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Multiply two numbers in standard form, then divide two numbers in standard form.

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Simplify, leaving the result in standard index form.

We use the rules for multiplying and dividing powers.

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To multiply powers we add, for example $10^2 \\times 10^6 = 10^{(2+6)} = 10^{8}$.

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To divide powers we subtract, for example $10^2 \\div 10^6 = 10^{(2-6)} = 10^{-4}$.

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#### a)

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\\\begin{align} (\\var{int} \\times 10^\\var{ran - 3} ) \\times (\\var{int - 11} \\times 10^\\var{ran}) &= \\var{int} \\times (\\var{int-11}) \\times 10^{(\\var{ran - 3} + \\var{ran})} \\\\&= (\\var{int*(int-11)}) \\times 10^{\\var{ran - 3 + ran}} \\end{align} \

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We want to write this number in standard form so we move decimal place one place to the left to get

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\$(\\var{int*(int-11)/10}) \\times 10^{(\\var{ran - 3 + ran} + 1)} = (\\var{int*(int-11)/10}) \\times 10^{\\var{ran - 2 + ran}} \\text{.}\$

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#### b)

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Similarly,

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\\\begin{align} (\\var{int*int} \\times 10^\\var{ran -4} ) \\div (\\var{int} \\times 10^\\var{ran - 2}) &= \\var{int*int} \\div \\var{int} \\times 10^{(\\var{ran - 4} - \\var{ran -2})} \\\\&= \\var{int} \\times 10^{-2} \\text{.}\\end{align} \

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$(\\var{int} \\times 10^\\var{ran - 3} ) \\times (\\var{int - 11} \\times 10^\\var{ran}) =$  [[0]]

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$(\\var{int*int} \\times 10^\\var{ran -4} ) \\div (\\var{int} \\times 10^\\var{ran - 2}) =$  [[0]]

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Add two numbers in standard form, then subtract two numbers in standard form.

The easiest way to do this is to convert these numbers in standard form into decimals, do the calculation with decimal forms, then change them back into standard form.

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#### a)

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\\\begin{align} \\var{B[0]} \\times 10^3 + \\var{B[1]} \\times 10^4 &= \\var{B[0]*10^3} + \\var{B[1]*10^4} \\\\&= \\var{B[0]*10^3 + B[1]*10^4} \\\\&= \\var{(B[0]*10^3 + B[1]*10^4)/10^4} \\times 10^4\\end{align}\

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#### b)

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\\\begin{align} \\var{B[2]} \\times 10^3 - \\var{B[2] - 1.70} \\times 10^2 &= \\var{B[2]*10^3} - \\var{(B[2] - 1.70)*10^2} \\\\&= \\var{(B[2]*10^3) - ((B[2] - 1.70)*10^2)} \\\\&= \\var{(B[2]*10^3 - (B[2] - 1.70)*10^2)/10^3} \\times 10^3\\end{align}\

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Calculate the following and write the result in standard index form (for example, for $2.01\\times 10^5$ we would write 2.01*10^5 in the gap).

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$\\var{B[0]} \\times 10^3 + \\var{B[1]} \\times 10^4 =$  [[0]]

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$\\var{B[2]} \\times 10^3 - \\var{B[2] - 1.70} \\times 10^2 =$  [[0]]

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+

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Questions on adding, subtracting, multiplying and dividing numbers in standard form.

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