Q. Round the number 69,212 to one significant figure.


Q. Round 16,412 to 3 significant figures.


Q. Round 0.00097151 to three significant figures.


Q. The density of hydrogen gas is 0.0899 kg/m³. Round this value to one significant figure.


Q. The approximate distance between the Earth and the moon is 238,000 km. Rewrite this distance to 2 significant figures.


Sometimes we need to just estimate numbers, just to give a guideline or an "rule of thumb" approximation where a simple guess will do pending (presumably) a further, more accurate calculation. For example if you were buying turf to re-lay your back garden you probably wouldn't measure it to the inch, probably not even to the nearest 6 inches or foot (that is perhaps the nearest centimetre or half meter/meter if we are working in SI units). For example my back garden is approximately 10 m wide and about 8 m from bottom to top, so I would need approximately 80 m² of turf. This will be sufficient for me to go to the nearest garden centre and obtain an approximate cost. When it came to an actual purchase I would probably get out a tape measure and be a little bit more accurate in my measurements for my final order.


So there is an example of why we might approximate. Using our knowledge of decimal places and significant figures we can now start to make approximations, let us take a look at a few examples:


Q. Estimate each of the following number calculations by first rounding each of the participant numbers to one significant figure:

       

(a) 102.2 multiplied by 4.2


(b) 3.9 divided by 5.1


(c) 142.75 multiplied by 9.56


(d) 542.04 multiplied by 1.88


(e) 494.275 divided by 5.05



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