1. 1 Section 1.3 Approximate Numbers and Significant Digits

2. 2 Approximate and Exact Numbers I. APPROXIMATE NUMBERS are determined by some ______________________. Most numbers in technical applications are approximate numbers. e.g. Length of pipe is 18.35 cm II. EXACT NUMBERS are numbers that have been determined by ______________ or a ______________ ________________. e.g. 1 ft. = 12 in. (definition) 11 students (counting)

3. 3 Significant digits of an approximate number Significant digits are all digits except for zeros that are used to locate a decimal point. 1.All non-zero digits are significant. 2.Zero digits that lie between non-zero digits are significant.

4. 4 Significant digits of an approximate number (continued) 3.Zero digits that lie to the right of both the decimal point and the last non-zero digit are significant. 4.Zeros at the beginning of a decimal number are NOT significant and, in a whole number, zeros after the last non-zero digit are NOT significant.

5. 5 Accuracy vs. Precision Accuracy refers to the number of significant digits. Precision refers to the decimal position of the last significant digit.

6. 6 Accuracy vs. Precision E.g. For the following pair of approximate numbers, determine which is more accurate and which is more precise. Accuracy: Precision:

7. 7 Rounding Numbers Round the following numbers to 3 sig. digits:

8. 8 Operations with Approximate Numbers *Be careful not to express the result to an accuracy or precision that is not valid.

9. 9 Guidelines 1.When adding or subtracting approximate numbers, the result is expressed with the precision of the least precise number (decimal place). 2.When multiplying or dividing approximate numbers, the result is expressed with the accuracy of the least accurate number.

10. 10 Guidelines 3.When you take the root of an approximate number, the result is expressed with the accuracy of the number. 4.When performing operations on exact and approximate numbers combined, the accuracy (or precision) of the result is dictated by the accuracy (or precision) of the approximate numbers.

11. 11 Take Note Unless otherwise indicated, when using a calculator, round off only the final result. Avoid rounding off in the intermediate steps, if possible.

12. 12 Practice See Worksheet!