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 accurateYou can be accurate and not precise

Sig Fig Rules

1. Sig Figs only apply to measured data

Are counted numbers measured?

What about ratios?

Sig Fig Rules

2. ALL nonzero digits are significant

What numbers are included in that statement

ALL whole numbers that are not zero

Sig Fig Rules

3. All zeros between nonzero digits are significant

For example1003 has 4 sig figs7.301 has 4 sig figs30201 has 5 sig figs

Sig Fig Rules

4. ALL trailing zeros after a decimal areSignificant

Examples30.0 has 3 sig figs

6.50000000000 has 12 sig figs

Sig Fig Rules

5. ALL leading zeros areNOT significant

Examples

011 has 2 sig figs0.011 has 2 sig figs0.0110 has 3 sig figs

Sig Fig Rules

6. If no decimal is present, trailing zeros areNOT significant

Examples

1500 has 2 sig figs15000000000000 has 2 sig figs

Sig Fig Rules

7. Scientific notation shows ONLY sig figs

Examples

1.50 x 103 has 3 sig figs4.567 x 108 has 4 sig figs1.00 x 10-11 has 3 sig figs

Sig Fig Rules

8. A decimal following a zero makes all zeros

SIGNIFICANT

Examples

10. has 2 sig figs15000. 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

1. If it ain’t zero count it

2. If zero is trapped count it

3. If zero follows numbers after zero and after a decimal, count it

4. If zero leads forget about it

Practice

Determine the number of significant digits in each of the following:

a) 6.571 gb) 0.157 kg c) 0.106 cmd) 0.12090 mme) 28.0 ml f) 0.0067 g g) 2.690 gh) 2500 mi) 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

1. 15.36 - .36 = ?2. 32.43 – 0.1 = ?3. 100 – 5 = ?4. 16.5 + 8 + 4.37 = ?5. 13.25 + 10.00 + 9.6 = ?6. 2.36 + 3.38 + 0.355 + 1.06 = ?7. 0.0853 + 0.0547 + 0.0370 + 0.00387

= ?8. 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

a) 2.6 x 3.78 = ?b) 6.54 x 0.37 = ?c) 3.15 x 2.5 x 4.00 = ?d) 0.085 x 0.050 x 0.655 = ?e) 35 / 0.62 = ?f) 39 / 24.2 = ?g) 3.76 / 1.62 = ?h) 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 answersa. 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

b. 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

1. If the math is not the same then do all the same stuff

2. Take the answer, go one number beyond the required sig fig, drop all other numbers

3. Finish the math4. 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

1. Angles are measured in radians in SI2. Radians are considered non-measured

numbers3. Degrees follow same procedure (round to

nearest tenth of a degree)4. Follow rules when converting