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Maths

Rounding and estimating

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# Significant figures

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:

• If the next number is 5 or more, we round up.
• If the next number is 4 or less, we do not round up.
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 the digit after it is more than 5, so you round up.

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.

Higher only

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.

Question

What is 0.000030456 to two significant figures?

Did you get the answer 0.000030?

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.

Question

What is 7.994 to two significant figures?

Did you get the answer 8.0?

The 2 first significant figures are 7 and 9. The digit after 9 is 9 again, so we have to round up, 7.99 rounds up to 8.00.

So 7.994 = 8.0 to 2 significant figures.

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