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Base unit-a defined unit of measurement based on an object or event in the physical world

Derived unit-a unit of measurement defined by a combination of base units

Five base units:TimeLengthMass Temperature

Volume Density

Energy

In science we use the SI Units(International system) for measuringMeasurements

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Accuracy : How close to a measured value is to an accepted value.

Precision: How close a series of measurements are to one another

Instruments have a certain level of accuracy

To be accurate always estimate another digit after last certain digit.  this is called your estimated digit.WHY? We know that this measurement is somewhere between 105 and 106. So our estimated value would be the tenths place Measurement would be around 105.5 ml

Measurements

How did we see this in the lab?

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We are given the 10s and 1s place here, so we will be estimating the 10th place

43.0 ml

Measurements

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PracticeMeasurements

• Only measurements have sig figs. Why?• Sig figs are all measured numbers plus one estimated

digit. • When we measure something, we can (and do) always

estimate between the smallest marks or increments. • The better the marks, the better we can estimate. • When reading a measurement, scientists always understand

that the last number measured is actually an estimate.

 

Significant figures are numbers that count or mean something in an experiment. They represent the level of certainty in measurement based on the equipment used.

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Rules for Sig FigsAll nonzero numbers (naturals) are always significant

If it is not a natural number then it must follow other rules... 

(a) 456 (b) 35 (c) 4 (d) 891

(e) 1,345 (f) 12,345 (g) 4.52

Rules for zero:

5)Counting numbers and conversion factors have infinite numbers of significant figures

2) All final zeros to the right of the decimal (and after a nonzero number) are significant

3) Placeholder zeros are not significant (all other zeros)

Rules for Sig Figs cont.

"AFTER, AFTER"

Rules for zero:1) Zeros between two nonzero numbers are always significant

"TRAPPED!"

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Sig Figs PracticeState how many sig figs are present in the following numbers0.0078956700700713404.40500045010.0980010050005602315

Which numbers were taken from the most precise instrument?

Which numbers were taken from the least precise instrument?

How do you know?

MULTIPLICATION and DIVISION

• Multiply or divide normally following the order of operations• The answer must contain the same number of significant figures

as the number with the least significant figures.

• Round to that number.

What is the density of a metal block that has a mass of 34.5 g and a volume of 13 mL?

Example:

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Practice:

a. 31.5 * 56b. 14.8 / 45c. 100 * 56.7d. 9870 / 89.0e. 99.9909 /10.0

• When adding numbers, align the decimals.• The answer must contain the same number of sig figs after the decimal as the number with the least amount of sig figs to the right of the decimal. Why?• Round to that number.

ADDITION and SUBTRACTION

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Practice:

a. 31.5 + 56.890b. 124.8 - 45c. 100.00 + 56.7d. 9870 + 89.03e. 99.9909 -10.0

Scientific Notation

Scientific notation is a form of writing numbers that are too large or too small to be written practically using placeholders.

It is also used to express numbers that cannot be written in standard notation and still have the correct amount of sig figs.

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To convert from standard notation to scientific notation...

1. Move the decimal to the right of the first sig fig.2. Remove all non significant zeroes3. Write "X 10" beside the number4. Count how many places the decimal moved and write that

number as an exponent above the 105. If the original number was a decimal, the exponent is negative6. If the original number was NOT a decimal, the exponent is positive.

Scientific Notation

a) 0.00000305

b) 102,000,000,000

c) 0.00000678000

d) 45000

e) 609.00

Practice: Put the following numbers in sci. notation

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Scientific Notation2.34 x 102

4.5 x 10­5

5.62 x 108

3.45 x 10­3

1.2 x 106

4 x 10­4

Practice: Put the following numbers in regular notation

Multiplication and Division of Scientific notation

Multiplication:1. Multiply the coefficients2. Add the exponents

EX: (2.25 x 102)( 1.9 x 105)

Division:1. Divide the coefficients2. subtract the exponents

(2.25 x 102) ( 1.9 x 105)

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A. 2.36 x 102 * 1.5 x 10­5

B. 5.82 x 102 / 3.45 x 10­3

C. 1.29 x 106 * 4.00 x 10­4

D. (3.388 x 1010)(9.5 x 10­3)

E. 1.02 x 108 / 3.165 x 10­2

F. (4.20 x 104)(4 x 10­4)

Examples:

Addition and Subtraction of Scientific notation

1. Make the exponents the same by moving the decimal to the right or to the left.

2. Add (or subtract) the coefficients

Example:

(5.6 x 103) + (4.3 x 104)

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A. 2.34 x 102 + 4.5 x 10­5

B. 5.62 x 108 ­ 3.45 x 10­3

C. 1.2 x 106 + 4 x 10­4

D. 3.388 x 1010 + 9.5 x 10­3

E. 1.02 x 108 ­ 3.165 x 10­2

F. 4.20 x 104 ­ 4 x 10­4

Examples

Error- the difference between an experimental value and an accepted value

Percent error- expresses error as the percentage of the accepted value

error = experimental value - accepted value

percent error = |error| X 100accepted value

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Bertha and Skeeter conducted an experiment on the amount of CO2 produced by three moles of CH4 and a liter of O2. They conducted their trials five different times. Below is their data.

trials: grams error? % error?1 129.52 124.63 128.04 127.05 120.2

According to their calculations they should have produced 132.2 grams

Two kinds of data or observations:Qualitative data: data that is more anecdotal and cannot or is not be measured, describes the qualities of somethingExample: shiny, blue, soft, viscous, etc.

Quantitative data:measurements recorded from experiments

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Dimensional Analysis is a method of using conversion factors to convert from one unit to another.

A conversion factor is a ratio of two factors that equal each other.Ex: one inch = 2.54 cm

Dimensional Analysis

Since both measurements in a conversion factor equal the exact same distance we can put them over each other and they equal one.

In math anything can be multiplied by one without changing the quantity. Therefore we can multiply by conversion factors to conveniently switch from one unit to another.

0.62 miles

1 kmor

0.62 miles

1 km

Example 2: 0.62 miles = 1 km

If I traveled I16.72 miles, how many meters did I go?

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Practice:

A. How many mL in .0034 L?

B. How many mg in 93 kg?

C. How many meters in 6.5 X 104 μm?