Significant Figures and Rounding

Significant Figures Significant figures - show accuracy in measurements &

calculations Significant figures in a measurement consist of all of the digits

known with certainty plus one digit that is an estimate. The number of significant figures in a measurement indicates

to precision in the measurement it is.

A balance that reads to the 1.0 gram is less certain in a measurement that a balance that reads to 1.000 grams.

Rules for Identifying sig. figs. In a Measurement

The digits 1 through 9 ( all non-zero digits) are ALWAYS significant.

243 Has 3 significant figures1.287 Four significant figures

How many significant figures are in 142.32 5 Significant digits

How many significant figures are in 3.1 2 significant digits

Rules for Identifying sig. figs. In a Measurement Middle zeros are ALWAYS significant figures (zeros

between non-zero digits)

207 Three significant figures1.0032 Five significant figures

How many significant figures are in 207.5 4 significant digits

How many significant figures are in 60,007 5 significant digits

Rules for Identifying sig. figs. In a Measurement Leading zeros are NEVER significant. Leading zeros

are zeros that occur at the beginning of a number. Leading zeros function to indicate the position of the decimal point.

0.0045 Two significant figures0.034009 Five significant figures

How many significant figures are in 0.0307 3 significant digits

How many significant figures are in 0.0037009 5 significant digits

Rules for Identifying sig. figs. In a Measurement Ending zeros are zeros at the end of the number. They

are SOMETIMES significant. They ARE significant if there is a decimal point anywhere in the number. If no decimal point, ending zeros are NOT significant.

200.0 Four significant figures2000. Four significant figures200 One significant figure

How many significant figures are in 62.00 4 significant digits

How many significant figures are in 24.70 4 significant digits

How many significant figures are in 360,000 2 significant digits

Counting, exact and defined numbers have an infinite number of significant figures.

Pi- 3.1415926535893238………

Avogadro’s number- 6.0221415 x 10^23

A bakers dozen

The do not affect the number of sig figs in your final answer

EXERCISE 1A. 10423

10423 5 sig figs B. 1230.0

1230.0 5 sig figs

C. 150 150 2 sig figs

D. 0.00320.0032 2 sig figs

E. 33003300 2 sig figs

F. 10.010.0 3 sig figs

G. 0.05010 0.05010 4 sig figs

RoundingRounding is the process of deleting extra digits from a calculated number.

1. If the first digit to be dropped is less than 5, that digit and all the digits that follow it are simply dropped.

1.673 rounded to three significant figures becomes 1.67

2.If the first digit to be dropped is greater than or equal to 5, the excess digits are all dropped and the last significant figure is rounded up.

62.873 rounded to three significant figures becomes 62.9

Round The followingA. 423.78 to three significant figures

424

B. 0.000123 to two significant figures0.00012

C. 22.550 to four significant figures22.55

D. 129.6 to three significant figures130. (must have

decimal) E. 0.365 to one significant figure

0.4

F. 7.206 to three significant figures7.21

Calculations Using Significant Figures

A calculated number cannot be more precise than the data numbers used to calculate it. In other words: the answer can’t be more precise than any of the original numbers in the problem.

Addition and Subtraction*Two different rules apply: The Rule for Addition & Subtraction is DIFFERENT than the Rule for Multiplication and Division 1. Addition & SubtractionIn addition and subtraction, the last digit in the answer must be expressed to the same decimal place value as the entry with the ____least________ accurate decimal position.  5.72 (accurate to the hundredths position) 0.00648 (accurate to the hundred thousandths position) 37.916__ (accurate to the thousandths position) 43.7008 Becomes 43.70 to the hundredths position 

78.4 (accurate to the tenths position) -3.628 (accurate to the thousandths position) 74.772 Becomes 74.8 to the tenths positionl

Addition and Subtraction

*Write the given calculated answer in the correct number of significant figures. Look at decimal places only a. 3.64 + 0.0829 = 3.7229

3.72b. 67.4 + 4.28 = 71.68

71.7c. 3.289 – 0.66 = 2.629

2.63d. 5.976 – 0.497 = 5.497

no changee. 269 + 3.27 + 4.6 = 276.87

no decimal place in first number 277f. 7.2 + 0.69 – 0.0324 = 7.8666

7.9

Multiplication and Division

In multiplication and division the number of significant figures in the product or quotient must be the same as in the number in the calculation that contains the least significant figures

This is the rule we mainly use!!!

6.038 x 2.57 = 15.51766 Correct answer is 15.5 because the three significant digits in

2.57 limits our answers to three significant digits

120.0 ÷ 4.000 = 30 Correct answer is 30.00 because each entry has four

significant digits so your answer must have four significant digits.

(3.130 x 3.14) ÷ 3.1 = 3.170387097 Correct answer is 3.2 because the least number of significant

digits in the entries is two so our answer must only have two significant digits.

Multiplication and Division Practice

.a. 3.751 x 0.42 = 1.57542

1.6b. 6.7321 x 0.0021 = 0.01420041

0.014

c. 3.27 / 4.6 = 0.710869565 0.71

d. 49.7 / 0.05976 = 831.6599732 832

e. (7.2 x 0.69) / 3.24 = 0.866666666 0.87

f. 269 / (3.270 x 4.6) = 17.88323602 18

Count total number of Sig Figs!!!!