Scientific Notation Objectives Students will recognize numbers in

Scientific Notation • • Objectives Students will recognize numbers in scientific notation Students will be able to convert numbers in standard notation (ordinary numbers) into scientific notation and vice versa

Scientific Notation • is a way of expressing really big numbers or really small numbers in a more concise (compact) form • is used to make these numbers easier to work with

A number in scientific notation consists of two parts: • A number between 1 and 10 (N) • A power of 10 (x) N x 10 x

The exponent (or power of 10) can be either positive (+) or negative (-) Positive Exponent: 2. 35 x 108 Negative Exponent: 3. 97 x 10 -7

Are the following in scientific notation? • • • 4. 19385930 x 104 98920. 188438 x 10 -3 2. 22221 x 10000 3. 9992934 x 101 1. 00 x 1056 • • • Yes No No Yes

When changing an ordinary number (Standard Notation) into Scientific Notation: 1) Move the decimal to the right of the first nonzero digit: 3258 2) 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

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: 1) 9872432 9. 872432 x 106 2). 0000345 3. 45 x 10 -5 3). 08376 8. 376 x 10 -2 4) 5673 5. 673 x 103

When changing scientific notation to standard notation, the sign of the exponent tells you in which direction to move the decimal, while the number value tells you how many spaces to move it 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!

With a negative (-) exponent, move the decimal to the left 4. 08 x 10 -3 = 408 Don’t forget to fill in your zeroes!

Try changing these numbers from Scientific Notation to Standard Notation: 1) 9. 678 x 104 • 96780 2) 7. 4521 x 10 -3 • . 0074521 3) 8. 513904567 x 107 • 85139045. 67 4) 4. 09748 x 10 -5 • . 0000409748