Significant digits require a strict set of rounding rules. The following rules apply to the digit immediately to the right of the place value we are rounding to.

If the value is...

For example, let's round the value 640.48 mL to the nearest milliliter. We first round the digit immediately to the right of the ones place value. Following rule #3, 4 rounds down, so we simply drop the trailing digits to give 640 mL.

Be careful not to make the mistake of double rounding. For example, if we were to start with the right-most digit of 640.48 mL, we would round this value up to 640.5 (using rule #2). If we repeat the process, 640.5 rounds up to 641 mL. Here, we rounded once for the tenths place value, and again for the ones place value. We got a different answer this time, emphasizing why you should never round twice.

Before we begin, let's review the rules of significant digits:

For this question, we are given two numbers, 24.5 and 120. The first number is very straightforward. We have three non-zero numbers, which are all significant.

The second number is trickier. We must first consider what the number represents. If we are given any count, trailing zeros before the decimal place are significant. This is because we can never have a fraction of something expressed in counts. For example, let's say we are given 10 apples. There is no uncertainty to this value, either we have the apple or we do not. Apples are also variable in size and no two apples are the exact same (e.g. a crab apple is very different from a McIntosh).

In question 6, we are given a measurement. All measurements have defined, empirical units, such as the milliliter. For measurements, trailing zeros before the decimal place are non-significant. This is because measurements have uncertainty.

How can we determine if our measurement is roughly or exactly 120 mL? Question 6 does not specify the accuracy of our measuring instrument, so we must assume the accuracy using significant digits. Recall, a quantity can only be as accurate as the measuring instrument. If we use a beaker that only has markings every 10 mL, we must estimate our measurement to the nearest 10 mL. We might be able to estimate to the nearest 0.1 mL, but we could be off by a little bit, creating uncertainty. In theory, our 120 mL measurement could be rounded from anywhere between 115 mL to 124 mL. We can safely add 20 mL, giving us 140 mL. However, we do not know if the remaining 4.5 mL brings us closer to or further from 140 mL. Thus, we omit this from the answer.

Note: To indicate that 120 mL is accurate to the nearest milliliter, it can be written using scientific notation: 1.20 x 10² mL.