Significant Digits and Rounding (A review) Chemistry 11 Ms. McGrath

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.

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

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

Rules for determining significant digits 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.

Rules for determining significant digits 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)

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

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.

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.

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

Significant Digits and Calculations 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