Significant Figures III:
Significant Figures in a + or - calculation.
The rule for significant figures in an addition or
subtraction calculation is a bit more complicated,
because you ignore significant figures!
Instead you look at how numbers line up with the
decimal point.
Significant Figures III:
Significant Figures in a + or - calculation.
In addition and subtraction calculations the first thing
you do is line all the numbers up and the decimal
point.
Next you find the number that has its last significant
digit in the farthest left hand column. This is the least
accurate number, and it sets the accuracy of the
overall calculation.
Your final answer can’t have any significant digits
in a column to the right of this least accurate
number.
Example 1: 2.35 + 22.00576
Lining up on the decimal
2.35
+ 22.00576
=
24.35576 (raw)
The first number is the least accurate, because it’s
last significant digit is in the hundredth’s place,
so your final answer has to round to the same
hundredth’s place.
Correct answer = 24.36
Note: Sig. fig. on this answer didn’t match with
the sig. fig. from any of the other numbers!
Example 2: 2.457 - .389
Lining up on the decimal
2.457
.389
=
2.068 (raw)
Both numbers are accurate to the thousandth’s
place, so your final answer has to round to the
same thousandth’s place.
Correct answer = 2.068
Example 3: 2.457 – 2.395
Lining up on the decimal
2.457
2.395
=
0.062 (raw)
Both numbers are accurate to the thousandth’s
place, so your final answer has to round to the
same thousandth’s place.
Correct answer = .062
Only 2 sig figs in answer!
Example 4: 2680 + 1.356
Lining up on the decimal
2680
+
1.356
=
2681.356 (raw)
The trailing zero in 2680 is not significant, so the
first number is only accurate to the tenth’s place.
Our answer must be rounded to the tenth’s place
as well!
Correct answer = 2680
Practice Problems
Work your way through the following examples
and answers to see if you have this down.
Practice Problems
.469 + .0038 = ?
.473
.469
+ .0038
=.4728
But can only have 3 digits to the right of the decimal
so you round to .473
Practice Problems
465005 - 2500 = ?
462500
465005
2500
=462505
But the last significant digit in 2500 is in the
hundred’s place, so the answer must be rounded
to the hundred’s as well, 462500.
Practice Problems
465005 – 2500. = ?
462505
465005
2500.
=462505
With the decimal, the last significant digit in 2500.
is in the one’s place, so this answer can keep the
one’s digit: 462505.
Practice Problems
2300 + 34658.74 + .000687 = ?
3.70 x 104
2300
34658.74
+
.000687
= 36958.740687
The last significant digit in 2300 is in the hundred’s
place so we must round our answer to the same
level. When we round correctly we we get 37000,
but the zero in the hundred’s place is significant.
I have to switch to scientific notation to show that
the zero in the hundred’s place is significant