Maths work

[Kiera]

My daughter has maths homework.

Can you explain :
1. Round off each of the following numbers to 1 significant figure.

a) 46 313 b) 0.005 84 c) 30 569 d) 167.77

Can anyone please explain the above as my daugher has more of these to finish.


Thank you

[Bloss]

One Significant figure means use only ONE number other than zero to best represent the given number.

So for 46313 you will either use 40000 or round up to 50000, depending on whether the number after the first digit is a 5 or above.
The next number is a 6, so round up to 50000.

So 0.00584 can be 0.005 or 0.006, because the next digit is 8 it is closer to 0.006.

30 569 can be 30000 or 40000,
the next digit to the 3 is a 0 (which is less than 5), so you select 30000.
You cannot use 31000 because that uses 2 numbers other than zero.

167.77 can be 100 or 200. Closer to 200, confirmed by the 6 next to the first digit.

Hope these examples help, can create some more if not.

Good luck. Hope my reply is not too late for her homework deadline.

[Kiera]

Thanks very much.

My daughter was very grateful for your help.

She is handing her homework in on Monday.

[Bloss]

Terrific.

Happy to help.

[Teddio]

The zeros are significant. The number 50000 is to 5 significant figures. To quote this to one significant figure standard form should be used: 5 X 10 to the power of 5.

[Bloss]

I disagree with teddio. If what he said was the case I wouldn't be able to teach significant figures BEFORE teaching standard form.. and I have done for 19 years!!

Trust me, Keira.

[Bloss]

or even Kiera!

[Teddio]

In the real world the degree of uncertainty in the measurement of a quantity is important.
For instance the number 50200 may have 3, 4 or 5 significant figures. The number 3000000 may have 7 significant figures. The last digit may be significant. To avoid ambiguity the number should always be written in standard form.
3.000000 X 10 to the power of 7 is written unambiguously to 7 significant figures.

[derrynoose]

Zeros at the start or at the end of numbers are not significant. 2600 has2 sig. figs. .003 has one, 2.104 has three.
An answer rounded to a required number of significant figures must give an idea of the size of the original.For example, 3200 rounded to one sig. fig. is 3000 rather than ,say, 3 or 30 or 300000 or .03, all of which have one sig.fig. only.

[Teddio]

Zeros at the end of a number may be significant, it depends on the context. For instance if a Sellafield worker measuring the mass of Plutonium writes down 200000 milligrams then it is likely that all the zeros are significant and the mass is written to 6 significant figures. To avoid confusion use standard form: 2.00000 X 10 to the power of 5.

[derrynoose]

The original post was a query relating to a maths homework. Significant figure exercises at GCSE or A level are distinct from exercises on Standard Form.
Kiera, please follow the advice in the responses which did not advise the use of numbers in standard form.