Measurements

Scientists use two word to describe how good the measurements are

Accuracy- how close the measurement is to the actual value

Precision- how well can the measurement be repeated

Accuracy vs. Precision

Good accuracyGood precision

Poor accuracyGood precision

Poor accuracyPoor precision

Differences

Accuracy can be true of an individual measurement or the average of several

Precision requires several measurements before anything can be said about it

Let’s use a golf anaolgy

Accurate? No Precise? Yes

10

Accurate? Yes Precise? Yes

12

Accurate? No Precise? No

13

Accurate? Yes Precise? We cant say!

18

Accuracy vs. Precision AccuracyAccuracy - how close a measurement is to

the accepted value

PrecisionPrecision - how close a series of measurements are to each other

ACCURATE = CORRECT

PRECISE = CONSISTENT(Reproducible)

In terms of measurement

Three students measure the width of the classroom to be 10.2 m, 10.3 m and 10.4 m across.

Were they precise? Were they accurate?

In Chemistry….

7.0 does not equal 7.00

If your lab partner has 5.50 cm as an answer and you have 5.5 cm, one of you will not earn credit!!!

Because in science 5.50 cm does not equal 5.5 cm

How are these measurements different?

Significant Digit Rules

All non-zero digits are significant

• 145 has three significant digits

• 1,376 has four significant digits

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

2. Zeros

a. Leading Zeros – NEVER significant

b. Middle Zeros – ALWAYS significant

c. Trailing Zeros – SOMETIMES significant

(Depends on the presence of a decimal point)

i. If decimal point is present:

IS significant

ii. If decimal point is not present:

IS NOT significant

4. 0.080

3. 5,280

2. 402

1. 23.50

Examples

1. 23.50

2. 402

3. 5,280

4. 0.080

4 sig figs

3 sig figs

3 sig figs

2 sig figs

Let’s Practice!!!

Take 2 minutes to answer the practice problems at the bottom of the page.

Put your pencil down when you are finished and we can check our answers together.

A Memory Trick – The USA

Pacific

If there is a decimal….

Start on the left and stop at the first non zero.

That # and everything after it is significant!!

EX: .03560 g

Atlantic

If there is no decimal….

Start on the right and stop at the first non zero.

That # and everything after is are significant!

EX: 35600 g

Many calculators display several additional, meaningless digits.  Be sure to record your answer with the correct number of significant digits.  Calculator answers are not rounded to significant digits. You will have to round-off the answer to the correct number of digits.

Significant Digits and Calculators

Significant Digits Calculating with Significant Digits

• Multiply/Divide - The number of significant digits in the answer should be equal to the number of significant digits in the least accurate factor.

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

324 g

4 SF 3 SF3 SF

Significant Digits Calculating with Significant Digits (con’t)

• Addition and Subtraction - The number of decimal places in the answer should be equal to the number of decimal places in the number with the fewest decimal places

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

Significant Digits

5. (15.30 g) ÷ (6.4 mL)

Practice Problems

= 2.390625 g/mL

18.1 g

6. 18.9 g

- 0.84 g18.06 g

4 SF 2 SF

2.4 g/mL2 SF

Reporting Measurements

Using significant figures

Report what is known with certainty

Add ONE digit of uncertainty (estimation)

Significant Digits

The purpose of significant digits is to indicate the precision of a measurement.

Recording Significant Digits

• Significant digits in a measurement include the known digits plus a final estimated digit

1.19 cm

Centimeters

0 1 2 3 4 5

Practice Measuring

4.5 cm

4.54 cm

3.0 cmcm0 1 2 3 4 5

cm0 1 2 3 4 5

cm0 1 2 3 4 5