Standards of Measurements

Chapter 1.2

Accuracy and Precision

Accuracy – how close a measured value is to the actual value

Precision – how close the measured values are to each other

Significant Figures

All nonzero digits are significant. 1, 2, 3, 4, 5, 6, 7, 8, 9

Zeros within a number are always significant. Both 4308 and 40.05 have four significant figures.

Significant Figures

Zeros that set the decimal point are not significant. 470,000 has two significant figures.

Trailing zeros that aren't needed to hold the decimal point are significant. 4.00 has three significant figures.

Significant Figures

If the least precise measurement in a calculation has three significant figures, then the calculated answer can have at most three significant figures.

Mass = 34.73 grams Volume = 4.42 cubic centimeters.

Rounding to three significant figures, the density is 7.86 grams per cubic centimeter.

Scientific Notation

For large numbers, moving the decimal to the left will result in a positive number 346500 = 3.46 x 105

For small numbers, moving the decimal to the right will result in a negative number 0.000145 = 1.45 x 10-4

For numbers less than 1 that are written in scientific notation, the exponent is negative.

Scientific Notation

Before numbers in scientific notation can be added or subtracted, the exponents must be equal. 5.32 x 105 + 9.22 x 104

5.32 x 105 + 0.922 x 105

5.32 + 0.922 x 105

6.24 x 105

Scientific Notation

When numbers in scientific notation are multiplied, only the number is multiplied. The exponents are added.

(3.33 x 102) (2.71 x 104) (3.33) (2.71) x 102+4

9.02 x 106

Scientific Notation

When numbers in scientific notation are divided, only the number is divided. The exponents are subtracted.

4.01 x 109

1.09 x 102

4.01 x 109-2

1.09

3.67 x 107

Scientific Notation

A rectangular parking lot has a length of 1.1 × 103 meters and a width of 2.4 × 103 meters. What is the area of the parking lot?

(1.1 x 103 m) (2.4 x 103 m) (1.1 x 2.4) (10 3+3) (m x m) 2.6 x 106 m2

SI Units

Kilo- (k)

1000

Milli- (m)

Hecto- (h)

Deka- (da)

Base Unit

Deci- (d)

Centi- (c)

100

10

m, L, g

0.1

0.01

0.001Mnemonic device:

King Henry Died By Drinking Chocolate Milk

Metric System

Meter (m) – The basic unit of length in the metric system

Length – the distance from one point to another A meter is slightly longer

than a yard

Metric System

Liter (L) – the basic unit of volume in the metric system A liter is almost equal to a

quart

Metric System

Gram (g) – The basic unit of mass

Derived Units

Combination of base units Volume – length width height

1 cm3 = 1 mL Density – mass per unit volume (g/cm3)

D = MV D

M

V

Density

1) An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass.

GIVEN:

V = 825 cm3

D = 13.6 g/cm3

M = ?

WORK:

M = DV

M = 13.6 g x 825 cm3

cm3 1

M = 11,220 gDM

V

Density

2) A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid?

GIVEN:

D = 0.87 g/mL

V = ?

M = 25 g

DM

V

WORK:

V = M D

V = 25 g

0.87 g/mL

V = 28.7 mL

Density

3) You have a sample with a mass of 620 g & a volume of 753 cm3. Find the density.

GIVEN:

M = 620 g

V = 753 cm3

D = ?

DM

V

WORK:

D = M V

D = 620 g

753 cm3

D = 0.82 g/cm3

Unit Factors

Slopes

Percentage Error

Temperature

A degree Celsius is almost twice as large as a degree Fahrenheit.

You can convert from one scale to the other by using one of the following formulas:

Temperature

Convert 90 degrees Fahrenheit to Celsius oC = 5/9 (oF - 32)

oC = 5/9 (90 - 32)

oC = 0.55555555555555556 (58)

oC = 32.2

Temperature

Convert 50 degrees Celsius to Fahrenheit oF = 9/5 (oC ) + 32

oF = 9/5 (50 ) + 32

oF = 1.8 (50) + 32

oF = 90 + 32

oF = 122

Temperature

The SI base unit for temperature is the kelvin (K). • A temperature of 0 K, or 0 kelvin, refers to the

lowest possible temperature that can be reached. • In degrees Celsius, this temperature is

–273.15°C. To convert between kelvins and degrees Celsius, use the formula:

Temperature