2 3 measured_number_and_sig

Measured Numbers A measuring tool is used to determine a quantity such as the length or the mass of an object provides numbers for a measurement called measured numbers Basic Chemistry Copyright © 2011 Pearson Education, Inc.

. l 2 . . . . l . . . . l 3 . . . . l . . . . l 4 . . cm The markings on the meterstick at the end of the orange line are read as The first digit 2 plus the second digit 2.7 The last digit is obtained by estimating. The end of the line might be estimated between 2.7–2.8 as half-way (0.05) or a little more (0.06), which gives a reported length of 2.75 cm or 2.76 cm. Reading a Meterstick Basic Chemistry Copyright © 2011 Pearson Education, Inc.

Known + Estimated Digits In the length reported as 2.76 cm, the digits 2 and 7 are certain ( known ) the final digit 6 was estimated ( uncertain ) all three digits (2.76) are significant including the estimated digit Basic Chemistry Copyright © 2011 Pearson Education, Inc.

Solution . l 8 . . . . l . . . . l 9 . . . . l . . . . l 10 . . cm The length of the red line could be reported as 2) 9.03 cm or 3) 9.04 cm The estimated digit may be slightly different. Both readings are acceptable. Basic Chemistry Copyright © 2011 Pearson Education, Inc.

. l 3 . . . . l . . . . l 4 . . . . l . . . . l 5 . . cm For this measurement, the first and second known digits are 4.5. Because the line ends on a mark, the estimated digit in the hundredths place is 0. This measurement is reported as 4.50 cm . Zero as a Measured Number Basic Chemistry Copyright © 2011 Pearson Education, Inc.

Significant Figures in Measured Numbers Significant figures obtained from a measurement include all of the known digits plus the estimated digit. The number of significant figures reported in a measurement depends on the measuring tool. Basic Chemistry Copyright © 2011 Pearson Education, Inc.

All nonzero numbers in a measured number are significant. Measurement Number of Significant Figures 38.15 cm 4 5.6 ft 2 65.6 lb 3 122.55 m 5 Counting Significant Figures Basic Chemistry Copyright © 2011 Pearson Education, Inc.

Sandwiched zeros occur between nonzero numbers are significant Measurement Number of Significant Figures 50.8 mm 3 2001 min 4 0.0702 lb 3 0.40505 m 5 Sandwiched Zeros Basic Chemistry Copyright © 2011 Pearson Education, Inc.

Trailing zeros follow nonzero numbers in numbers without decimal points are placeholders are not significant Measurement Number of Significant Figures 25 000 cm 2 200 kg 1 48 600 mL 3 25 005 000 g 5 Trailing Zeros Basic Chemistry Copyright © 2011 Pearson Education, Inc.

Leading zeros precede nonzero digits in a decimal number are placeholders are not significant Measurement Number of Significant Figures 0.008 mm 1 0.0156 oz 3 0.0042 lb 2 0.000262 mL 3 Leading Zeros Basic Chemistry Copyright © 2011 Pearson Education, Inc.

Significant Figures in Scientific Notation In scientific notation all digits including zeros in the coefficient are significant Scientific Notation Number of Significant Figures 8 x 10 4 m 1 8.0 x 10 4 m 2 8.00 x 10 4 m 3 Basic Chemistry Copyright © 2011 Pearson Education, Inc.

A. Which answer(s) contain three significant figures? 1) 0.4760 2) 0.00476 3) 4.76 x 10 3 B. All the zeros are significant in 1) 0.00307 2) 25.300 3) 2.050 x 10 3 C. The number of significant figures in 5.80 x 10 2 is 1) one 3) two 3) three Learning Check Basic Chemistry Copyright © 2011 Pearson Education, Inc.

A. Which answer(s) contain three significant figures? 2) 0.00476 3) 4.76 x 10 3 B. All the zeros are significant in 2) 25.300 3) 2.050 x 10 3 C. The number of significant figures in 5.80 x 10 2 is 3) three Solution Basic Chemistry Copyright © 2011 Pearson Education, Inc.

In which set(s) do both numbers contain the same number of significant figures? 1) 22.0 and 22.00 2) 400.0 and 4.00 x 10 2 3) 0.000015 and 150 000 Learning Check Basic Chemistry Copyright © 2011 Pearson Education, Inc.

Solution In which set(s) do both numbers contain the same number of significant figures? 3) 0.000015 and 150 000 Both numbers contain two (2) significant figures. Basic Chemistry Copyright © 2011 Pearson Education, Inc.

Exact Numbers An exact number is obtained when objects are counted Example : counting objects 2 baseballs 4 pizzas from numbers in a defined relationship Example : defined relationships 1 foot = 12 inches 1 meter = 100 cm Basic Chemistry Copyright © 2011 Pearson Education, Inc.

Learning Check A. Exact numbers are obtained by 1. using a measuring tool 2. counting 3. definition B. Measured numbers are obtained by 1. using a measuring tool 2. counting 3. definition Basic Chemistry Copyright © 2011 Pearson Education, Inc.

Learning Check Classify each of the following as exact (E) or measured numbers (M). Explain your answer. A.__Gold melts at 1064 °C. B.__1 yd = 3 ft C.__The diameter of a red blood cell is 6 x 10  4 cm. D.__There are 6 hats on the shelf. E.__A can of soda contains 355 mL of soda. Basic Chemistry Copyright © 2011 Pearson Education, Inc.

Classify each of the following as exact (E) or measured numbers (M) . A. M A measuring tool is required. B. E This is a defined relationship. C. M A measuring tool is used to determine length. D. E The number of hats is obtained by counting. E. M The volume of soda is measured. Solution Basic Chemistry Copyright © 2011 Pearson Education, Inc.

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