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Standard form, and my teacher training maths homework...
By Liz Woolf (T2092) on Wednesday, February 9, 2000 - 08:04 pm:

I'm training as a teacher and I need to get my maths back up to scratch. So far so good, but I can't remember how to put numbers into standard form and could really do with some examples to test myself on. Help.

Also - I need to answer this by next week...
When I multiply two numbers together I get 20. When I add the same 2 numbers, the answer is 10. What are the 2 numbers?
The best I can do is 7.236 and 2.764, although when I multiply them the answer is 20.000304. My tutor checked before he gave us this that none of us had a maths degree from Cambridge University, so this seems an appropriate place to ask.

Thanks.

By Dan Goodman (Dfmg2) on Wednesday, February 9, 2000 - 08:21 pm:

Your second problem is basically this, find two numbers, x and y such that:

(1) x+y=10
(2) xy=20

Try substituting y=10-x into the second equation and solving the one equation you are left with for x using a well known formula.

By Simon Munday (Sjm78) on Thursday, February 10, 2000 - 08:55 pm:

Hi Liz

The idea of standard form is that you write a number x, say, in the form x = y×10n,
where y is a number between 1 and 10 (or -1 and -10 if x is negative), and n is an
integer (positive or negative or zero).

To find y, simply move the decimal point so that it is just to the right of the first
non-zero digit. E.g.

1. 13235.546 becomes 1.3235546
2. 0.000455 becomes 4.55
3. 100 becomes 1

To find n, count the number of places that you moved the decimal point to the left
(this will be a negative number if you moved the decimal point to the right).

In example 1, n = 5
In example 2, n = -4
In example 3, n = 2

Now just put it all together!

1. 13235.546 = 1.3235546×105
2. 0.000455 = 4.55×10(-4)
3. 100 = 1×102

Have a go a doing the same for these numbers:

a) 123.55
b) 155.0003
c) 0.0001003
d) 123000

I hope you've got the hang of it.

S

By Liz Woolf (T2092) on Sunday, February 13, 2000 - 07:48 am:

Thanks Simon. What about multiplying and dividing etc when numbers are written in standard form? whenever I do it I seem to lose or gain the power by one.

Eg if the answer is meant to be 3.6×1013, I always seem to get ×1014 or ×1012

What am I doing wrong?

By The Editor on Thursday, October 19, 2000

I have seen this error many times when a scientific calculator is being used. The mistake being made in this case is usually in understanding the EXP/EE button. That button does the "times 10 to the power", and so you do not need to press ×10 first: that gives you "times 10 times 10 to the power".

If you are not using a calculator, I'm not so sure what the error is. Remember that if what you get when multiplying the two numbers (ignoring the powers of 10) together is NOT between 1 and 10, you need to make it so, and adjust the power of 10 accordingly.