Top 5 Most Confusing Things About Sig Figs (Significant Figures)

Sig Figs, Sig Digs, Satan’s contribution to math and science — whatever you want to call them, they are one of the most hated and commonly confused concepts in science and math. Ignore them at your own peril, since those half points off will add up and turn your A’s into B’s, or your B’s into C’s if you’re not careful. The thing is, sig figs really are NOT THAT HARD to master, and if you know these 5 concepts, then you’ll have a leg up on everyone else who still can’t figure out the ins and outs of sig figs.

1. How To Deal With Zeros

• Sandwiched zeros are significant
• 300 has one sig fig, but 303 has three sig figs because the middle 0 becomes significant
• If trailing zeros come after a decimal point, then they are significant
• 1.000 (4 sig figs) is a more precise measurement than 1.0 (2 sig figs)
• If trailing zeros come after a number without a decimal point, then they are NOT significant
• 5,000 has 1 sig fig, but 5,000. has 4 sig figs because of the decimal point
• Leading zeros are NEVER significant
• 0.0003 has one sig fig, but 0.3003 has four sig figs since the 0’s are sandwiched

2. How To Multiply and Divide With Sig Figs

• Plug in each number exactly as it appears in the problem
• Look at the number of sig figs in each number
• Round your answer so it contains the least number of sig figs out of all the numbers being multiplied or divided
• ex: 325.0 (four sig figs) / 2.0 (two sig figs) = 162.5, but the answer should only have two sig figs, so you’d round it to 160 (two sig figs; 0 is not a sig fig) as your answer

3. What About Multiplying With Unit Conversions?

• The numbers you use for unit conversions do not count as sig figs
• ex: if you want to convert 38.5 grams into kilograms, your answer would have 3 sig figs still, even if you use the conversion 1kg/1,000g

4. Adding and Subtracting With Sig Figs

• Sig Figs DO NOT MATTER when adding and subtracting numbers
• Instead, your answer should contain the least number of decimal places
• ex: 4.32 + 5.1 should have one decimal point, so you find the exact answer (9.42) and round it to an answer with one decimal point (9.4)

5. How To Measure Volumes With Sig Figs

• There will often be a curve, or meniscus, in the top of a liquid — always measure the bottom of the meniscus
• When you are measuring the volume of something in a beaker or graduated cylinder, look at each tick mark, then go one decimal point further when recording your calculation

• ex: since this measurement device goes to the tenths place (each increment is 0.2 mL), you would want to record your measurement to the hundredths place, so an appropriate answer would be something like 3.28 mL