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Welcome to the all new SATS How-to page. Here we will teach you valuble techniques that can be applied in your Maths, English & Science SATS exams, whatever the level. Forgotten how to convert a fraction? Unsure about how to plan an essay? Then the SATS How-to is for you!
Simply select your desired category from the list below and start learning...
how to deal with scientific notataion and standard form
We sometimes have to deal with very large or very small numbers. These are often approximations of real quantities which cannot be measured accurately.
e.g. The planet Pluto is, on average, 3,500,000,000 miles from the earth
To work with a number which has lots of 0s is difficult and prone to error
We therefore use standard notation to reduce the figures to a workable form.
We do this by writing the number multiplied by powers of 10.
101 = 10 x 1 = 10
102 = 10 x 10 = 100
103 = 10 x 10 x 10 = 1000
etc.
Similarly,
10-1 = 1/10
10-2 = 1/100
10-3 = 1/1000
A very large number like the one above is usually written in the form of a number between 1 and 10 multiplied by 10x
e.g. 3,500,000,000 = 3.5 x 109
0.000 000 000 023 = 2.3 x 10-14
Simply count the number of places the decimal point has to be moved in either direction.
Operations on numbers in Standard Form
Obviously multiplying, adding or dividing very large or very small numbers is liable error:
32, 000,000,000 x 2,000,000 = 64,000,000,000,000,000 ; counting the "0"s takes longer than writing them!
We can perform operations on numbers in standard form:
e.g.
multiply 5.6 x 104 by 5.1 x 105
5.6 x 5.1 = 28.56
104 x 105 = 109 (Add the indices when multiplying)
N. B. 28.56 x 109 is not incorrect, but is usually written 2.8 x 1010
Divide 2.1 x 106 by 7 x 103
2.1 x 106 = 0.3 x 103 = 0.3 x 102
7 x 103
Add 7 x 104 to 5 x 104
(7 + 5) = 12, x 104 = 1.2 x 105
Note: you do not add the indices when you are adding, only when multiplying. It is probably easier to understand why if we write out the whole sum
70,000
50,000
120,000
Add 5 x 105 and 6 x 106
To do this we have to write both numbers in the same power of 10:
6 x 106 is the same as 0.6 x 105
(5 + 0.6) = 5.6 x 105
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