2. Chapter 1 - Chemistry I Working with Numbers

3. Significant Digits In science numbers are not just numbers they are measurements, and as we have already discovered ALL measurements have some degree of uncertainty inherently in them. Because of this, when we combine certain measurements we must have the ability to reflect are uncertainty in our final results. Scientists’ Answer: SIGNIFICANT DIGITS

4. Significant Digits (Cont.) Significant Digits are determined in measurements by following four distinct rules. Rule 1: ALL non-zero digits are significant. (1-9) Rule 2: Zeros preceding (coming before) the first non-zero number are NEVER significant. (Leading Zeros) Rule 3: Zeros in between non-zero numbers are ALWAYS significant. (Trapped Zeros) Rule 4: Trailing zeros (zeros at the end of a number) are only significant if a decimal is present.

5. Rule 1: ALL non-zero digits are significant. Example: 12.345 has 5 significant digits since all numbers are non-zero numbers.

6. Rule 2: Zeros preceding (coming before) the first non-zero number are NEVER significant. (Leading) Zeros Example: 0.0123 has only 3 significant digits. The zeros preceding the number 1 are just keeping space in the number.

7. Rule 3: Zeros in between non-zero numbers are ALWAYS significant. (Trapped Zeros) Example: 10,023 has only 5 significant digits. The zeros between the numbers 1 and 2 are a part of the measurement and must be counted.

8. Rule 4: Trailing zeros (zeros at the end of a number) are only significant if a decimal is present. Example: 100 has only one significant digit since there is no decimal present in the number. 100. Has three significant digits, however, since there is a decimal present. WHY?

10. How Many Sig. Digs. Do the following numbers have? 0.00267001 m 19.0550 kg 3500 V 1,809,000 L Answers 6 significant digits 2 significant digits 4 significant digits

11. Significant Digits (Cont.) In scientific calculations we must account for significant digits because of our uncertainty in measurement. We have two separate rules for Addition/Subtraction and Multiplication/Division

12. Significant Digits (Cont.) Rule for Addition/Subtraction The number of significant digits allowed in our calculated answer depends on the number with the largest uncertainty. Example:951.0 g +1407 g + 23.911 g + 158.18 g 2539.091 g

13. Significant Digits (Cont.) 951.0 g +1407 g + 23.911 g + 158.18 g 2539.091 g 4 sig digs 5 sig digs 7 sig digs The answer is 2540. g with 4 sig digs. We can only express our answer to the most uncertain measurement that we have. In this case, the ones spot.

14. Significant Digits (Cont.) Rule for Multiplication/Division The measurement with the smallest number of significant digits determines the number of significant digits in the answer. Example: V = (3.052 m)(2.10 m)(0.75 m)

15. Significant Digits (Cont.) V = (3.052 m) x (2.10 m) x (0.75 m) (4 sig figs)(3 sig figs)(2 sig figs) V = 4.8069 m 3 (5 sig figs) V = 4.8 m 3

16. Significant Digits (Cont.) One Last Rule Any numbers that are exact, do not affect the number of significant digits in the final answer. Exact numbers are constants: 12 inches/foot; 3.14, 2.54 cm/inch