When you are doing a science problem, it is very likely that your teacher will want you to write the answer using significant figures. It’s also very likely that you are going to wonder exactly what that is.
When you were learning to round numbers, you learned that the number to be changed is determined by the number to the right of it. For example, if you rounded the number 384 you would round it down to 380 because the last number is lower than 5. If the original number had been 385 or 386 (or higher) you would have rounded that number to 390. But without anyone telling you what to round to, such as tens or hundreds, how do you know how small to round the number down to? This is where significant numbers come in.
There are two rules for significant figures. One for addition and subtraction and one for division and multiplication
- Addition and subtraction:Leave the same number of decimal places in the answer as there are in the quantity with the least amount of significant places.
- Division and multiplication: Leave as many significant figures in the answer as there are in the quantity with the least amount of significant figures.
Significant numbers are determined by the number in the original problem that has the least amount of numbers listed. For instance, look at the problem below.
3.84 x 12.312 = 47.27808 You would round the answer down based on the number with the smallest amount of numbers in it, 3.84.
Therefore your answer would be 47.3
However, if you were adding these numbers the answer would be different because the rule is different.
3.84 + 12.3212 = 16.1612 You would round the answer down based on how many numbers follow the decimal in the number with the smallest amount of numbers after the decimal. Since 3.84 has only two numbers following the decimal, the answer would be 16.16
To keep these straight, just remember that addition and subtraction are based on decimal places while multiplication and division are based on the total amount of numbers, but both are based on the smallest amount of numbers.