Scientific Notation Learning Targets: 12. I can determine which numbers in a measurement are significant and use these rules to make precise calculations. 13. I am able to convert values from standard form into scientific notation and vise-versa

How wide is our universe? 210,000,000,000,000,000,000,000 miles (22 zeros) This number is written in decimal notation. When numbers get this large, it is easier to write them in scientific notation. 2.1 x 1023

When using Scientific Notation, there are two kinds of exponents: positive and negative Positive Exponent: 2.35 x 108 Negative Exponent: 3.97 x 10-7

An easy way to remember this is: If an exponent is positive, the number gets larger, so move the decimal to the right. If an exponent is negative, the number gets smaller, so move the decimal to the left.

When changing scientific notation to standard notation, the exponent tells you how you should move the decimal: With a positive exponent, move the decimal to the right: 4.08 x 103 = 4 0 8 Don’t forget to fill in your zeroes!

The exponent also tells how many spaces to move the decimal: In this problem, the exponent is +3, so the decimal moves 3 spaces to the right.

When changing scientific notation to standard notation, the exponent tells you how you should move the decimal: With a negative exponent, move the decimal to the left: 4.08 x 10-3 = 4 0 8 Don’t forget to fill in your zeroes!

The exponent also tells how many spaces to move the decimal: In this problem, the exponent is -3, so the decimal moves 3 spaces to the left.

Try changing these numbers from Scientific Notation to Standard Notation: 9.678 x 104 7.4521 x 10-3 8.51 x 107 4.09 x 10-5 96780 .0074521 85,100,000 .0000409

When changing from Standard Notation to Scientific Notation: 1) First, write only the sig figs in the number. Move the decimal after the first sig fig: 3 2 5 8 2) Second, add your multiplication sign and your base (10). 3 . 2 5 8 x 10 3) Count how many spaces the decimal moved and this is the exponent. 3 . 2 5 8 x 10 3 3 2 1

When changing from Standard Notation to Scientific Notation: 4) See if the original number is greater than or less than one. If the number is greater than one, the exponent will be positive. 348943 = 3.48943 x 105 If the number is less than one, the exponent will be negative. .0000000672 = 6.72 x 10-8

Try changing these numbers from Standard Notation to Scientific Notation: 9,070,000 .0000345 .08376 5,670 9.07 x 106 3.45 x 10-5 8.376 x 10-2 5.67 x 103

Scientific Notation Math Multiplication - multiply the numbers, add the indices 1.2 x 104 multiplied by 5 x 106 = Division - divide the numbers, subtract the indices 5.5 x 108 divided by 1.1 x 102 = (For all operations reconvert answers to full scientific notation)

Convert the following numbers between standard form and scientific notation: 1.7 x 103 2.4503 x 105 7.9 x 1011 2.8 x 10-3 7.45 x 10-1 2.3 x 10-7 329 700,000 20090 0.000034 0.01023 123.4 45.607

Convert the following numbers/sums into correct scientific notation: 3.59 x 103 5.56 x 106 2.2 x 10-3 3.48 x 10-4 1.805 x 105 3.04 x 10-7 3,590 5,560,000 0.0022 0.000348 180,500 0.000000304

^ ^ On a Calculator Locate these buttons: , , , LOG 10X DRG Sci/Eng Locate these buttons: , , , Scientific  Standard given 1.2 x 105 1.2 x 10 5 = 120,000 1.2 5 = 120,000 Standard  Scientific given 120,000 120,000 = select Sci = To undo: select Flo = ^ 2nd ^ LOG 10X 2nd DRG Sci/Eng DRG Sci/Eng