SIGNIFICANT SIGNIFICANT FIGURESFIGURES

What are they?What are they?

It is important to be honest when reporting It is important to be honest when reporting a measurement, so that it does not appear a measurement, so that it does not appear to be more accurate than the equipment to be more accurate than the equipment used to make the measurement allows.used to make the measurement allows.

Using significant figures communicates Using significant figures communicates your accuracy in the measurement or your accuracy in the measurement or calculation.calculation.

Which numbers are significant?Which numbers are significant?

All nonzero digits are significantAll nonzero digits are significant Examples:Examples: 1457 has 4 sig figs1457 has 4 sig figs

54.1 has 3 sig figs54.1 has 3 sig figs

Which numbers are significant?Which numbers are significant?

All nonzero digits are significantAll nonzero digits are significant Examples:Examples: 1457 has 4 sig figs1457 has 4 sig figs

54.1 has 3 sig figs54.1 has 3 sig figs

Leading zeroes are NOT significantLeading zeroes are NOT significant Examples:Examples: 0125 has 3 sig figs0125 has 3 sig figs

0.003 has 1 sig fig0.003 has 1 sig fig

Which numbers are significant?Which numbers are significant?

All nonzero digits are significantAll nonzero digits are significant Examples:Examples: 1457 has 4 sig figs1457 has 4 sig figs

54.1 has 3 sig figs54.1 has 3 sig figs Leading zeroes are NOT significantLeading zeroes are NOT significant

Examples:Examples: 0125 has 3 sig figs0125 has 3 sig figs

0.003 has 1 sig fig0.003 has 1 sig fig

Captive zeroes are significantCaptive zeroes are significant Examples:Examples: 1002 has 4 sig figs1002 has 4 sig figs

0.203 has 3 sig figs0.203 has 3 sig figs

Which numbers are significant?Which numbers are significant? All nonzero digits are significantAll nonzero digits are significant

Examples:Examples: 1457 has 4 sig figs1457 has 4 sig figs

54.1 has 3 sig figs54.1 has 3 sig figs Leading zeroes are NOT significantLeading zeroes are NOT significant

Examples:Examples: 0125 has 3 sig figs0125 has 3 sig figs

0.003 has 1 sig fig0.003 has 1 sig fig Captive zeroes are significantCaptive zeroes are significant

Examples:Examples: 1002 has 4 sig figs1002 has 4 sig figs

0.203 has 3 sig figs0.203 has 3 sig figs

Trailing zeroes are significant Trailing zeroes are significant IF AND IF AND ONLY IFONLY IF they are to the right of the they are to the right of the decimal pointdecimal point ExamplesExamples 1.00 has 3 sig figs1.00 has 3 sig figs

150 has 2 sig figs150 has 2 sig figs

Which numbers are significant?Which numbers are significant? All nonzero digits are significantAll nonzero digits are significant

Examples:Examples: 1457 has 4 sig figs1457 has 4 sig figs54.1 has 3 sig figs54.1 has 3 sig figs

Leading zeroes are NOT significantLeading zeroes are NOT significant Examples:Examples: 0125 has 3 sig figs0125 has 3 sig figs

0.003 has 1 sig fig0.003 has 1 sig fig Captive zeroes are significantCaptive zeroes are significant

Examples:Examples: 1002 has 4 sig figs1002 has 4 sig figs0.203 has 3 sig figs0.203 has 3 sig figs

Trailing zeroes are significant Trailing zeroes are significant IF AND ONLY IFIF AND ONLY IF they are to the right of the decimal they are to the right of the decimal pointpoint

ExamplesExamples 1.00 has 3 sig figs1.00 has 3 sig figs150 has 2 sig figs150 has 2 sig figs

Exact numbers have infinite significant figures.Exact numbers have infinite significant figures. ExamplesExamples 25 students has infinite sig figs25 students has infinite sig figs

Reporting Calculations with correct Reporting Calculations with correct Sig FigsSig Figs

For For addition and subtractionaddition and subtraction, the limiting , the limiting term is the one with the smallest number of term is the one with the smallest number of decimal places.decimal places. Example:Example:

