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Mastering Math: Rounding & Sig Figs

Learn to round numbers accurately and understand significant figures (Sig Figs) in mathematical calculations. Practice examples for addition, subtraction, multiplication, and division rules.

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Mastering Math: Rounding & Sig Figs

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  1. Math with SIG FIGS. Read the instruments below 20 dL 10 dL 0 dL 9 g 10 g 11 g

  2. 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 ??

  3. 10.00 g / 3.0 mL = .33333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333… g /mL = How precise does this answer look?

  4. Too precise. But the answer is…….

  5. 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.

  6. 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

  7. ROUNDING Round the following 52.38 round to 3 SF 52.38 round to 2 SF 52.38 round to 1 SF 49.56 round to 3 SF 49.56 round to 2 SF 49.56 round to 1 SF

  8. Round the following .00070008 round to 4 SFs .00070008 round to 3 SFs .00070008 round to 2 SFs .00070008 round to 1 SFs 50095 round to 4 SFs 50095 round to 3 SFs 50095 round to 2 SFs 50095 round to 1 SFs

  9. Don’t forget of the place values 123,456. 1’s place 10’s place 100,000’s place 100’s place 10,000’s place 1,000’s place .1234 10,000ths place 10ths place 100ths place 1,000ths place

  10. 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.

  11. 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

  12. 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

  13. 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

  14. Addition and Subtraction I have done the math ahead. Let round the answers. 53 g + 72.1 g = 125.1 g A shortcut if both numbers have decimals. Only keep the least number of decimal places as you started with 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

  15. Addition and Subtraction I have done the math ahead. Let round the answers. 13.4 g - 2 g = 11.4 g A shortcut if both numbers have decimals. Only keep the least number of decimal places as you started with 5500 m - 26 m = 5474 m 620 mg - 100 mg = 520 mg .4 dL - .202 dL = .198 dL

  16. 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

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