1. Introduction to Chemistry for Allied Health Sciences Scientific Notation Kirk Hunter Chemical Technology Department Texas State Technical College Waco

2. Scientific Notation

3. SCIENTIFIC NOTATION Any number can be written as power of ten. 356 = 3.56 x 10 2 0.046 = 4.6 x 10 -2

4. SCIENTIFIC NOTATION When you write numbers in scientific notation, the decimal is always after the first non- zero digit. This number is called the coefficient. The power of ten is called the exponent.

5. SCIENTIFIC NOTATION If the original number is greater than ten, the exponent is positive. Example: 325 = 3.25 x 10 2 If the original number is less than one, the exponent is negative. Example: 0.00278 =2.78 -3

6. SCIENTIFIC NOTATION Write the following numbers in scientific notation. 1250.54640,897 23.4106567 0.07320.00480.00035

7. SCIENTIFIC NOTATION Write the following numbers in scientific notation. 1250.54640,897 23.4106567 0.07320.00480.00035 1.25 * 10 2 5.46 * 10 -1 4.0897 * 10 4 6.7 * 10 1 3.5 * 10 -4 4.8 * 10 -3 1.065 * 10 3 7.32 * 10 -2 2.34 * 10 1

8. SCIENTIFIC NOTATION Math operations Multiplication (3.5 x 10 2 ) x (2.0 x 10 3 ) = ? Multiply the coefficients, add exponents. (3.5 x 2.0) x 10 (2 + 3) = 7.0 x 10 5

9. SCIENTIFIC NOTATION Math operations Multiply the following: A. (2.1 x 10 3 )x (2.0 x 10 2 ) B. (3.1 x 10 -1 ) x (3.0 x 10 -2 ) C. (4.0 x 10 5 ) x (2.0 x 10 -3 )

10. SCIENTIFIC NOTATION Math operations Division 4.2 x 10 4 / 2.0 x 10 2 = ? Divide the coefficients, subtract the exponents (4.2/2.1) x 10 (4-2) = 2.1 x 10 2

11. SCIENTIFIC NOTATION Math operations Divide the following: A. (3.4 x 10 5 )/(1.7 x10 -2 ) B. (6.3 x10 -3 )/(2.1 x 10 -3 )

12. SCIENTIFIC NOTATION Math operations Addition (1.5 X10 3 )+ (2.3 X 10 2 )+ (2.0 X 10 3 ) All NUMBERS MUST HAVE THE SAME POWERS OF TEN (1.5 + 0.23 + 2.0) X 10 3 = 1.73 X 10 3

13. SCIENTIFIC NOTATION Math operations Add: A. ( 2.0 X 10 4 )- (3.0 X 10 3 ) B. (6.4 X 10 2 )+ (2.3 X 10 3 ) + (4.5 X 10 4 )