Accuracy, Precision, and Significant Figures

Accuracy, Precision, and Significant Figures Accuracy – Precision – the extent to which a series of measurements of the same quantity made in the same...
Author: Domenic Weaver
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Accuracy, Precision, and Significant Figures Accuracy – Precision – the extent to which a series of measurements of the same quantity made in the same way agree with one another **precision conveys nothing about accuracy Think of 4 targets

Percent error – used to compare the ______________________ of the average experimental value with the correct or ______________________ value.

Percent error =

Value accepted – Value experimental

x 100%

Value accepted Example: A handbook give the density of calcium as 1.54 g/mL. What is the percent error of a density calculation of 1.25 g/mL based on lab measurements?

For your information: Scientific Notation  used to express large or small numbers General Format: Z.ZZ x 10x For large numbers the exponent is positive For small numbers the exponent is negative4 Examples: 602000 becomes 6.02 x 105 (the decimal place was moved over 5 places) 0.000035 becomes 3.5 x 10-5

**Entering scientific notation on calculator Enter 6.02 x 105 Press 6 . 0 2 EE or exp 5 NOT **You must use the EE button or EXP button.

6 . 0 2 x 1 0 ^ 5

Significant Figures Significant figures –

Measurements – are never exact, always rounded off with the last digit an estimate Exact numbers – are not rounded off Example: how many eggs are in a dozen? People in this room? Determining sig figs 56,000 people attended a Vikings game. What place is it rounded to? Estimated digit: 6  2 sig figs (zeros are not significant) Ruler: Draw the ruler

Counting Sig Figs Ask 2 questions 1. Find the first nonzero digit 2. Is there a decimal point a. No  find the last nonzero digit (it’s estimated) 2500  2 s.f. b. Yes  find the last digit zero or nonzero 3.503  4 s.f.

Rules for determining significant figures Handout from Ms. D

Practice problems 1.030 cm

0.00320 m

2074000 s

601500 km

0.00001 g

1570500 cm

0.00080 kg

47000 m

367.52 g

0.1020 l

2500.00 m

0.700 L

Rules for Rounding off numbers If the digit immediately to the right of the last significant digit you want to retain is: 1. Greater than or equal to 5 2. Less than 5

Increased by 1 Stay the same

42.68  42.7 17.32  17.3

Practice problems 63.47 (3)

90.45 (3)

102.53 (4)

156.15 (4)

2623 (2)

9.335 (3)

0.0465 (2)

24.850 (3)

Scientific Notation When determining sig figs in scientific notation, only worry about the number not the x 10x. Examples:

2.02 x 103  3 sig figs

3.9565 x 10-16  5 sig figs

Significant Figures in Calculations Multiplication and Division:

52.8

x

1.0258

=

54.16624

Addition and Subtraction: Answer is rounded to same place as least specific number in problem **HINT: Line numbers up vertically 625.3 + 2.005 =

+

625.3 2.005 627.3005  627.3

1323 + 2500 3823  3800

Exact Conversion Factors -No _______________ and do not limit the number of digits in a calculation -They result from definitions or__________________________ 1000 mm = 1 m Dimensional Analysis or Factor Label Method 1. 2. Multiply by a conversion factor a. Put the unit you want to cancel out on bottom b. Put the unit you want on top (numerator) 3. Do the math a. If in numerator_____________________ b. If in denominator ______________________ 1A = 26 Z  this is a conversion factor Problem: How many Z’s are in 56 A’s

1A = 26 Z 1Z = 25 B’s Problem: How many B’s are in 19 A’s

***Remember when determining the number of sig figs conversion factors are exact numbers

METRIC CONVERSIONS Basic Unit Length

Name

Abbrev.

liter Mass s

Conversion Factor Prefix mega Kilo

Abbrev. M

1 Mm = 1,000,000

Power of 10 106

Multiplier 1,000,000

BASE UNIT deci

0.1 10-2 c 1 mm = 0.001 m

micro

m 

nano

n

0.000001 10-9

0.000000001

One Step Metric Conversion 7.84 m  cm 1. write what you know 2. Multiply by a _________________________________________ a. Put what needs to be canceled on the ____________________________ 3. Put what you want to go to on top 4. Put a 1 by the abbreviation with 2 ________________________________ 5. Put the multiplier from table above 6. Do the math Example

Two Step Metric Conversions 33.0 mL to cL 1. Convert to the ______________________ unit a. mL to L 2. Convert to________________________ unit a. L to cL Bridge Conversions **** 1 mL = 1 cm3 **** Convert 54.3 mL to cm3

Squared and Cubed Conversions *In my experience students who right out m3 (m x m x m) tend to get the correct answer, because they remember to multiply the conversion factor 3 times Convert 1.234 m3 to cm3

Convert 83 m3 to L

Density Conversions 1. Write the problem out the fraction way not the ________________________ way

2. Convert the top unit, ignoring the bottom unit 3. Convert the bottom unit ignoring the top unit 4. Do the math Convert 34.5 g/mL to dg/L

Density Information 

Density – the ratio of ____________________ to _____________________ Density = mass / volume



Units usually are g/mL or g/cm3



Density of water is __________________________________



If something floats density < 1 if something sinks density > 1

Determine density of a 343 g object that occupies 1033 cm3 of space?

Density is a conversion factor that is not____________________ and must be considered when determining the number of sig figs.

How much does a piece of aluminum weigh if it has a density of 2.702 g/cm3 of space? Conversion factor- do not start with this information Conversion factor may be written two ways (write in)

Work and answer