SIGNIFICANT digits (a.k.a. Sig Figs)

What are sig figs?  It is important to be honest when reporting a measurement, so that it does not appear to be more accurate than the equipment used to make the measurement allows.  Using significant figures communicates your accuracy in the measurement or calculation.

Which numbers are significant?   Any and all nonzero digits are significant Examples:1457 has 4 sig figs Examples:1457 has 4 sig figs 54.1 has 3 sig figs

Which numbers are significant?  Leading zeroes are NOT significant Examples:0125 has 3 sig figs Examples:0125 has 3 sig figs has 1 sig fig

Which numbers are significant?  Captive zeroes are significant, those zeroes between any non zero digits. Examples:1002 has 4 sig figs Examples:1002 has 4 sig figs has 3 sig figs

Which numbers are significant?  Trailing zeroes are significant IF AND ONLY IF they are to the right of the present decimal point Examples1.00 has 3 sig figs Examples1.00 has 3 sig figs 150 has 2 sig figs

Summary!!!  All nonzero digits are significant Examples:1457 has 4 sig figs Examples:1457 has 4 sig figs 54.1 has 3 sig figs  Leading zeroes are NOT significant Examples:0125 has 3 sig figs Examples:0125 has 3 sig figs has 1 sig fig  Captive zeroes are significant Examples:1002 has 4 sig figs Examples:1002 has 4 sig figs has 3 sig figs  Trailing zeroes are significant they are to the right of the present decimal point  Trailing zeroes are significant IF AND ONLY IF they are to the right of the present decimal point Examples1.00 has 3 sig figs Examples1.00 has 3 sig figs 150 has 2 sig figs

Reporting Calculations with correct Sig Figs  For addition and subtraction, the limiting term is the one with the smallest number of decimal places (smallest number of sig figs). Example: Example:  two decimal places 18.0  one decimal place  three decimal places  three decimal places  answer reported w/ correct sig figs

Reporting Calculations with correct Sig Figs  For multiplication and division, the limiting term is the one with the smallest number of sig figs. Example: Example: 1.2x4.56=5.472  5.5 final answer is only allowed two sig figs ÷2.2=  130 final answer is only allowed two sig figs

ROUNDING REVISITED  When the answer to a calculation contains too many significant figures, it must be rounded off.  If the digit to be removed is less than 5, the preceding digit stays the same. is less than 5, the preceding digit stays the 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 increased by 1. is equal or greater to 5, the preceding digit is increased by 1. Example5.56 rounds to be 5.6Example5.56 rounds to be 5.6

SCIENTIFIC NOTATION ~REVIEWED  A shorthand way of representing very large or very small numbers  Allows us to remove zeroes that are only serving as place holders

SCIENTIFIC NOTATION ~REVIEWED  The number is written with one nonzero digit to the left of a decimal point multiplied by ten raised to a power 1.3 x (Remember the exponent can be positive or negative)

SCIENTIFIC NOTATION ~REVIEWED  If you move the decimal point to the left, the exponent increases. Example: Example: 256,000,000  2.56 x 10 8  If you move the decimal point to the right, the exponent decreases. Example: Example:  2.8 x

Calculations w/ Scientific Notation  Adding/subtracting  exponents must be made the same* then add or subtract Example: Example: 1.4 x x x x x x x 10 4 (one decimal place) Convert all others to the largest exponent.

Calculations w/ Scientific Notation  Multiplying  multiply numbers and add exponents then make sure you have proper sig figs. Example: Example: (2.5 x )(1.1 x 10 3 ) = (2.5)(1.1) x 10 (12+3) = 2.75 x  2 sig figs  2.8 x  Dividing  divide number and subtract exponents then make sure you have proper sig figs Example: Example: (2.5 x 10 5 )/(3.6 x 10 7 ) = (2.5/3.6) x 10 (5-7) = x  6.9 x 10 -3