# Number

looking at numbers at ib maths studies level

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## Maths Numbers, 3 significant figures and 3 decimal

For 3 significant figures, all you have to do is have 3 numbers. for example; 6.5879 turns into 6.59.

For 3 decimal points, all you need to do is have 3 numbers after the decimal point for example; 6.5879 turns into 6.588.

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## Standard form

the formula goes; a x 10 to the power of n. where a is in between 1 and 10.

so if we have this number; 2,780,000, we firstly need to convert it so its a number between 1 and 10...this would be 2.78 then we have to figure out how many places the decimal point has moved from, which in this case is 5, therefore the power is 5.

so the final formula goes; 2.78 x 10 to the power of 5.

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## Arithmetic and Geometric sequence

An arithmetic sequence is one where the numbers go up (or down) by adding (or subtracting) by the same number each time, known as the common difference. A geometric sequence is one where the numbers go up (or down) by multiplying by the same number each time, known of the common ratio.

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## Factorising

how to factorise... factorise simply means introducing brackets.

for example, the equation; 4 x to the power of 2 + 12 will be factorised to 4(x to the power of 2 + 3) the three has been introduced because 3 x 4 = to 12.

equations which need two brackets, are simpler factorised;

x to the power of 2 + bx + c

this is how the factorising should look like, (x + p) (x + q),

p and q multiplied will give c and added will give b.

for example; x to the power of 2 – 5x + 6

6 is c, so therefore find all the pairs which are multiplied to get c. which are 2 and 3, 1 and 6, -2 and -3, -1 and -6, then from these you need to find which also adds up to make b. which is -2 and -3 = -5. therefore (x - 2) (x - 3) is your answer.

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quadratic equation always equal to 0. for example; (x – 3) (x + 4) = 0

therefore ( x - 3) and ( x + 4) must equal to 0

3 - 3 = 0 whereas -4 + 4 = 0

therefore x= 3 and -4

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## quadratic equations on a graph

a x to the power of 2 + b x + c, c always equals to the y intercept and x intercept is the a and b.

to factorise an equation by a graph, all you have to do is find the two x intercepts, for example the equation is x to the power of 2 – 2x – 10

and the x intercept is -2 and 5, therefore to factorise the equation all you do is (x - 5) and (x + 5).

also when x = 0 on a graph then we are looking at the y intercept

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