Significant Figures IV:
Significant figures in complicated
calculations
How about this problem:
[(2.46-.389)/(2.4967-2.395)]+10.12
In a problem like this, where there are several
levels of calculations imbedded in parenthesis,
you have to determine the significant figures
within each parenthesis and work your way out
to the final answer.
[(2.46-.389)/(2.4967-2.395)]+10.12
Let’s start with the two innermost parenthesis
2.46-.389= 2.071(raw)
Subtraction, so line up on the decimal: 2.07
2.4967-2.395 = .1017 (raw)
Subtraction, so line up on the decimal : .102
Now let’s look at the calculation with these
numbers substituted in.
(2.07/.102)+10.12
(2.07/.102)+10.12
Now let’s look at the division in parenthesis
2.07/.102= 20.2941(raw)
Division, so look at the sig figs of the number,
in this case our numbers both have 3 sig figs, so
The answer is: 20.3
Now let’s look at the calculation with this
number substituted in.
20.3 + 10.12
20.3 + 10.12
Back to addition, so lining up on the decimal
20.3 + 10.12= 30.42(raw)
Rounding back to the tenths place : 20.3
So with all that work your final answer is
three significant figures.
Practice Problems
Work your way through these practice problems.
Practice Problems
(5.468-.245)/256.34
.02038
5.468 - .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) x (1/1000)
.03552
35.53-.01 =35.52 (raw) = 35.52
(Match hundredth’s place of numbers)
1/1000= .001 (raw) = .001
This looks like a decimal unit conversion, so I regard
the 1, the 1000 and the final .001 as exact numbers
with infinite precision!
35.52 x .001 = .03552(raw) = .03552 (4 sig. fig.)
Practice Problems
(23.4x86.85) + (.00254/.01058)
2030
23.4x86.85 =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)