Arithmetic & Significant Figures

Adding and Subtracting with Significant Figures. You learned in algebra that you can only add or subtract like terms. In science like terms = like units. Since these instruments are measuring the same property, we can compare their accuracy and precision by seeing how many decimal points each instrument measures to.

Adding and Subtracting with Significant Figures. You may have heard the saying that a chain is only as strong as its weakest link. That is the idea here. When we add these masses, we can’t pretend like the first scale is more precise than it is. Because of this, our answer can only have one place past the decimal. 7.1 g + 13.311 g 20.4 g

Adding and Subtracting with Significant Figures. Once again, when adding and subtracting your answer should have the same amount of significant digits to the RIGHT OF THE DECIMAL as your least precise number! 8.0 g + 12.730 g 20.7 g

What is the volume of this object? 20.5 mL 9.5 mL Volume = 11.0 mL 11.0 mL

Multiplying and Dividing with Significant Figures. You learned in algebra that you can multiply and divide between any units. As we multiply and divide these, we do not have a way to directly compare the precision of measuring different quantities since they are fundamentally different. Mass Volume Density = What is the density of this object?

Multiplying and Dividing with Significant Figures. In order to make sure that we do not mislead anyone with the precision of these results, we always report our answer with the same total amount of significant digits as our least precise measurement when we multiply or divide. Volume = 11.0 mL

Multiplying and Dividing with Significant Figures. Mass = 12.567 grams Volume = 11.0 mL Mass Volume 12.576 g 11.0 mL Density = =

3 sig figs Mass Volume 12.576 g 11.0 mL Density = = When we put this in a calculator, we get a result of 1.143272727 g/mL. The calculator does not account for precision, and this number is far too precise for our measurements. How many sig figs should we record our density with? 3 sig figs (This matches the number of sig figs from our least precise measurement.) 1.143272727 g/mL rounds to 1.14 g/mL

You will get to use the significant figure rules on your STAAR Reference Sheet, but you have to memorize the rules for addition/subtraction and multiplication/division. Addition/Subtraction: Your answer has the same number of digits past the decimal as the least precise measurement. Multiplication/Division: Your answer has the same amount of total sig figs as the least precise measurement.

Each of the problems below shows what the calculator reported as the answer. Correctly round each answer to the correct number of significant figures based on the operation that was performed.