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 0.006g 1 Significant Figure 350mL 2 Significant Figures 0.25cm 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 1.002x1015 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