Scientific Notation Ch. 3.1

Definitions: 1. scientific notation – a shorthand way to write very large or very small numbers. 2. standard form – writing a number as we normally see it.

Very Important concepts VIC #1: When changing into scientific notation, if the number is greater than 1, then the exponent will be positive. VIC #2: When changing into scientific notation, if the number is less than 1, then the exponent will be negative.

Very Important concepts (cont.) VIC #3 When changing into scientific notation, you need to move the decimal to where there is only one counting number in front of the decimal.

Five steps to writing a number in scientific notation. Step 1: Find the decimal point. Step 2: Move the decimal point to the right or left until there is only one counting number in front of the decimal. Step 3: Count the number of places you moved the decimal point. This will be your exponent on the 10. If the number you started with is greater than one, then your exponent will be positive, but if it’s less than 1, the exponent will be negative.

Five steps to writing a number in scientific notation (cont.) Step 4: Rewrite the decimal and drop zeros that don’t have counting numbers behind them. Step 5: Behind the decimal in step 4, put a multiplication sign and the 10 and its exponent. This is your solution.

Very Important concepts (cont.) VIC #4 When going to standard form, if the exponent is positive, move the decimal to the right. VIC #5 When going to standard form, if the exponent is negative, move the decimal to the left.

Steps to changing from scientific notation to standard form Step 1: Decide which way to move the decimal (positive to right, negative to left) and how many times (the exponent) Step 2: Write decimal without the x 10power Step 3: Move the decimal based on step 1. Fill in the blank spaces with zero. Step 4: Rewrite the number, putting in commas if needed. That is your solution.

Practice: Change the following into scientific notation. 5,750,000,000 0.0000006 56 million 

Practice Answers 5,750,000,000 = 5.75 x 109 0.0000006 = 6.0 x 10-7 5.6 x 107  = 56 million

practice: Write the following in standard form 2.52 x 105 8.08 x 109 7.5 x 108

Practice answers 2.52 x 105 = 0.0000252 8.08 x 109 = 8,080,000,000

Multiplying Scientific Notation Example: (5.1 x 107)(2 x 102) = (5.1 x 2)(10(7 + 2)) = (10.2)(109) = 10.2 x 109 = (move decimal one place to put in scientific notation) 1.02 x 1010 Practice: (2.3 x 104)(4.5 x 105) =

Dividing Scientific Notation Example: 7.2 x 105 = 4 x 103 (7.2  4) (105(3)) = 1.8 x 102 Practice: 5.1 x 106 = 1.5 x 102

practice 1. (5 x 102)(1.4 x 104) 2. (1.035 x 103)  (4.5 x 102) =