A measurement is a quantity that has both a number and a ... Measurement 5. Zeros at the rightmost end of a measurement without a decimal point are not significant. 7000 meters 27,210

Scientific Measurement

A measurement is a quantity that has both

a number and a unit

Some numbers encountered in science can

be either very large or very small

We use scientific notation to make those

numbers easier to work with.


In scientific notation, a given number is written as a coefficient and an exponent

The coefficient is a number more than 1, but less than 10

6 300 000.

94 700.

0.000 008

0.00 736


In chemistry, the meanings of accuracy and

precision are quite different.

Accuracy is a measure of how close a

measurement comes to the actual or true value of

whatever is measured.

Precision is a measure of how close a series of

measurements are to one another, irrespective of

the actual value.


To evaluate the accuracy of a

measurement, the measured value must be

compared to the correct value.

To evaluate the precision of a

measurement, you must compare the

values of two or more repeated

measurements.


Good Accuracy,

Good Precision

Poor Accuracy,

Good Precision

Poor Accuracy,

Poor Precision

The closeness of a dart to the bull’s-eye corresponds to the degree of accuracy. The closeness of several darts to one another corresponds to the degree of precision.


There is a difference between the accepted

value, which is the correct value for the

measurement based on reliable references, and

the experimental value, the value measured in

the lab.

Percent error indicates the difference between

the accepted and experimental values

Percent Error = |Accepted-Experimental|

Accepted Value X 100


This estimated number, 22.9°C, has

three digits. The first two digits (2 and 2) are

known with certainty, while the

rightmost digit (9) has been estimated

and involves some uncertainty.

These reported digits all convey useful

information, however, and are called

significant figures.


The significant figures in a

measurement include all of the digits

that are known, plus a last digit that

is estimated.

There are six rules to determine if a

number is significant.


1. Every nonzero digit in a reported measurement is assumed to be significant.

24.7 meters

2. Zeros appearing between nonzero digits are significant.

7003 meters


3. Leftmost zeros appearing in front of nonzero digits

are not significant.

0.0071 meters

0.0901 meters

4. Zeros at the end of a number and to the right of a

decimal point are always significant.

43.00 meters

0.010 meters


5. Zeros at the rightmost end of a measurement without a decimal point are not significant.

7000 meters

27,210 meters

To make 7000 meters have four significant figures we must add a decimal point - 7000. meters

6. There are two situations in which numbers have an unlimited number of significant figures.

A number that is counted is exact: 21 students in class Exactly defined quantities: 60 min = 1 hr


How many significant figures are in each measurement?

a. 123 m

b. 40506 mm

c. 9.8000 x 104 m

d. 22 metersticks

e. 0.070 80 m

f. 98000 m


In general, a calculated answer cannot be

more precise than the least precise

measurement from which it was

calculated. It must be rounded to make it consistent with

the measurements from which it was

calculated.


For an addition or subtraction calculation The answer should be rounded to the same number of

decimal places (not digits) as the measurement with

the least number of decimal places.

a. 12.52 meters + 349.0 meters + 8.24 meters

b. 74.626 meters – 28.34 meters


For a multiplication and division

calculation The answer should be rounded to the same

number of significant figures as the

measurement with the least number of

significant figures.

a. 7.55 meters x 0.34 meter

b. 0.365 meter2 ÷ 0.0200 meter


The International System of Units

(abbreviated SI) is a revised version of

the metric system. The SI units were adopted by international

agreement in 1960.

SI units are used for consistency among the

scientific community

Scientific Measurement There are seven SI base

units.

From these base units,

all other SI units of

measurement can be

derived. Derived units are used for

measurements such as

volume, density, and

pressure.

SI Base Units

Quantity SI base

unit

Symbol

Length meter m

Mass kilogram kg

Temperature kelvin K

Time second s

Amount of

substance mole mol

Luminous

intensity candela cd

Electric

current ampere A


Each SI unit is based on a measurable

standard They are not arbitrary units

Sometimes it is necessary to modify the

base unit using a prefix. Some prefixes make units larger and others make

units smaller


Small Metric Prefixes

Prefix Symbol Factor

deci d 0.1

centi c 0.01

milli m 0.001

micro μ 0.000 001

nano n 0.000 000 001

Large Metric Prefixes

Prefix Symbol Factor

giga G 1 000 000 000

mega M 1 000 000

kilo k 1000

•Although, the derived SI unit for volume is m3, we

commonly use the liter (L)

1 cm3 = 1 mL


A conversion factor is a ratio of

equivalent measurements. The measurement in the numerator is

equivalent to the measurement in the

denominator. Therefore you actually multiplying by 1

Conversion factors are useful in solving

problems in which a given measurement must

be expressed in some other unit of measure.


Conversion factors within a system of

measurement are defined quantities or exact

quantities. Therefore, they have an unlimited number of significant

figures and do not affect the rounding of a calculated

answer.


Weight and mass are two different measurements

Weight is a force that measures the pull on a given mass by gravity.

Mass is the measure of the amount of matter.


Scientists commonly use two equivalent units of temperature, the degree Celsius (˚C) and the kelvin (K).

The Celsius scale sets the freezing point of water

at 0°C and the boiling point of water at 100°C. On the Kelvin scale, the freezing point of water is

273.15 kelvins (K), and the boiling point is 373.15 K.


The Kelvin scale is based on absolute

zero

Absolute zero is the point where particle

motion seizes

Absolute zero is 0 Kelvin


Because one degree on the Celsius scale is equivalent to one kelvin on the Kelvin scale, converting from one temperature to another is easy.

You simply add or subtract 273, as shown in the following equations.

K = °C + 273

°C = K – 273


Density is the ratio of the mass of an object to its volume.

Density is an intensive property

The volume of most substances increases as the temperature increases, while the mass remains the same.

Since density is the ratio of an object’s mass to its volume, the density of a substance generally decreases as its temperature increases.

Water is an important exception.

mass

volume

Density =


Calculating Density

A copper penny has a mass of 3.10 g and a

volume of 0.35 cm3. What is the density of

copper?

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A measurement is a quantity that has both a number and a ... Measurement 5. Zeros at the rightmost end of a measurement without a decimal point are not significant. 7000 meters 27,210