1 23SIGNIFICANT FIGURES

I. SIGNIFICANT FIGURES IN MEASUREMENT

• Includes all the digits that are known, plus one that is estimated

A. MEASURING WITH A RULER1. Measuring error = 1/10 of smallest division

ii.

iii.

i.

What is the following measurement with the proper number of sig. figs.?

1. PRACTICE SET 1

B. MEASURING A LIQUID

**Measure from the

bottom of the

meniscus

1. PRACTICE SET 2

i. ii.

iii. iv.

II. SIGNIFICANT FIGURES

P A

Present vs. Absent

• If the decimal is present find the first non-zero digit starting from the left, count the digit and all digits to the right as significantEx. 1: 200.0 Ex. 2: 0.0030

• If the decimal is absent find the first non-zero digit starting from the right, count the digit and all digits to the left as significantEx. 1: 2930

4 s.f. 2 s.f.

3 s.f.

Greater than or equal to 1

Find the first nonzero digit,

everything after is significant **for zeros use the “after

after” rule

Is there a decimal point?

Every nonzero number is

significant **for zeros use the “Oreo cookie” rule

Everything is

significant

YES

YESNO

NO

“Oreo cookie rule”• Zeros between nonzero digits are significant

Ex) 50,006 has five significant figures

“After After rule”• Zeros after a non zero digit and after a decimal

point are significant Ex) 0.0456000 has six significant figures

A. PRACTICE SET 3

1. How many significant figures are in the numbers below?

i. 23,459ii. 300,004iii. 0.042iv. 35.00000

5 sig figs6 sig figs2 sig figs7 sig figs

IV. ROUNDING SIGNIFICANT FIGURES

A. Determine how many significant figures are needed

B. Find the counting number— first nonzero number (starting from the left)

C. Count how many sig. figs. you needD. Underline the last digit counted

E. Round the underlined digit by:1. If the digit to the right of the underlined digit

is less than five, the underlined digit stays the same and everything else becomes a zero place holder or gets dropped off

2. If the digit to the right of the underlined digit is more than five, the underlined digit is increased by one and everything else becomes zero place holder or gets dropped off

**Five or more add one next door

F. PRACTICE SET 4

i. 3.454 (3 sig. fig.) goes toii. 125,000 (2 sig. fig.) goes toiii. 7,905 (1 sig. fig.) goes toiv. 0.00369847 (2 sig. fig.) goes tov. 629.55 (3 sig. fig.) goes to

3.45130,0008,0000.0037630 ( you can’t

get three sig. fig. unless using Scientific Notation)

A. Round each number to the specified number of sig. figs.

VI. SIGNIFICANT FIGURES IN SCIENTIFIC NOTATION

A. All digits in the coefficient are significantB. The exponent is not significant

1. 2.80 ×106 has 3 significant figures

C. PRACTICE SET 5

1. Give the correct number of significant figures

i. 2.3445 x 10-6

ii. 2.69 x 10iii. 3.4 x 103

2.3445 (5)2.69 (3)3.4 (2)

2. Round each number to 3 significant figuresi. 87.073 metersii. 4.3621 x 108

iii. 0.01552 meteriv. 9009 metersv. 1.77777 x 10-3

87.1 meters4.36 x 108

0.0155 meters9010 meters1.78 x 10-3

1 23SIGNIFICANT FIGURES WITH CALCULATIONS

I. MULTIPLICATION AND DIVISION

A. Round the answer to the same number of significant figures as the measurement with the least number of significant figures

1. 7.55 × 0.34 = 2.567 3 sig. fig. 2 sig. fig.

Answer ≈2.6 (2 sig. figs.)

2. 2.105 × 0.762 = 1.60401 4 sig fig. 3 sig. fig.

Answer is 1.60 (3 sig. fig.)

3. 2.4526 ⁄ 8.4 =0.2919761 5 sig. fig 2 sig. figAnswer is 0.29 (2 sig. fig.)

B. PRACTICE SET 1

1. Calculate using the appropriate number of sig. fig.

i. 23.4 x 56ii. 1.456 x 5iii. 0.065 x 23.5iv. 25/60v. 245.00 / 5.00

1300 (1310.4)7 (7.28)1.5 (1.5275) 0.4 (0.416667)49.0 (49)

II. ADDITION AND SUBTRACTION WITH SIG. FIG.

A. Your answer must have the same number of digits to the right of the decimal point as the value with the fewest digits to the right of the decimal point

1. 28.0 + 23.538 + 25.68 = 77.218 (1) (3) (2)

Rounded correctly is 77.2 (1 place)

B. PRACTICE SET 21. Add or subtract using the correct number

of significant figures

i. 23.445 + 14 +34.6ii. 26.9 – 19iii. 34.543 + 12.56 + 34.2iv. 45.5654 – 34.2

72 (72.045)8 (7.9)81.3 (81.303)11.4 (11.3654)