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Rounding - Significant FiguresDescription: Rounding to Significant Figures

## Objective:

The purpose of this module is to learn a better method of rounding than to a certain number of decimal places which ensures a certain level of accuracy in your measurement. This method is Significant Figures.

## Help on this Topic:

The point of rounding was there was no point talking about the size of a pin when you were measuring kilometers.
What we are really interested in are the :  Most Important digits (or figures).
The figures which make up MOST of what we are looking at.

If we want to include at least 90% of what we are looking at we need 2 significant figures / digits.
e.g.  A man might be :
1.7 meters tall (two digits)
The width of a human hair might be :
0.000075 meters (two digits)

If we want to include at least 99% of what we are looking at we need 3 digits.
e.g.  A man might be :
1.76 meters tall (3 digits)
The width of a human hair might be :
0.0000772 meters (3 digits)

•To include at least 99.9% of the distance
40,208,000,000,000 km away
40,210,000,000,000  (4 significant figures)
147,390,000 kmaway
147,400,000 (4 significant figures)

Notice that we use the first 4 most significant figures here (1473), then we round these up to 1474 because the next digit is a 9.
But of course we put the digits in the same column they were in in the beginning (units, tens, hundreds, thousands, etc)
147,400,000
I'll repeat that:  We use the most important digits (1, 4, 7, and 4), but they must go in the right place so they have the correct value

Significant Figures are the number of digits from the first non zero digit to the last non zero digit

For example if the distance from Dublin to Cork is given as 255.30296000 km
Then there are 8 significant digits.
The most significant is the 2 which represents Two hundred kilometres.
The least significant is the 6 which represents Six centimeters.

The first (or most) significant figure is the first non zero digit.
The last (or least) significant figure is the last non zero digit.
The most significant is of much greater importance or significance than the lease significant digit.

If the width of a hair is given as 0.0000176000 metres.

Then there are 3 significant digits given.

The most significant is the 1 representing TEN micrometers.
The lease significant is the 6 representing 600 nanometers.

Now the exercise is a little hard to see what is being asked so here is an example:

Complete the missing numbers from the table.

 Number Number corrected to 1 decimal place Number corrected to  2 decimal places Number corrected to 1 significant figure Number corrected to 2 significant figures 3.2454 3.2 3.25 3 3.2 18.6151

It is quite hard to see but there are five columns here.
The first column shows an example number 3.2454 and underneath that example is the question that we are asked to work on.
So the number we are interested in is the number 18.6151.
Remember that 1 significant figure means there is ONLY ONE non zero digit in our answer.
Remember that 2 significant figures means there are ONLY TWO non zero digits in our answer.

The first answer we have to give is this number corrected to 1 decimal place.  The example answer is 3.2.  Our number (18.6151) to 1 d.p. is 18.6
The second answer we have to give is this number corrected to 2 decimal place.  The example answer is 3.25.  Our number (18.6151) to 2 d.p. is 18.62
The third answer we have to give is this number corrected to 1 significant figure.  The example answer is 3.  Our number (18.6151) to 1 s.f  is 20
The fourth answer we have to give is this number corrected to 2 significant figures.  The example answer is 3.2.  Our number (18.6151) to 2 s.f. is 19

We are told to seperate our answers with commas so our answer is:
18.6 , 18.62 , 20, 19

The idea is that you will understand clearly the difference between significant figures and decimal places.