NUMBERS IN PHYSICS

I. MeasurementsII. Significant Figures

Indicate precision of a measurement.

Recording Sig Figs◦ Sig figs in a measurement include the known digits

plus a final estimated digit

2.35 cm

Significant Figures (sig figs/sig digs)

◦ All non-zero numbers are significant

◦ Zeros:

If the decimal is in the number 0.0025

0.002500

If there is no decimal point in the number2,500

4. 0.080

3. 5,280

2. 402

1. 23.50

Counting Sig Fig Examples

1. 23.50

2. 402

3. 5,280

4. 0.080

4 sig figs

3 sig figs

3 sig figs

2 sig figs

Calculating with Sig Figs◦A calculated answer cannot be more

precise than the worst measurement. ◦Significant figures are needed for final

answers when you do any calculating.

THIS WILL BE TRUE FOR THE ENTIRE THIS WILL BE TRUE FOR THE ENTIRE YEAR!!!YEAR!!!

It will always be included as partial credit on all It will always be included as partial credit on all tests.tests.

Calculating with Sig Figs (con’t)◦ Add/Subtract - The # with the lowest decimal value

determines the place of the last sig fig in the answer.

3.75 mL

+ 4.1 mL

7.85 mL

224 g

+ 130 g

354 g 7.9 mL 350 g

3.75 mL

+ 4.1 mL

7.85 mL

224 g

+ 130 g

354 g

Calculating with Sig Figs◦ Multiply/Divide - The # with the fewest sig figs

determines the # of sig figs in the answer.

(13.91g/cm3)(23.3cm3) = 324.103g

324 g

4 SF 3 SF3 SF

(15.30 g) ÷ (6.4 mL)

= 2.390625 g/mL

18.1 g

18.9 g

- 0.84 g18.06 g

4 SF 2 SF

2.4 g/mL2 SF

Calculating with Sig Figs (con’t)◦ Exact Numbers do not limit the # of sig figs in the

answer. Counting numbers: 12 students Exact conversions: 1 m = 100 cm “1” in any conversion: 1 in = 2.54 cm

III. Scientific NotationIV. Proportions/Graphing

Put your calculator in SCI mode (easiest)

Converting into Sci. Notation:

◦ Move decimal until there’s 1 digit to its left. Places moved = exponent.

◦ Large # (>1) positive exponentSmall # (<1) negative exponent

◦ Only include sig figs.

65,000 kg 6.5 × 104 kg

A number between 1 and 10

A power of 10

N x 10x

Calculating5.44 × 107 g

8.1 × 104 mol =

5.44EXPEXP

EEEE ÷÷EXPEXP

EEEE ENTERENTER

EXEEXE7 8.1 4

= 671.6049383

= 670 g/mol = 6.7 × 102 g/mol

Type on your calculator:

Graph data to find patterns more easily

Look for easy things like smooth lines and curves

Slopes give us constants y=mx + b Area under the curve can represent values we are looking for

xy

xy

1