# GCSE Maths Unit 1 - Standard Form

##### November 9, 2015

**GCSE Maths – Standard Form**

Numbers that are very large or very small can be awkward to write down, so there is a standardised form for writing all numbers;

A × 10^{n}, where 1 ≤ A < 10 and n is an integer.

**Examples**

36520 = 3.652 x 10^{4}, 0.0247 = 2.47 x 10^{-2,} 473= 4.73 x 10^{2}, 9.45 x 10^{-3} = 0.00945

Multiplying two standard form numbers is quite straightforward; just multiply the two As and add the two ns

**Examples**

36520 x 0.0247 = (3.652 x 2.47) x 10^{(4-2)} = 9.02044 x 10^{2}

36520 x 473 = (3.652 x 4.73) x 10^{(4+2)} = 17.27396 x 10^{6} = 1.727396 x 10^{7}

Adding or subtracting two standard form numbers requires a little bit more care as the two numbers must first be expressed in terms of the same power of 10

**Examples**

3.652 x 10^{4} + 4.73 x 10^{2} = 365.2 x 10^{2} + 4.73 x 10^{2} = 369.93 x 10^{2} = 3.6993 x 10^{4}

2.47 x 10^{-2} + 9.45 x 10^{-3} = 24.7 x 10^{-3} + 9.45 x 10^{-3} = 34.15 x 10^{-3 }= 3.415 x 10^{-2}

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