Rounding and Significant Figures in Calculations
Part 04
Rounding and Sig figs in
Calculations
page 25-26
What is the purpose of rounding?
To limit the precision of a number. To make a number less specific.
When you limit the precision of a number you need to start removing
digits from right to left. When you get to the last digit to removed, that
digit will indicate whether to round up or down.
For example, round 5.66 to one decimal
place.
5.7
For example, round 5.64 to one
decimal place.
5.6
Rounded down
Rounded up
These rounded numbers make sense because the answer is as close to
the actual number as possible.
What happens when the last removed digit is a 5, which is not closer to
rounding up or down?
First, if there are any nonzero numbers to the right of this 5, then round
up. This makes sense because this number is closer to the rounded up
number
If the last removed digit is a 5 and no nonzero numbers after it
then…???
Then… round to the even number.
This makes it 50/50 up/down.
For example, round 5.65 to one
decimal place.
5.6
Rounded down
For example, round 5.6500001 to one
decimal place.
5.7
Rounded up
Round the following to three sig figs.
569.4
0.89560
0.0068
500.1
5604
0.9999
1
4.56098 x 10
5
25650
569
0.896
0.00680
500.
Need the decimal!
1.00
1.00
4.56 x 10
5
25600
Sig figs in Calculations
When
multiplying/dividing
, the answer must contain the same
number of sig figs as the measurement with the
LOWEST number of
significant figures.
5.50 cm x 3.500cm =
19.2 cm
2
(55 m)
3
=
170000 m
3
2 x 10
-8
mm
Sig figs in Calculations
When
adding/subtracting
, the answer must contain the same precision
as the measurement with the
LOWEST precision.
Usually lowest
precision = lowest number of
decimal places.
5.50 cm – 3.500 cm =
2.00 cm
35.55 m + 0.0044 m =
35.55 m
2400 ft. + 565 ft. =
3000 ft.
Sig figs in Calculations
Exact numbers
have an infinite number of sig figs so they are
never the LOWEST sig figs or precision.
You can ignore them
when finding the lowest.
Exact numbers are counting numbers like how many students are in the
class right now. Also, defined numbers like there are 12 inches in 1 ft or
60 seconds in 1 minute.
Assignment
•
Worksheets 02 and 03: p 7-8
Rounding is done to limit the precision of numbers, ensuring they are not overly specific. When rounding, the last digit to be removed determines whether to round up or down. If the digit is 5 and there are non-zero numbers following it, you round up; otherwise, you round to the nearest even number. Following specific rules for sig figs in calculations for both multiplication/division and addition/subtraction ensures the accuracy of your results.
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Presentation Transcript
Part 04 Rounding and Sig figs in Calculations page 25-26
What is the purpose of rounding? To limit the precision of a number. To make a number less specific. When you limit the precision of a number you need to start removing digits from right to left. When you get to the last digit to removed, that digit will indicate whether to round up or down. 5.7 For example, round 5.66 to one decimal place. Rounded up For example, round 5.64 to one decimal place. 5.6 Rounded down These rounded numbers make sense because the answer is as close to the actual number as possible.
What happens when the last removed digit is a 5, which is not closer to rounding up or down? First, if there are any nonzero numbers to the right of this 5, then round up. This makes sense because this number is closer to the rounded up number If the last removed digit is a 5 and no nonzero numbers after it then ??? Then round to the even number. This makes it 50/50 up/down. For example, round 5.65 to one decimal place. 5.6 Rounded down For example, round 5.6500001 to one decimal place. 5.7 Rounded up
Round the following to three sig figs. 569 0.896 0.00680 569.4 0.89560 0.0068 500.1 5604 0.9999 1 4.56098 x 105 25650 500. 0 56 _ 0 1.00 1.00 4.56 x 105 25600
Sig figs in Calculations When multiplying/dividing, the answer must contain the same number of sig figs as the measurement with the LOWEST number of significant figures. 19.2 cm2 5.50 cm x 3.500cm = 170000 m3 (55 m)3 = 02801 . 0 3 ( ) mm 10 mm = 2 x 10-8 mm 6 . 5 00 x mm
Sig figs in Calculations When adding/subtracting, the answer must contain the same precision as the measurement with the LOWEST precision. Usually lowest precision = lowest number of decimal places. 5.50 cm 3.500 cm = 2.00 cm 35.55 m + 0.0044 m = 35.55 m 2400 ft. + 565 ft. = 3000 ft.
Sig figs in Calculations Exact numbers have an infinite number of sig figs so they are never the LOWEST sig figs or precision. You can ignore them when finding the lowest. Exact numbers are counting numbers like how many students are in the class right now. Also, defined numbers like there are 12 inches in 1 ft or 60 seconds in 1 minute.
Assignment Worksheets 02 and 03: p 7-8
