Transcript ppt
SIGNIFICANT FIGURES 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. Which numbers are significant? All nonzero digits are significant Examples: 1457 has 4 sig figs 54.1 has 3 sig figs Which numbers are significant? All nonzero digits are significant Examples: 1457 has 4 sig figs 54.1 has 3 sig figs Leading zeroes are NOT significant Examples: 0125 has 3 sig figs 0.003 has 1 sig fig Which numbers are significant? All nonzero digits are significant Examples: 1457 has 4 sig figs 54.1 has 3 sig figs Leading zeroes are NOT significant Examples: 0125 has 3 sig figs 0.003 has 1 sig fig Captive zeroes are significant Examples: 1002 has 4 sig figs 0.203 has 3 sig figs Which numbers are significant? All nonzero digits are significant Examples: 1457 has 4 sig figs 54.1 has 3 sig figs Leading zeroes are NOT significant Examples: 0125 has 3 sig figs 0.003 has 1 sig fig Captive zeroes are significant 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 Examples 1.00 has 3 sig figs 150 has 2 sig figs Which numbers are significant? All nonzero digits are significant Examples: 1457 has 4 sig figs 54.1 has 3 sig figs Leading zeroes are NOT significant Examples: 0125 has 3 sig figs 0.003 has 1 sig fig Captive zeroes are significant 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 Examples 1.00 has 3 sig figs 150 has 2 sig figs Exact numbers have infinite significant figures. Examples 25 students has infinite sig figs Reporting Calculations with correct Sig Figs For addition and subtraction, the limiting term is the one with the smallest number of decimal places. Example: 12.11 two decimal places 18.0 one decimal place + 1.013 three decimal places 31.123 31.1 answer reported w/ correct sig figs Reporting Calculations with correct Sig Figs For multiplication and division, the limiting term is the one with the smallest number of sig figs. Example: 1.2 x 4.56 = 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 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. • Example 1.33 rounds to be 1.3 is equal or greater to 5, the preceding digit is increased by 1. • Example 5.56 rounds to be 5.6 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 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 1025 (Remember the exponent can be positive or negative) SCIENTIFIC NOTATION ~REVIEWED If you move the decimal point to the left, the exponent increases. Example: 256,000,000 2.56 x 108 If you move the decimal point to the right, the exponent decreases. Example: 0.000000000028 2.8 x 10-11 Calculations w/ Scientific Notation Adding/subtracting exponents must be made the same* then add or subtract Example: 1.4 x 103 + 2.5 x 104 0.14 x 104 + 2.5 x 104 2.64 x 104 2.6 x 104 Convert all others to the largest exponent. Calculations w/ Scientific Notation multiply numbers and add exponents then make sure you have proper scientific notation Multiplying Example: (2.5 x 1012)(1.1 x 103) = (2.5)(1.1) x 10(12+3) = 2.75 x 10152 sig figs2.8 x 1015 Dividing divide number and subtract exponents then make sure you have proper scientific notation Example: (2.5 x 105)/(3.6 x 107) = (2.5/3.6) x 10(5-7) = 0.694 x 10-2 6.9 x 10-3