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Year 7Navigate using the menu above to get help from your teacher in your year… 3 comments to Year 7 |
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hello
Just for future reference for maybe upcoming tests, how do you round a number to 2 significant figures?
Thanks if you can reply!!
Hi Sophie,
The significant figures are the ones carrying ‘real’ information, the ones which would still be there for example if you were changing the units of a measurement
eg a length of 5.4mm = 0.54cm = 0.0054m
the significant figures here are the 5 and 4. The zeros are just keeping those numbers in their correct columns.
This is important for deciding where to start counting the sig fig from.
eg in 0.02741, the first sig fig is the 2 not the zero at the start of the number.
If we were rounding the above number to 2 sf, the 2 is the 1st sf and the 7 is the 2nd, so we are going to chop off the tail of the number after the 7. However, we need to check that using 7 gives us the best approximate value of the number in case the real number is actually closer to 0.028. We decide this by looking at the digit after the ‘chop’. If it is 5 or more, then the number is actually past halfway to the next digit so we would round up.
Sometimes we need to replace the chopped off digits with zeros so that the numbers we keep mean their correct value. For example, if we round 25,659 to 3 sig fig then we want to keep the 256 and lose the 59. Two problems here: the 5 means we are past halfway so the 6 needs to be rounded up to a 7, and if we write 257, the answer doesn’t make sense! 25 thousand, six hundred and fifty nine isn’t about 257! We need to keep our 25 thousands so we need zeros. The rounded number is therefore 25700 to 3sf.
You don’t need the zeros at the END of a decimal number because the digits are already in the right place. eg if we had 0.0025659 then this would become 0.00257 to 3sf. The first zeros are keeping things in the right place now so they stay, but you don’t count them in the sig fig.
That’s a very long explanation but hope it helps.
Have a look here for some more worked examples:
http://www.bbc.co.uk/schools/gcsebitesize/maths/number/roundestimaterev3.shtml
Mrs T