*Significant Figures*-Important numbers needed for a particular measurement based on the degree of certainty.

• All non-zero digits are significant.

• Zeros in between non-zero digits are significant.

• Zeros before the first nonzero digit are not significant. (leading zeros)

• Zeros after the last nonzero digit may or may not be significant. (trailing zeros)

– If there is a decimal point in the number, all trailing zeros are significant.

– If there is no decimal point in the number, all trailing zeros are NOT significant.

• Exact numbers are considered to have an infinite numbers of significant figures.

In MULTIPLICATION and DIVISION, consider the least number of SF’s.

Examples:

• 6.35 X 4.1 = 26.035 ® 26 since given has 2 SF’s as the least number of SF’s

• 27.922 ¸ 3.3 = 8.4612 ® 8.5 since given has 2 SF’s as the least number of SF’s

In ADDITION and SUBTRACTION, consider the least number of decimal places.

Examples:

• 3.36 + 21.1 = 24.46 ® 24.5 since given has 2 decimal places as the least number of decimal places

• 47.82 – 6.1 = 41.7 since given has 2 decimal places as the least number of decimal places

Rules of rounding off

• If the digit to the right of the number to be rounded off is 5 or greater, round up (add 1 to the number).

ex: 45.678 ® 45.68

26.4345 ® 26.435

• If the digit to the right of the number to be rounded off is less than 5, round down (retain the number).

ex: 45.672 ® 45.67

26.4340 ® 26.434

•

*Precision*– tells how close several measurements are to the same value.

•

*Accuracy*– tells how close a measurement is to the true or accepted value.

**• Body parts and objects in the natural surroundings were used by ancient man as bases for measurements.**

*History of Measurements*

– Early Babylonian and Egyptian records and the Bible indicate that

• length ð forearm, hand, or finger

• time ð periods of the sun, moon, and other heavenly bodies.

• capacities ð plant seeds gourds or clay or metal vessels (they were filled which were then counted to measure the volumes)

• mass ð plant seeds and stones

– “carat” - mass unit for gems (carob seed)

• The English System originated from England. Units included “digit”, “palm”, “span”, “cubit”, which later evolved into “inch”, “foot”, and “yard”.

– "pes," or foot ð unciae (Roman)

– "gird" or "yard" ð circumference of a person's waist (Saxon)

– "inch" and "ounce" ð (Latin)

• The Metric System originated in France. This was established to have a single worldwide coordinated measurement system.

• The Metric System uses the base “10” and meter is used as the unit of length defined as 1/10 millionth of the distance from the north pole to the equator.

• In 1860’s, the “Treaty of Meter” was created to set up well-defined metric standards for length and mass.

• The International Bureau of Weights and Measures at Sevres, France, coordinates the exchange information about the use and refinement of metric system.

• In 1960, the General Conference adopted an extensive revision and simplification of the system. The name Le Systeme International d’Unites (International System of Units), with the international abbreviation SI, was adopted for this modernized metric system.

**Physical Quantities of Measurement**Length

Mass

Time

Temperature

Amount of substance

Electric current

Luminous intensity

LENGTH (meters)

- distance between two points.

TEMPERATURE (Kelvin)

- degree of hotness or coldness.

- measure of the average kinetic energy of the particles in a sample of matter.

AMOUNT OF SUBSTANCE (mole)

- physical quantity which is proportional to the number of elementary entities present.

TIME (seconds)

- defined by the process of measurement and by the units chosen.

ELECTRIC CURRENT (ampere)

- measure of the amount of electrical charge transferred per unit time.

LUMINOUS INTENSITY (candela)

- the quantity of visible light that is emitted in unit

time per unit solid angle

*Physical Quantities.Unit.Abbreviation of Unit*

**SI (Systeme Internationale) Base Units**

Length.meter.m

Mass.kilogram.kg

Time.second.s

Temperature.kelvin.K

Amount of substance.mole.mol

Electric current.ampere.A

Luminous intensity.candela.cd

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