12.11 12.11 two decimal places two decimal places

18.0 18.0 one decimal place one decimal place

+ 1.013+ 1.013 three decimal places three decimal places

31.12331.123

31.131.1 answer reported w/ correct sig answer reported w/ correct sig figsfigs

Reporting Calculations with correct Reporting Calculations with correct Sig FigsSig Figs

For For multiplication and divisionmultiplication and division, the limiting , the limiting term is the one with the smallest number of term is the one with the smallest number of sig figs.sig figs. Example:Example:

1.21.2 xx 4.564.56 == 5.4725.472 5.55.5

final answer is only allowed two sig final answer is only allowed two sig figsfigs

284.2284.2 ÷÷ 2.22.2 == 129.18129.18 130130

final answer is only allowed two sig final answer is only allowed two sig figsfigs

ROUNDING REVISITEDROUNDING REVISITED

When the answer to a calculation contains When the answer to a calculation contains too many significant figures, it must be too many significant figures, it must be rounded off. rounded off.

If the digit to be removedIf the digit to be removed is less than 5, the preceding digit stays the is less than 5, the preceding digit stays the

same.same.• Example 1.33 rounds to be 1.3Example 1.33 rounds to be 1.3

is equal or greater to 5, the preceding digit is is equal or greater to 5, the preceding digit is increased by 1.increased by 1.• ExampleExample 5.56 rounds to be 5.65.56 rounds to be 5.6

SCIENTIFIC NOTATION SCIENTIFIC NOTATION ~REVIEWED~REVIEWED

A shorthand way of representing very A shorthand way of representing very large or very small numberslarge or very small numbers

Allows us to remove zeroes that are only Allows us to remove zeroes that are only serving as place holdersserving as place holders

SCIENTIFIC NOTATION SCIENTIFIC NOTATION ~REVIEWED~REVIEWED

The number is written with one nonzero The number is written with one nonzero digit to the left of a decimal point multiplied digit to the left of a decimal point multiplied by ten raised to a powerby ten raised to a power

1.3 x 101.3 x 102525

(Remember the exponent can be positive or (Remember the exponent can be positive or negative)negative)

SCIENTIFIC NOTATION SCIENTIFIC NOTATION ~REVIEWED~REVIEWED

If you move the decimal point to the left, If you move the decimal point to the left, the exponent increases.the exponent increases. Example:Example:

256,000,000 256,000,000 2.56 x 10 2.56 x 1088

If you move the decimal point to the right, If you move the decimal point to the right, the exponent decreases.the exponent decreases. Example:Example:

0.000000000028 0.000000000028 2.8 x 10 2.8 x 10-11-11

Calculations w/ Scientific NotationCalculations w/ Scientific Notation

Adding/subtractingAdding/subtracting exponents must be exponents must be made the same* then add or subtractmade the same* then add or subtract Example:Example:

1.4 x 101.4 x 1033

+ 2.5 x 10+ 2.5 x 1044

0.14 x 104

+ 2.5 x 104

2.64 x 104

2.6 x 104

Convert all others to the largest exponent.

Calculations w/ Scientific NotationCalculations w/ Scientific Notation Multiplying Multiplying multiply numbers and add multiply numbers and add

exponents then make sure you have exponents then make sure you have proper scientific notationproper scientific notation Example:Example:

(2.5 x 10(2.5 x 101212)(1.1 x 10)(1.1 x 1033) = (2.5)(1.1) x ) = (2.5)(1.1) x 1010(12+3)(12+3)

= 2.75 x 10= 2.75 x 1015152 sig figs2 sig figs2.8 x 102.8 x 101515

DividingDividing divide number and subtract divide number and subtract exponents then make sure you have exponents then make sure you have proper scientific notation proper scientific notation Example:Example:

(2.5 x 10(2.5 x 1055))/(3.6 x 10/(3.6 x 1077) = (2.5/3.6) x 10) = (2.5/3.6) x 10(5-7)(5-7)

= 0.694 x 10= 0.694 x 10-2-2 6.9 x 106.9 x 10-3-3