Standards for Measurement

Lesson 3.1, Continued… Accuracy & Precision Significant Figures Scientific Notation

Accuracy & Precision

Precision: How closely individual measurements compare

with each other The “fineness” of a measurement

Accuracy: how closely individual measurements compare with the true or accepted value

Accurate or Precise?

Precise!(but not accurate)

What is the temperature at which water boils?

•Measurements: 95.0°C, 95.1°C, 95.3°C

•True value: 100°C

Accurate or Precise?

Accurate!(it’s hard to be accurate without being precise)

What is the temperature at which water freezes?

•Measurements: 1.0°C, 1.2°C, -5.0°C

•True value: 0.0°C

Accurate or Precise?

Not Accurate & Not Precise(don’t quit your day job)

What is the atmospheric pressure at sea level?

•Measurements: 10.01 atm, 0.25 atm, 234.5 atm

•True value: 1.00 atm

Accurate or Precise?

Accurate & Precise(it’s time to go pro)

What is the mass of one Liter of water?

•Measurements: 1.000 kg, 0.999 kg, 1.002 kg

•True value: 1.000 kg

Significant figures (“sig figs”): the digits in a measurement that are reliable (or precise). The greater the number of sig figs, the more precise that measurement is.

A more precise instrument will give more sig figs in its measurements.

Significant Figures

Every measurement has some degree of uncertainty.

Uncertainty examples: To measure the time for a pencil to fall…

compare a stopwatch and a wall clock.

To measure the volume of a liquid…compare a graduated cylinder and a beaker.

The stopwatch & graduated cylinder are more precise instruments…so the readings

they produce will have more sig figs.

A graduated cylinder:

50

100 mL Beaker

50 mL Graduated cylinder

A beaker:

41.0

41.2 mL (3 sig figs = very precise)

40. mL (2 sig figs = not as precise)

When are digits “significant”?

“PACIFIC”

Decimal point is PRESENT. Count digits from left side, starting with the first nonzero digit.

The “Atlantic-Pacific” Rule

40603.23 ft2

0.01586 mL

= 7 sig figs

= 4 sig figs

PACIFIC

PACIFIC

When are digits “significant”?

“ATLANTIC”

Decimal point is ABSENT. Count digits

from right side, starting with

the first nonzero digit.

40600 ft2

1000 mL

3 sig figs =

1 sig fig =

ATLANTIC

ATLANTIC

0.00932Decimal point present → “Pacific” → count digits from

left, starting with first nonzero digit= 3 sig figs

4035Decimal point absent → “Atlantic” → count digits from right, starting with first nonzero digit= 4 sig figs

27510Decimal point absent → “Atlantic” → count digits from right, starting with first nonzero digit= 4 sig figs

Examples

Scientific Notation

“Writing a number as a power of 10.”

Why? It makes very large and very small numbers more manageable to write and use. Rule of thumb: Use when number is greater than 100

or smaller than 0.10. Or, you may always use it!

The number of sig figs are clearly shown in a measurement.

2.4: Scientific Notation

How important is a change in the power of 10?

Diameter of Earth’s orbit around the sun

≈ 100,000,000,000 m = 1.0*1011 m

Diameter of an atom

≈ 0.0000000001 = 1.0*10-10 m

1. Move the decimal point in the original number so that it is located to the right of the first nonzero digit.

2. Multiply the new number by 10 raised to the proper power that is equal to the number of places the decimal moved.

3. If the decimal point moves: To the left, the power of 10 is positive. To the right, the power of 10 is negative.

Writing in scientific notation

Write the following measurements in scientific notation, then record the number of sig figs.

1. 789 g2. 96,875 mL3. 0.0000133 J4. 8.915 atm5. 0.94°C

7.89*102 g9.6875*104 mL

1.33*10-5 J8.915 atm9.4*10-1 °C

3 sig figs5 sig figs3 sig figs4 sig figs2 sig figs

Requirements for this class:

Write answers using 3 significant figures

Use scientific notation for all numbers greater than 1000 and smaller

than 0.001

Accuracy or Precision?

When deciding on accuracy, precision, both, or neither….it is quantitative data (numerical), not qualitative

(descriptive)

1) The recipe calls for 25 chocolate chips per cookie. The cookies analyzed have 34, 35, and 32 respectively.

2) The percent NaCl is 99%, 99%, and 98%.

3) The number of grams of KF required is 0.04 g. The amounts used were 0.038, 0.039, 0.041, and 0.040.

4) To win, Henry must earn 500 points. In his three trials, he earned 400, 480, and 395 points.

Rounding

Look at digit following specified rounding value. If it is 5 or greater, then round up. If not, truncate (cut off the rest of

the numbers).

Round to the nearest tenth 6.7512 6.7777 6.7499 6.9521

6.86.86.77.07.0

Practice Problems p. 39-40

12. State the abbreviation for each of the following units:

a) milligramb) kilogramc) meterd) nanometere) angstromf) microliter16. State the number of

significant figures in each of the following numbers:

a) 40.0b) 0.081c) 129,042d) 4.090 x 10-3

18. Round each of the following numbers to three significant figures:

a) 8.8726

b) 21.25

c) 129.509

d) 1.995 x 106

20. Write each of the following numbers in exponential (scientific) notation:

a) 0.0456

b) 4082.2

c) 40.30

d) 12,000,000

mg

kg

m

nm

AL

3

2

6

4

8.87

21.3

130. or 1.30 x 102

2.00 x 106

4.56 x 10-2

4.08 x 103

4.03 x 101

1.20 x 107