Measurements in science are never exact. The last digit of a measurement is considered to be an estimate. For example, the length of my textbook is 31.5 cm. We are quite sure about the 3 and the 1 in this measurement but the 5 is an estimate. This is why scientific measurements include uncertainty for example 31.5 ± 0.5 cm.

# Determining Significant Figures

**DEFINE** - the number of significant figures in a measurement include all digits that are certain plus the first uncertain digit. The precision of a measurement is determined in part by the number of significant figures. Using an instrument with a finer scale generally produces more precise measurements.

The 10 cm^{3} graduated cylinder on the left is more precise than the 100 cm^{3} graduated cylinder on the right.

**USE** - Significant figures are most used when rounding the result of calculations using measured values. fore doing the math. If you are the type of student who is often not sure whether to multiply or divide, then these techniques will work for you.

Video: Counting significant figures

Video: ZEROS . . . are they significant or not?? : This video will tell you with lots and lots of examples.

**SUMMARY - the rules for counting significant figures**

**APPLY** - Work through this excellent tutorial on counting significant figures. When you reach the above flowchart you can practice further on this worksheet.

# Calculations with Significant Figures

Once you have mastered counting significant figures, you can see how they affect the results of calculations.

Introduction to Rounding (Multiplication and Division calculations)

More Rounding (more Multiplication and Division calculations)

More Rounding (Introduction to Addition and Subtraction)

Scientific Notation and Significant Zeros

**APPLY** - Finish the tutorial then look at Practice questions Part 2 on this worksheet

FINAL NOTES

For multiplication and division, the result should have as many significant digits as the **measured** number with the smallest number of significant digits

For addition and subtraction, the result should have as many decimal places as the **measured** number with the smallest number of decimal places.

Round only the final answer - when performing a calculation, keep at least a couple of extra digits as is practical to avoid rounding errors

BAD BAD

- Writing more digits in an answer (intermediate or final) than justified by the number of digits in the data.
- Rounding-off, say, to two digits in an intermediate answer, and then writing three digits in the final answer.

text book s and SFG

Constants and SF

INDEX

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