1. All measurements are subject to uncertainties. All instruments used are influenced by external circumstances, and the accuracy of a measurement may be affected by the person making the reading. In everyday language, the words precise and accurate mean roughly the same thing... not in science.

2. A measurement is accurate if it is close to the accepted value. The accuracy of an individual measurement depends on the quality and performance of the instrument used to make the measurement.

3. The precision of a measurement is the degree of exactness to which it can be reproduced. After taking a lot of measurements, you will find that they are close to each other. The precision of an instrument is limited by the smallest division on the measurement scale.

5. For example, A measurement of the mass of the clock made with this scale would be more precise than a measurement made with this one.

6. When you read any measuring device, you always record the measurement by.... reading the smallest division on the scale and then “guessing at” or estimating, the tenth of the smallest division.

7. Record the correct readings on the ruler. a)13.50 cm b)11.10 cm c) 14.35 cm e) 12.26 cmd) 12.63 cm = estimated digit

8. Record the correct readings from the thermometers. 32.6 °C8.95 °C8.2 °C- 8.3 °C = estimated digit

9. I can “sig dig” it. Grooovy baby! Significant digits are all those digits obtained from a properly taken measurement: all of the certain digits plus the one estimated digit. The number of significant digits indicates the precision of the measurement. More sig digs means a more precise measurement. For example,10.0 cm10.0365 cm less precisemore precise

10. Count from left to right, beginning with the first digit that is not zero. Do not count zeros that are in front of a value, these are merely placeholders. Exact numbers have an infinite number of significant digits, because they do not involve an estimated measurement. Exact numbers are: a) numbers that are definitions eg. 1000 m = 1 km 1 dozen = 12 b) numbers that result from counting objects eg. 40 students 150 books

11. For each of the following measured values, indicate the number of significant digits. 1) 12.7 m3 2) 10.03 kg4 3) 0.0034 s2 these zeros are placeholders 4) 200 min3 5) 200 studentsinfinite 46) 2.746 x 10 12

12. What happens when we perform mathematical operations with these estimated, measured values? The result contains some significant figures and some that are not because the arithmetic was performed with uncertain numbers. Our answer can NEVER be more precise than the least precise value we used in our calculations.

13. When adding or subtracting, add or subtract, then round off the answer to the least number of decimal places of the numbers that you used. 1) 42.3 g + 16.452 g =58.8 g 2) 924 + 63.2 + 27.54 =1015 3) 205.65 kg – 60 kg =146 kg

14. When multiplying or dividing, multiply or divide, then round off the answer to the least number of significant digits of the numbers that you used. 1) 1.32 m × 0.4 m =0.5 m 2 2)8.33 x 10 -5 3) 25.7 × 2403 =6.18 × 10 4 4) 0.0028 × 983 ÷ 6.5 × 10 -7 =4.2 x 10 6 Use scientific notation when the number of sig digs in your calculator is greater than the number you need to round to!

15. When doing a series of calculations to arrive at an answer, never round off your sub-steps. Only round your final answer. If possible, keep the significant digits in your calculator. A good rule of thumb is to write three more significant digits than you’ll need to round to at the end.

16. Sig Digs review sheet