1. Significant Digits and Rounding (A review) FOOD SCIENCE MS. MCGRATH

2. Significant Digits Measurements have uncertainty due to: measuring device; a person’s inability to perceive and interpret a reading The last (farthest right) digit is always an estimate.

3. Rules for determining significant digits Rule 1 All non-zeros are significant 7886 has _____ s.d. 19.4 has _____ s.d. 527.266992 _____ s.d.

4. Rules for determining significant digits Rule 2 All zeros that are located between two non-zero numbers are significant 408 has _____ s.d. 25074 has _____ s.d. 10203 has _____ s.d.

5. Rules for determining significant digits Rule 3 Zeros that are located to the left of a measurement are not significant 0.0907 has _____ s.d. 000102 has _____ s.d. 0303 has _____ s.d.

6. Rules for determining significant digits Rule 4 Zeros located to the right of a measurement may or may not be significant 22700 has _____ s.d. 22.700 has _____ s.d. (because of decimal)

7. Significant Digits and Calculations Final answers must not imply more certainty than measured quantities

8. Significant Digits and Calculations Rule 1 – Multiplying and Dividing The value with the fewest number of significant digits, going into a calculation, determines the number of significant digits that you should report in your answer.

9. Significant Digits and Calculations Rule 2 – Adding and Subtracting The value with the fewer number of decimal places, going into a calculation, determines the number of decimal places that you should report in your answer.

10. Significant Digits and Calculations Rule 3 – Rounding To get the appropriate number of significant digits (Rule 1) or decimal places (Rule 2), you may need to round your answer. 1. if your answer ends in a number that is greater than 5, increase the preceding digit by 1. ex. 2.346 is rounded to 2.35 2. if your answer ends with a number that is less than 5, leave the preceding number unchanged. ex. 5.73 is rounded to 5.7 3. if your answer ends with 5, increase the preceding number by 1 if it is odd. Leave the preceding number unchanged if it is even. ex. 18.35 can be rounded to 18.4 ex. 18.25 can be rounded to 18.2