Significant Figures

Significant Figures

Rules for Counting Significant Figures

• Any number 1-9 is significant

• 0 in LAST DECIMAL PLACE is significant

• 0 in BETWEEN significant digits is significant

Examples

• a.  both 0's are significant because one is in final decimal place and the other is between significant digits.

• b.  all 4 0's are significant because one is in final decimal place and the others are between significant digits.

• c. all 3 0's are significant because one is in the final decimal place and the others are between significant digits.

• d.  only 1 of the 0's is significant because it is between significant digits.   The others are not AFTER the decimal  

Fill in the Blanks

How many significant digits are in the following number?

10,000

Fill in the Blanks

How many significant digits are in the following number?

10,500

Fill in the Blanks

How many significant digits are in the following number?

0.0054

Fill in the Blanks

How many significant digits are in the following number?

0.005300

Fill in the Blanks

10.003040

But Why? ROUNDING!!

• Whenever you calculate numbers in science the calculator will give you a bunch of numbers.

• NOT ALL THOSE NUMBERS ARE SIGNIFICANT!!!

• Why?  Because you answer can only be as precise as the LEAST precise measurement you used in your calculation.

• There are 2 ways to round using significant figures.

Rounding Rules for + and - with Sig Figs:

• Add or Subtract numbers as usual.

• The answer needs to be rounded to the LEAST amount of DECIMAL PLACES in the measurements you added or subtracted.

• Use rounding rules you learned in middle school to figure out if you need to round up or leave that decimal place.

Fill in the Blanks

Complete the mathematical operation and round your answer to the correct amount of decimal places.

1.457 + 83.2 =

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Complete the mathematical operation and round your answer to the correct amount of decimal places.

0.0367 - 0.004322 =

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Complete the mathematical operation and round your answer to the correct amount of decimal places.

101.25 + 3536.2 + 123.448 =

Rounding Rules for x and / Sig Figs:

• Count number of sig figs in each number.

• Perform the calculation

• Round the answer to the LEAST amount of SIG FIGS as the measurements you calculated.  

Fill in the Blanks

Complete the mathematical operation and round your answer to the correct amount of decimal places.

38.65 x 105.93 =

Fill in the Blanks

Complete the mathematical operation and round your answer to the correct amount of decimal places.

32.27 x 1.54 =

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Complete the mathematical operation and round your answer to the correct amount of decimal places.

5.892 / 6.10 =

BUT, BUT, BUT!!  What if I CANT round to the correct number of sig figs???

• There is always a way!!!

• Can use SCIENTIFIC NOTATION TO MAKE IT WORK FOR YOU!!!

• You only count the sig figs in the part before the x 10 part.

Fill in the Blanks

Complete the mathematical operation and round your answer to the correct amount of decimal places.

280 x 25 =

Fill in the Blanks

Complete the mathematical operation and round your answer to the correct amount of decimal places.

28.7907869 x 521 =

This is the end of Sig Figs!   

• please email me with any questions.

• Another great tutorial on this topic can be found at:

• https://www.youtube.com/watch?v=6oj4y0d44nQ