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Measurement & Significant Figures. Rules for Measurement Significant Figures Scientific Notation Rounding in Science. I. Significant Figures. All the digits in a measurement up to the estimated digit are called significant figures All numbers except zero are always significant
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Measurement & Significant Figures Rules for Measurement Significant Figures Scientific Notation Rounding in Science
I. Significant Figures • All the digits in a measurement up to the estimated digit are called significant figures • All numbers except zero are always significant • Zero is not considered significant when it is used as a place holder, that is when it wasn’t measured • Zeros is at the end of a non-decimal number are place holders and are not significant • Ex. 3,400mL Has 2 significant figures • Zeros at the beginning of a decimal number are also place holders and are not significant • Ex. 0.000651L Has 3 significant figures • Zeros between numbers are part of the measurement and are significant • Ex. 3.006m Has 4 significant figures • Zeros at the end of a decimal were are not simply place holders and are part of the measurement; therefore, they are significant • Ex. 0.0200 Has 3 significant figures
Comprehension Check • How many significant figures are in each number below? • 3.250 g • 4 Significant Figures • 11.01cm • 4 Significant Figures • 0.006g • 1 Significant Figure • 350mL • 2 Significant Figures • 0.25cm • 2 Significant Figures • 100.662g • 6 Significant Figures
I. Scientific Notation • Scientific Notation is a shorthand method for writing really large or small numbers • For example, the number below is an important number in chemistry called Avogadro’s Number 602,213,700,000,000,000,000,000 atoms in scientific notation the number is 6.022137x1023 atoms • Writing a number is scientific notation does not change the value of the number, only its appearance • Move the decimal place to the right of the first significant figure • If moving the decimal place makes the number smaller, the power must increase to compensate • If moving the decimal place makes the number larger, the power must decrease to compensate
Comprehension Check • Write the following numbers in scientific notation • 1,002,000,000,000,000 g • 1.002x1015 g • 683,010,000,000,000,000,000 L • 6.8301x1020 g • 0.0000000203g • 2.03x10-8 g • 0.0000200m • 2.00x10-5 g • 64,000,000,000,000,000,000,000,000m • 6.4x1025 g
Rounding in Science • The number of significant figures reported tells everyone how accurate the measurements were • We never want to over or under report the accuracy of measurements • This means that we have to be careful when rounding answers to math problems • Rules for rounding answer to calculations • For multiplication and division • Round the final answer to same number of significant figures as the number with the least number of significant figures • For addition and subtraction – we’ll learn this later
Comprehension Check • Calculate the following and round the answers to the appropriate number of Sig Figs • 10.333g / 3.1mL • 3.333225806 g/mL 3.3 g/mL • 37.25m2 / 11.58m • 3.216753022 m 3.217 m • 894.005g (0.0758 mL/g) • 67.765579 mL 67.8 mL • 1,250,000m (0.00002300 s/m) • 28.75 s 28.75 s