Rounding and estimating
We do not always need to give exact 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 important. The closer a digit is to the beginning of a number, the more important - or significant - it is.
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.
We round off a number using a certain number of significant figures. The most common are \(1,\,2\,or\,3\) significant figures.
Questions
Question
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 as the digit after it \((6)\) is greater than \(5\), you should round up.
Sometimes you have to fill in zeros to keep the number the right size.
Question
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.
Question
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.