The Significance of the Eleven Plus
A very pleasant mother came in today and looked over her eleven plus daughter’s shoulder while we were marking a rounding exercise. Mum started arguing with her daughter about the difference between rounding and significant figures. The pair agreed to ask the father to be the final arbiter – and that both parties would agree on his decision. The mother then smiled, and said very quietly: “My maths result was better than his.”
The daughter, then smiled and said: “We agree on rounding, but not on significant figures.”
When a measurement is given as 124 cm we know that this is an accurate measurement in terms of centimetres – as no millimetres appear to be involved. 124 is correct to three significant figures.
A number 0.00897 is correct to three significant figures because it is possible to ignore the leading zeros.
When a zero comes between other digits we then count it. 0.0205 is correct to three significant figures.
0.230 is not correct to three significant figures since the 0 is not significant.
But
123.73 – 34.63 = 89.10 – so the zero is significant. (But 89.1 is significant to three significant figures.)
But
43.56 times 1.8 = 78 because the product of two approximate numbers has no more accurate significant digits than the smaller of the number of significant figures. (I would be very interested to hear your explanation of this last statement to your nine year old!)
It may be politic to suggest to your child that it would be better to calculate the question using all the digits – and then try to sort out if they are significant or not.
Those of us who had to read Macbeth at school will remember Macbeth talking about Lady Macbeth’s death. He starts off: `She should have died hereafter. There would have been time for such a word.’ Macbeth then goes on to declaim: `Out, Out brief candle’. This is followed by, `It is a tale told by an idiot, full of sound and fury, signifying nothing.’
If your significant other is brave enough to argue with your explanation of significant figures, simply remind `the other’ of what happened to both Macbeth and Lady Macbeth.
The daughter, then smiled and said: “We agree on rounding, but not on significant figures.”
When a measurement is given as 124 cm we know that this is an accurate measurement in terms of centimetres – as no millimetres appear to be involved. 124 is correct to three significant figures.
A number 0.00897 is correct to three significant figures because it is possible to ignore the leading zeros.
When a zero comes between other digits we then count it. 0.0205 is correct to three significant figures.
0.230 is not correct to three significant figures since the 0 is not significant.
But
123.73 – 34.63 = 89.10 – so the zero is significant. (But 89.1 is significant to three significant figures.)
But
43.56 times 1.8 = 78 because the product of two approximate numbers has no more accurate significant digits than the smaller of the number of significant figures. (I would be very interested to hear your explanation of this last statement to your nine year old!)
It may be politic to suggest to your child that it would be better to calculate the question using all the digits – and then try to sort out if they are significant or not.
Those of us who had to read Macbeth at school will remember Macbeth talking about Lady Macbeth’s death. He starts off: `She should have died hereafter. There would have been time for such a word.’ Macbeth then goes on to declaim: `Out, Out brief candle’. This is followed by, `It is a tale told by an idiot, full of sound and fury, signifying nothing.’
If your significant other is brave enough to argue with your explanation of significant figures, simply remind `the other’ of what happened to both Macbeth and Lady Macbeth.
posted by Shaun at
7:58 PM
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