**Significant Figures**

Exact Numbers

Exact numbers are those that can be guaranteed.

Obtained when you count objects

2 soccer balls

5 pizzas

1 watch

Obtained from a defined relationship

10 mm = 1cm

1 m = 100 cm

Not obtained with a meausring tool

Measured Numbers

Measured numbers are anything measured. No measurements are 100% accurate

When a measuring tool is used to determine a quantity such as a height or weight the numbers obtained are measured numbers.

For Example:

Worksheets

Worksheets

**Conclusion**

Rounding Significant Figures

What digits are significant?

There are some basic rules that tell you which digits in a number are significant:

All non-zero digits are significant

Any zeros between significant digits are also significant

Trailing zeros to the right of a decimal point are significant

Non - Significant Digits

Significant Digits

What digits aren't significant?

The only digits that aren't significant are zeros that are acting only as place holders in a number. These are:

Trailing zeros to the left of the decimal point

Leading zeros to the right of the decimal point

Estimating using Significant Figures

We can use significant figures to get an approximate answer to a problem.

We can round off all the numbers in a maths problem to 1 significant figure to make 'easier' numbers. It is often possible to do this in your head.

Significant Figures

There are two types of numbers:

Exact numbers

Measured number

Counting Significant Figures

There are certain rules to follow in order to determine how many significant digits a number contains

1. Identify how many digits you are required to round to

2. Locate the the required significant figures

3. If the following number is 1-4 leave the same

4. If the following number is 5-9 raise the number

For example,

Round 0.00784 to 2 significant figures

1. You are required to round to 2 sig figs

2. You are required to round to 0.0078

4. The following number is 4 so the number stays the same

The answer = 0.0078

Round each of the numbers to 1 significant figure

19.4832 + 0.00057 =

20 (1 sig fig) + 0.0006 (1 sig fig)

= 20.0006

Check the exact answer using a calculator

19.4832 + 0.00057 = 19.48377

so 20.0006 is a good estimate

Measured and Exact Numbers:

https://docs.google.com/document/d/1iAaCqWrgllKO5sjdckohfS3Au2sAgj1YfSXCip1o6zM/edit

Counting Significant Figures:

http://misterguch.brinkster.net/PRA006.pdf

Addition and Subtraction:

http://www.math-aids.com/cgi/pdf_viewer_9.cgi?script_name=significant_add_subtract.pl&addtwo=1&subtraction=1&language=0&memo=&answer=1&x=116&y=37

Multiplication and Division:

http://www.math-aids.com/cgi/pdf_viewer_9.cgi?script_name=significant_multi_divide.pl&multitwo=1&ddivide=1&language=0&memo=&answer=1&x=122&y=25

Estimating using significant figures:

https://docs.google.com/document/d/1JBCcCAtnVenOnkurjPLjI-_puRtZLamvDbj2WsbETxo/edit

Multiplication and Division

Addition and Subtraction

When quantities are being added or subtracted, the number of decimal places (not significant digits) in the answer should be the same as the least number of decimal places in any of the numbers being added or subtracted.

For example :

8.57 + 6.392 = 14.962

(2 d.p) (3 d.p)

The least number of decimal places is 2 so the answer must only contain 2

Rounded off = 14.96

In a calculation involving multiplication or division, the number of significant digits in the answer should equal the least number of significant digits in any one of the numbers being multiplied or divided

For example:

22.37 x 3.10 = 69.347

(4 s.f) ( 3 s.f)

The least number of significant figures is 3 so the answer must only contain 3

Rounded off = 69.3