Rounding and estimating
Sometimes we do not always need to give detailed answers to problems - we just want a rough idea. When we are faced with a long number, we could round it off to the nearest thousand, or nearest million. And when we get a long decimal answer on a calculator, we could round it off to a certain number of decimal places.
Another method of giving an approximated answer is to round off using significant figures.
The word significant means: having meaning.
With the number 368249, the 3 is the most significant digit, because it tells us that the number is 3 hundred thousand and something. It follows that the 6 is the next most significant, and so on.
With the number 0.0000058763, the 5 is the most significant digit, because it tells us that the number is 5 millionths and something. The 8 is the next most significant, and so on.
Be careful however with numbers such as 30245, the 3 is the first significant figure and 0 the second, because of its value as a place holder.
We round off a number using a certain number of significant figures. The most common are 1, 2 or 3 significant figures.
Remember the rules for rounding up are the same as before:
What would you get if you wrote the number 368249 correct to 1 significant figure?
Did you get the answer 400000?
3 is the first significant figure, and the digit after it is more than 5, so you round up.
What would you get if you wrote the number 0.00245 correct to 1 significant figure?
Did you get the answer 0.002?
2 is the first significant figure and the digit after this is less than 5, so you do not round up.
What would you get if you wrote 0.0000058763 correct to 2 significant figures?
Did you get the answer 0.0000059?
You had to round up the 8 to 9.
If you had problems, remember that the 2 most significant figures are 5 and 8. The digit after 8 is 7, so we have to round up 8 to 9.
So 0.0000058763 = 0.0000059 to 2 significant figures.
What is 0.000030456 to two significant figures?
Did you get the answer 0.000030?
You had to round down.
If you had problems, remember that the 2 first significant figures are 3 and 0. The digit after 0 is 4, so we have to round down.
So 0.000030456 = 0.000030 to 2 significant figures.