimal point is moved.

Scientific Notation #’s that are less than 1 (0.blah) have a NEGATIVE exponent EXAMPLE .0027 2.7 x 10 –3 = 0.0027 number between 1 and 10 always there the number of places the decimal point is moved.

Positive EXAMPLE 3.0 x 10 8 = 300,000,000 10 is always there number between 1 and 10 10 is always there the number of places the decimal point is moved. If the starting number is positive (10 8), move the decimal to the right. If the starting number is greater then 10 (3000,000,000), move the decimal to the left.

Negative EXAMPLE 2.7 x 10 –3 = 0.0027 10 always there number between 1 and 10 10 always there the number of places the decimal point is moved. If the starting number is negative (10 -3), move the decimal to the left. If the starting number is less then one (.0027), move the decimal to the right.

Write in scientific notation Step by step 5,000,000,000 Write in scientific notation

add decimal point if It is not already there Step by Step 5,000,000,000.0 add decimal point if It is not already there

Step by Step 5,000,000,000.0 Your answer needs to be a number between 1-9. In this example, the answer should be 5.

Step by Step 5,000,000,000.0 Count the number of places the decimal will need to be moved to get that whole number.

Step by Step 5, 0 0 0 , 0 0 0, 0 0 0 .0 9 8 7 6 5 4 3 2 1

Step by Step 5. 0 0 0 0 0 0 0 0 0 You moved it 9 places

Step by step 5. Remove the extra zeros

Write down the X symbol and the 10 because they are always there. Step by step 5.0 x 10 Write down the X symbol and the 10 because they are always there.

Step by Step 5.0 X 10 9 Write the exponent behind the10. This number should be the number of places you moved the decimal point.

Step 1. multiply numbers before the X sign. Step 2. add the exponents. Multiplication – Step 1. multiply numbers before the X sign. Step 2. add the exponents. Step 3. Simplify to a number between 1-10 For Example: (4 x 102) x (4 x 102) = =16x104 =1.6 x10 5

Step 1. divide the numbers before the x sign Division – Step 1. divide the numbers before the x sign Step 2. subtract exponents Step 3. Simplify to a number between 1-10 For example: (4 x 102) / (4x103) = =1 x 10-1 (4 x 103) / (4x102) = =1 x 101

Addition/Subtraction- exponents must be the same. Scientific Notation Addition/Subtraction- exponents must be the same. If exponents aren’t same, change the numbers before the x sign to do the math. If exponents are same, do math, keep exponent same.

Addition/Subtraction- exponents must be the same. Scientific Notation Addition/Subtraction- exponents must be the same. If exponents aren’t same, change the numbers before the x sign to do the math. If exponents are same, do math, keep exponent same.