# 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.

• Sometimes the term significant figures is abbreviated to sig. figs or just s.f.

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.

• The normal rules for rounding up and down apply with significant figures:
• If the next number is $$5$$ or more, we round up.
• If the next number is $$4$$, we do not round up.

## 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.