Lab 2

Metric System Review, Data Analysis and Graphing

Accuracy of Data and Decimal Numbers

The number of decimals reflects the accuracy of the data

Rounding of numbers (depends on data collected, type of

measurements, data presentation and equipment used)

A decimal to the right that > 5 raises the next decimal

A decimal to the right that < 5 has no effect on the next decimal

Don’t round off until the end of your calculation

Rounding and calculating: 3.7+2.6 = 4+3 = 7

Calculating and rounding: 3.7+2.6 = 6.3 = 6

Rules for deciding the number of significant figures in a

measured quantity:

1) All nonzero digits are significant:

1234 g has ___ significant figures

1.234 g has ____ significant figures

1.2 g has ____ significant figures

2) Zeroes between nonzero digits are significant:

1002 kg has ____ significant figures

3.07 ml has ____ significant figures

3) Zeros left of the first nonzero digits (leading zeros) are not

significant:

0.001 oC has only ____ significant figure

0.012 g has ____ significant figures

Accuracy of Data and Significant Figures

(4) Trailing zeros that are to the right of a decimal point in a

number are significant:

0.0230 mL has ____ significant figures

0.20 g has ____ significant figures

(5) When a number ends in zeros that are not to the right of a

decimal point, the zeros are not necessarily significant:

190 miles may be 2 or 3 significant figures

50,600 calories may be 3, 4, or 5 significant figures

Accuracy of Data and Significant Numbers

The potential ambiguity in the last rule can be avoided by the use

"scientific notation”

N = (coefficient x10e)*

50,600 calories as:

5.06 × 104 calories (3 significant figures)

5.060 × 104 calories (4 significant figures)

5.0600 × 104 calories (5 significant figures)

In addition and subtraction, the result is rounded off so that

it has the same number of digits as the measurement having

the fewest decimal places

For example, 100.2 + 23.643 = 123.843, which should be

rounded to ____

In multiplication and division, the result should be rounded

off so as to have the same number of significant figures as in

the component with the least number of significant figures

For example, 3.0 (2 significant figures ) × 12.60 (4

significant figures) = 37.800 which should be rounded to ___

The accuracy of a calculated result is limited by the least accurate

measurement involved in the calculation

Accuracy of Data and Significant Numbers

Determine the number of significant figures in the following

measurements:

1) 0.0009

2) 15,450.0

3) 6 × 103

4) 87.990

5) 30.42

Write the following numbers in scientific notation:

1) 3675.890

2) 0.005643

3) 76904

4) 0.0067890

Metric System

o Decimal based system

o Base units:

grams (g)

liters (l)

meters (m)

moles (M)

o Prefixes used to change the base unit by factors of 10

Giga (G), mega (M), kilo (k), deci (d), centi (c), milli (m),

micro (μ) and nano (n)

Prefix Symbol Exponent of 10

kilo k 103

Base Unit BU 100

deci d 10-1

centi c 10-2

milli m 10-3

micro μ 10-6

nano n 10-9

Prefix kilo Base

Unit

deci centi milli micro nano

Symbol k BU d c m μ n

Exponent

of 10

103 100 10-1 10-2 10-3 10-6 10-9

25 kg = ? cg 25 kg = 25kg x 105cg

1kg

35 nm = ?dm

The World of the Micrometer (Micron)

10-6 meters

The World of the Nanometer

10-9 meters

Data Analysis

o Mean

o Median

o Mode

o Standard Deviation

o Correlations

o Linear Regression

o Graphing

Consider the following date:

7.3 m, 5.2 m, 5.2 m, 4.8 m, 6.7 m, 8.1 m

Mean = average

Median = central value after numbers have been

arranged from lowest to highest or vice versa

Mode = most frequently occurring number in a set of

data

Data Analysis/ Looking at the center of the data

Variance (σ2): measurement of the spread between

numbers in a data set/ average of the squared differences

from the mean

Standard Deviation (σ): dispersion of the data from the

mean/ square root of variance

Standard Error of the Mean (SEM): measure of how

precise is our estimate of the mean

Data Analysis/ Looking at how scattered and precise

the data is

Standard Deviation for Normally Distributed Data

Measure of how far each observed value is from the mean

small standard deviation/ indicator of the closeness of the data

points to the arithmetic mean

Large standard deviation/ indicator that the data values are

dispersed over a wide range

Correlation: Relationship between two variables/ zero,

positive, negative

Data Analysis

Linear regression/ prediction of the values of one

variable from the values of a second variable

The variable we are predicting is called the criterion

variable and is referred to as Y

The variable we are basing our predictions on is called

the predictor variable and is referred to as X

Best-fit line

Interpolation

Extrapolation

Data Analysis

Use the entire graph paper

Choose a range for your X and Y axis scales so that your data will fill

the entire page

Don’t crowd axes to the edge of the page. Leave enough room

to show and label your scales for X and Y axes

Good Graphing Rules

Have a descriptive TITLE that tells the reader what they are

viewing

Plot the independent variable on the X axis

(Time is always plotted on the X axis)

Plot the dependent variable on the Y axis

If appropriate, draw a line of best fit for each data set

(DO NOT USE POINT-TO-POINT TO DRAW A LINE)

If appropriate, add error bars

Show a LEGEND defining each symbol, line, and error bars

(SD or SEM)

Use different symbols for different data sets

Draw the symbols large enough to be easily viewed

Good Graphing Rules