Significant Figures

What is accuracy? The exactness of a measured number What? How close is the measurement to the true number That is accuracy

What is Precision? Who closely grouped are is the data? The tighter the grouping the more precise.  You can be precise and not accurate You can be accurate and not precise

Sig Fig Rules Sig Figs only apply to measured data Are counted numbers measured? What about ratios?

Sig Fig Rules ALL nonzero digits are significant What numbers are included in that statement ALL whole numbers that are not zero

Sig Fig Rules All zeros between nonzero digits are significant For example 1003 has 4 sig figs 7.301 has 4 sig figs 30201 has 5 sig figs

Sig Fig Rules ALL trailing zeros after a decimal are Significant Examples 30.0 has 3 sig figs 6.50000000000 has 12 sig figs

Sig Fig Rules ALL leading zeros are NOT significant Examples 011 has 2 sig figs 0.011 has 2 sig figs 0.0110 has 3 sig figs

Sig Fig Rules If no decimal is present, trailing zeros are NOT significant Examples 1500 has 2 sig figs 15000000000000 has 2 sig figs

Sig Fig Rules Scientific notation shows ONLY sig figs Examples 1.50 x 103 has 3 sig figs 4.567 x 108 has 4 sig figs 1.00 x 10-11 has 3 sig figs

Sig Fig Rules A decimal following a zero makes all zeros SIGNIFICANT Examples 10. has 2 sig figs 15000. has 5 sig figs 200000000000000. has 15 sig figs

Sig Fig Rules Do you want more rules? ME EITHER Let’s make it easier 

MY Sig Fig Rules If it ain’t zero count it If zero is trapped count it If zero follows numbers after zero and after a decimal, count it If zero leads forget about it

Practice Determine the number of significant digits in each of the following: 6.571 g 0.157 kg 0.106 cm 0.12090 mm 28.0 ml 0.0067 g 2.690 g 2500 m 0.0700000 g

Adding and subtracting The sum or difference cannot be more significant than the least precise measurement. HUH?! The answer can only have as many sig figs as the smallest number (in terms of sig figs)

Practice 15.36 - .36 = ? 32.43 – 0.1 = ? 100 – 5 = ? 16.5 + 8 + 4.37 = ? 13.25 + 10.00 + 9.6 = ? 2.36 + 3.38 + 0.355 + 1.06 = ? 0.0853 + 0.0547 + 0.0370 + 0.00387 = ? 25.37 + 6.850 + 15.07 + 8.056 = ?

Multiplication and Division The product or quotient of measured data cannot have more sig figs than the least precise measured data. HUH?! The answer cannot have more sig figs than the smallest measured number (in terms of sig figs)

Practice 2.6 x 3.78 = ? 6.54 x 0.37 = ? 3.15 x 2.5 x 4.00 = ? 0.085 x 0.050 x 0.655 = ? 35 / 0.62 = ? 39 / 24.2 = ? 3.76 / 1.62 = ? 0.075 / 0.030 = ?

Compound Calculations If the operations in a compound calculation are all of the same kind (multiplication/division OR addition/subtraction) complete the operations simultaneously using standard order of operations before rounding to the correct number of significant figures. Do ALL the MATH 1st and then round

Compound Calculations If a solution to a problem requires the combination of both addition/subtraction and multiplication/division operations, rounding the intermediate solutions may introduce excess rounding answers For intermediate calculations, you should underline the estimated digit in the result and retain at least one extra digit beyond the estimated digit. Drop all remaining numbers and do not round Round the final calculation to the correct sig fig according to the applicable math rules taking into account the underlined estimated digits in the intermediate answers.

Compound Calculations If the math is not the same then do all the same stuff Take the answer, go one number beyond the required sig fig, drop all other numbers Finish the math Use sig fig rules for final answer

Example Three students are assigned the task of calculating the total floor area of the school’s science lab. The first student finds that the area of the main lab floor is 9.3 m by 7.6 m. Meanwhile, the second student measures the floor area of the chemical storage area to be 3.35 m by 1.67 m. The third student determines that the closet floor area is 93.5 cm by 127.6 cm. What is the total floor area in square meters?

Trigonometry Angles are measured in radians in SI Radians are considered non-measured numbers Degrees follow same procedure (round to nearest tenth of a degree) Follow rules when converting