Significant Figures II: Significant Figures in a  or  calculation.

Significant Figures IV:Significant figures in complicatedcalculationsHow about this problem:[(2.46-.389)/(2.4967-2.395)]+10.12In a problem like this, where there are severallevels of calculations imbedded in parenthesis,you have to determine the significant figureswithin each parenthesis and work your way outto the final answer.

[(2.46-.389)/(2.4967-2.395)]+10.12Let’s start with the two innermost parenthesis2.46-.389= 2.071(raw)Subtraction, so line up on the decimal: 2.072.4967-2.395 = .1017 (raw)Subtraction, so line up on the decimal : .102Now let’s look at the calculation with thesenumbers substituted in.(2.07/.102)+10.12

(2.07/.102)+10.12Now let’s look at the division in parenthesis2.07/.102= 20.2941(raw)Division, so look at the sig figs of the number,in this case our numbers both have 3 sig figs, soThe answer is: 20.3Now let’s look at the calculation with thisnumber substituted in.20.3 + 10.12

20.3 + 10.12Back to addition, so lining up on the decimal20.3 + 10.12= 30.42(raw)Rounding back to the tenths place : 20.3So with all that work your final answer isthree significant figures.

Practice ProblemsClick you may through these practice problems

Practice Problems(5.468-.245)/256.34.020385.468 - .245 =5.223(raw) =5.223(Match thousandth’s place of least determined number)5.223/256.34 = .0203753(raw) = .02038(4 sig. Fig.)

Practice Problems(32.53-.01)(1/1000).0355235.53-.01 =35.52 (raw) = 35.52(Match hundredth’s place of numbers)1/1000= .001 (raw) = .001This looks like a decimal unit conversion, so I regardthe 1, the 1000 and the final .001 as exact numberswith infinite precision!35.52 .001 = .03552(raw) = .03552 (4 sig. fig.)

Practice Problems(23.486.85) + (.00254.01058)203023.486.85 =2034.63(raw) =2030( 3 sig. fig.).00254.01058 =.0240076(raw) = .240(3 sig. Fig.)2030 + .240 = 2030.240(raw) = 2030(tens place of least determined number)