1. SIGNIFICANT FIGURES

2. What are they?  It is important to be honest when reporting a measurement, so that it does not appear to be more accurate than the equipment used to make the measurement allows.  Using significant figures communicates your accuracy in the measurement or calculation.

3. Which numbers are significant?  All nonzero digits are significant Examples:1457 has 4 sig figs Examples:1457 has 4 sig figs 54.1 has 3 sig figs

4. Which numbers are significant?  All nonzero digits are significant Examples:1457 has 4 sig figs Examples:1457 has 4 sig figs 54.1 has 3 sig figs  Leading zeroes are NOT significant Examples:0125 has 3 sig figs Examples:0125 has 3 sig figs 0.003 has 1 sig fig

5. Which numbers are significant?  All nonzero digits are significant Examples:1457 has 4 sig figs Examples:1457 has 4 sig figs 54.1 has 3 sig figs  Leading zeroes are NOT significant Examples:0125 has 3 sig figs Examples:0125 has 3 sig figs 0.003 has 1 sig fig  Captive zeroes are significant Examples:1002 has 4 sig figs Examples:1002 has 4 sig figs 0.203 has 3 sig figs

6. Which numbers are significant?  All nonzero digits are significant Examples:1457 has 4 sig figs Examples:1457 has 4 sig figs 54.1 has 3 sig figs  Leading zeroes are NOT significant Examples:0125 has 3 sig figs Examples:0125 has 3 sig figs 0.003 has 1 sig fig  Captive zeroes are significant Examples:1002 has 4 sig figs Examples:1002 has 4 sig figs 0.203 has 3 sig figs  Trailing zeroes are significant IF AND ONLY IF they are to the right of the decimal point Examples1.00 has 3 sig figs Examples1.00 has 3 sig figs 150 has 2 sig figs

7. Which numbers are significant?  All nonzero digits are significant Examples:1457 has 4 sig figs Examples:1457 has 4 sig figs 54.1 has 3 sig figs  Leading zeroes are NOT significant Examples:0125 has 3 sig figs Examples:0125 has 3 sig figs 0.003 has 1 sig fig  Captive zeroes are significant Examples:1002 has 4 sig figs Examples:1002 has 4 sig figs 0.203 has 3 sig figs  Trailing zeroes are significant IF AND ONLY IF they are to the right of the decimal point Examples1.00 has 3 sig figs Examples1.00 has 3 sig figs 150 has 2 sig figs  Exact numbers have infinite significant figures. Examples25 students has infinite sig figs Examples25 students has infinite sig figs

8. Reporting Calculations with correct Sig Figs  For addition and subtraction, the limiting term is the one with the smallest number of decimal places. Example: Example: 12.11  two decimal places 18.0  one decimal place + 1.013  three decimal places + 1.013  three decimal places31.123 31.1  answer reported w/ correct sig figs

9. Reporting Calculations with correct Sig Figs  For multiplication and division, the limiting term is the one with the smallest number of sig figs. Example: Example: 1.2x4.56=5.472  5.5 final answer is only allowed two sig figs 284.2 ÷2.2=129.18  130 final answer is only allowed two sig figs

10. ROUNDING REVISITED  When the answer to a calculation contains too many significant figures, it must be rounded off.  If the digit to be removed is less than 5, the preceding digit stays the same. is less than 5, the preceding digit stays the same. Example 1.33 rounds to be 1.3Example 1.33 rounds to be 1.3 is equal or greater to 5, the preceding digit is increased by 1. is equal or greater to 5, the preceding digit is increased by 1. Example5.56 rounds to be 5.6Example5.56 rounds to be 5.6

11. SCIENTIFIC NOTATION ~REVIEWED  A shorthand way of representing very large or very small numbers  Allows us to remove zeroes that are only serving as place holders

12. SCIENTIFIC NOTATION ~REVIEWED  The number is written with one nonzero digit to the left of a decimal point multiplied by ten raised to a power 1.3 x 10 25 (Remember the exponent can be positive or negative)

13. SCIENTIFIC NOTATION ~REVIEWED  If you move the decimal point to the left, the exponent increases. Example: Example: 256,000,000  2.56 x 10 8  If you move the decimal point to the right, the exponent decreases. Example: Example: 0.000000000028  2.8 x 10 -11

14. Calculations w/ Scientific Notation  Adding/subtracting  exponents must be made the same* then add or subtract Example: Example: 1.4 x 10 3 + 2.5 x 10 4 + 2.5 x 10 4 0.14 x 10 4 + 2.5 x 10 4 2.64 x 10 4 2.6 x 10 4 Convert all others to the largest exponent.

15. Calculations w/ Scientific Notation  Adding/subtracting  exponents must be made the same then add or subtract Example: Example: 1.4 x 10 3 + 2.5 x 10 4 = 0.14 x 10 4 + 2.5 x 10 4 = 2.6 x 10 4 (1 decimal place)

16. Calculations w/ Scientific Notation  Multiplying  multiply numbers and add exponents then make sure you have proper scientific notation Example: Example: (2.5 x 10 12 )(1.1 x 10 3 ) = (2.5)(1.1) x 10 (12+3) = 2.75 x 10 15  2 sig figs  2.8 x 10 15  Dividing  divide number and subtract exponents then make sure you have proper scientific notation Example: Example: (2.5 x 10 5 )/(3.6 x 10 7 ) = (2.5/3.6) x 10 (5-7) = 0.694 x 10 -2  6.9 x 10 -3