In a previous post, I discussed the use of significant numbers. We know that when we perform calculations on a calculator, often, the number of digits we see on the screen is far more than we should report. And we now know how many to report, based on whether the computation involves multiplication, division, addiction, subtraction, or a combination of any of these.
When you report less digits than you see on the screen, you have to do some rounding. Rounding is a fairly simple concept and you should follow two rules when doing it. I will provide an explanation based on the Zumdahl and DeCoste text. I will discuss it with some examples.- Say you have the final answer 1.5678, but based on the operations involved in your calculation, you can only report this answer to two decimal places. What do you do?
- You must remove the 7 and 8 at the end of the number. Is the number 7 (the leftmost number to be dropped, in general) less than 5? Think about it. If so, you must leave the digit before the 7 (the last number to be retained) the way it is.
- Or, is the number 7 greater than or equal to 5? Check your answer to find out. If so, you must increase the digit preceding 7 (the last number to be retained) by a value of 1.
- In this example, the number preceding 7 is 6, which is greater than 5. Removing the final two digits and rounding to the nearest thousandth (two decimal places), the final answer is 1.57.
- When performing a number of different calculations, remember to apply proper mathematical rules, such as PEMDAS for example, if it is appropriate for the calculation. Moreover, do NOT round numbers off before your calculation is entirely complete. This means, if you are performing six different calculations as a part of one question, do not round with each step; simply, wait until you get your final answer, and then round off the final answer according to the rules for rounding and the use of significant figures in calculations. This ensures a higher level of accuracy, considering the fact that if you rounded at each step, your answer would be different from the answer you would receive from rounding only your final answer, due to accumulated errors with each calculation that may appear small at first but will be multiplied (no pun intended) along with each calculation.
- Note: Do not round using any other number than the number that is directly to the right of the last significant figure you are reporting (Zumdahl and DeCoste 2008).
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