Transcript check the number of SIG FIGS

20 dL
Math with SIG FIGS.
Read the instruments below
10 dL
0 dL
9g
10 g
11 g
10.00 g / 3.0 mL =
Means 2.9 mL or 3.1 mL
Means 9.99 g or 10.01 g
How many Sig Figs for each??
What units will the answer have ??
10.00 g / 3.0 mL =
.3333333333333333333333333333333333333
33333333333333333333333333333333333333
33333333333333333333333333333333333333
333333333333333333333… g /mL =
How precise does this answer look?
Too precise. But the answer is…….
Rounding
It’s easy. It’s fun and you have been doing it since 3rd grade.
The answer before properly rounded is .33 g / mL
How did I know when to round? We will get to that is a bit.
Rounding
Rather than rounding to a certain place value like the 100’s
place like you have done before, we will sometimes round to
a certain number of SIG FIGS.
To do this start with the leftmost SIG FIG and count over
how many SIG FIGs to keep.
If the number to its right is 4 or lower, round down
If the number to its right is 5 or more, round up
Add zeroes as place keepers if needed and
check the number of SIG FIGS
ROUNDING
Round the following
52.38
52.38
52.38
round to 3 SF
round to 2 SF
round to 1 SF
49.56
49.56
round to 3 SF
round to 2 SF
49.56
round to 1 SF
Round the following
.00070008
round to 4 SFs
.00070008
round to 3 SFs
.00070008
.00070008
round to 2 SFs
round to 1 SFs
50095
round to 4 SFs
50095
round to 3 SFs
50095
round to 2 SFs
50095
round to 1 SFs
Don’t forget of the place values
123,456.
1’s place
10’s place
100,000’s place
10,000’s place
100’s place
1,000’s place
.1234
10,000ths place
10ths place
100ths place
1,000ths place
Rules for Multiplication / Division
The answer to a multiplication or division problem should have an
equal number of SF’s as the least you began with.
1.) Multiply or Divide like normal
2.) Count the number of SF’s in each number to be multiplied or
divided (write it above the numbers).
3.) Find the least number of Sig Figs in #2
4.) Round your answer the number of sig figs found in #3
Your calculator has NO IDEA about precision, it just does
the math.
Examples of Multiplication / Division
I have done the math ahead.
Let round the answers and
put the right unit on them
25 m ·3 m = 75
120 g ·31.1 L = 3732
.0005 s ·1089 cm/s = .5445
9.41 m ·6.13 m ·5.24 m = 302.260492
.600 m2 ·.500 m = .3
21 people ·146 pounds / person = 3066
Examples of Multiplication / Division
I have done the math ahead.
Let round the answers and
put the right unit on them
33.3 m2 / 6.5 m = 5.123076923
125.9 g / 0.51 mL = 246.8627451
2.00 mi / .500 hr = 4
Addition and Subtraction
Addition and Subtraction follow a totally different rule!!!!!!
Here is how I do it.
1.) Line up the numbers so that the decimal points line up(optional)
2.) Circle the guess digit for each number (right most SF)
3.) Look for the guess digit that is in the biggest place value.
Note that place value. 100’s bigger than 10’s bigger than 1’s
4.) Add / Subtract like normal
5.) Round the answer to the place value in #3
It does not matter about the number of SF’s here, only place values
Addition and Subtraction
53 g + 72.1 g = 125.1 g
8.52 m + 6 m = 14.52 m
150 mg + 16 mg = 166 mg
6600 dL + 3900 dL = 10500 dL
.028 km + .08 km = .108 km
I have done the math ahead.
Let round the answers.
A shortcut if both numbers
have decimals. Only keep
the least number of decimal
places as you started with
Addition and Subtraction
13.4 g - 2 g = 11.4 g
5500 m - 26 m = 5474 m
620 mg - 100 mg = 520 mg
.4 dL - .202 dL = .198 dL
I have done the math ahead.
Let round the answers.
A shortcut if both numbers
have decimals. Only keep
the least number of decimal
places as you started with
Just a reminder…..
When multiplying and dividing, it’s the number of SF that
matters
When adding or subtracting, it is place values that matter