# All About Manipulating Significant Figures

**What is a Significant Figure?**

The number of meaningful digits expressed in a numerical value is referred to as its’ number of **significant figures**. To be both precise and accurate, and still facilitate calculation, experimental measurements are expressed using significant figures. Almost all of the confusion about significant digits comes from figuring out which ZEROS are significant!

#### Step 1

### Determining Significant Figures

Rules Explained:

**TEXT**: There are three rules when or for determining how many significant digits are in a number:

- Non-zero digits are always significant.
- Any zeros between two significant digits are significant.
- A final zero or trailing zeros in the decimal portion
__ONLY__are significant. (from: http://www.chemteam.info/SigFigs/SigFigRules.html) - Trailing zeros in a whole number or "placeholder zeros" are non-significant, and when using scientific notation, count the number of significant digits using the mantissa only.

**TEXT**: Practice what you learned

- Practice 1: http://www.chemistrywithmsdana.org/wp-content/uploads/2012/07/SigFig.html
- Practice 2: http://www.sigfig.dreamhosters.com
- Practice 3: http://chemsite.lsrhs.net/measurement/countingsigdigflash.html
- QUIZ: http://www.quia.com/quiz/114241.html?AP_rand=410473119

#### Step 2

### Adding and Subtracting & Multiplying and Dividing

Rules Explained:

**TEXT**: (+/-) For **addition and subtraction -** look at the decimal portion (i.e., to the right of the decimal point) of the numbers ONLY.

1) Count the number of significant figures in the decimal portion of each number in the problem. (The digits to the left of the decimal place are not used to determine the number of decimal places in the final answer.)

2) Add or subtract in the normal fashion.

3) Round the answer to the **FEWEST** number of places in the decimal portion of any number in the problem.

**TEXT**: (x/÷) For **multiplication and division**:

The **LEAST** number of significant figures in any number of the problem determines the number of significant figures in the answer.

(from: http://www.chemteam.info/SigFigs/SigFigRules.html)

**TEXT**: Practice what you learned

- Practice Adding & Subtracting: https://sigfigscalculator.appspot.com/tutorial/add_and_subtract
- http://www.chemistrywithmsdana.org/wp-content/uploads/2012/07/SigFigOperations.html
- Practice Multiplying and Dividing: https://sigfigscalculator.appspot.com/tutorial/multiply_and_divide
- Practice 3: http://www.rpi.edu/dept/phys/Dept2/APPhys1/sigfigs/sigfig/node17.html
- Quiz: http://ths.sps.lane.edu/chemweb/unit1/problems/significantfigures/

#### Step 3

### Rounding to the required number of Significant Figures

Rules Explained:

**TEXT**: When **rounding**, you examine the digit following (i.e., to the right of) the digit that is to be the last digit in the rounded off number. The digit you are examining is the first digit to be dropped.

1 If that first digit to be dropped is **less than 5** (that is 1, 2, 3 or 4), drop it and all the digits to the right of it.

2 If that first digit to be dropped is **5 or more **(that is 5, 6, 7, 8 or 9), increase by 1 the number to be rounded, that is, the preceding figure (to the digit being dropped).

(from: http://www.chemteam.info/SigFigs/SigFigRules.html)

**Example #1**

Suppose you wish to round 62.53__4__7 to four significant figures. Look at the fifth digit. It is a 4, a number less than 5. Therefore, you will simply drop every digit after the fourth, and the original number rounds off to 62.53. (rule #1 above)

**Example #2**

Round 3.78__7__21 to three significant figures. Look at the fourth digit. It is 7, a number greater than 5, so you round the original number up to 3.79. (rule #2 above)

**TEXT**: Practice what you learned

- Practice 1: http://www.sciencegeek.net/APchemistry/APtaters/sigfigs.htm
- Practice 2: http://www.transum.org/software/SW/Starter_of_the_day/Students/Rounding.asp