How to Use Significant Figures in Addition and Subtraction

A measurement is only as precise as the least precise step.
••• Jupiterimages/Stockbyte/Getty Images

You can't make imprecise numbers more precise just by combining them with ones that already are. That's why rules exist for mathematical operations with numbers of different precision, and these rules are based on significant digits. However, the rule for addition and subtraction is not the same as for multiplication and division. Also, the rule for addition and subtraction is sometimes easier to understand in terms of decimal places.

Addition and Subtraction

Suppose you have two scales. One reads in increments of 0.1 g, and the other in increments of 0.001 g. If you measure 2.3 g of salt on the first scale, and combine this with 0.011 grams of salt weighed on the second scale, what is the combined mass? Well, it depends on which scale you weigh it on. On the first scale it still comes in at 2.3 g, but on the second it could be 2.311 or 2.298 or 2.342. If all you know are the two original masses, then you can only assume a precision of 0.1 g. So, the precision of the final result is determined by the least number of decimal places in the two numbers, and you round to that number of decimal places. In this case, 2.3 + 0.011 → 2.3. Other examples: 100.19 + 1 → 101, 100.49 + 1 → 101, 100.51 + 1 → 102, and 0.034 + 0.0154 → 0.050. The trailing zero is because we maintain precision to three decimal places. However, 0.0340 + 0.0154 → 0.0494. We keep four decimal places because the 0 after the four in -.0340 is significant.

Related Articles

How to Break Apart Numbers You Are Subtracting
How to Convert Grams to Dry Ounces
Definition of Successor and Predecessor in Math
How to Convert Milligrams Per Liter to Molarity
How to Find a Z Score
Does Mahi Mahi Have Fins & Scales?
How to Calculate the Final Temperature of a Mixture
How to Use Significant Figures in Multiplication and...
How to Calculate the Percentage of Another Number
How to Calculate Load Current
How to Divide Rational Numbers
How to Find the Mass on a Triple Beam Balance
How Much Salt Does it Take to Make an Egg Float in...
How to Calculate the Midpoint Between Two Numbers
How to Determine if Two Ratios Are Equivalent
How to Dissolve Sodium Bicarbonate
The Effects of Temperature on the pH of Water
How to Calculate Correlation
The Difference Between a Triple Beam Balance & Double...
How to Solve Inequalities

Dont Go!

We Have More Great Sciencing Articles!