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?

- Answer
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?

- Answer
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?

- Answer
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?

- Answer
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.

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