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Long and short scales
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==Definition== In both scales, names are given to orders of magnitude at increments of 1000. Both systems use the same names for magnitudes less than 10<sup>9</sup>. Differences arise from the use of identical names for larger magnitudes. For the same magnitude name (''n''-illion), the value is 10<sup>3''n''+3</sup> in the short scale but 10<sup>6''n''</sup> in the long scale for positive integers ''n''.<ref name="pilatol1" /><ref name="Guitel1" /><ref name="Guitel2" /> In some languages, the long scale uses additional names for the intermediate multipliers, replacing the ending ''-ion'' with ''-iard''; for example, the next multiplier after ''million'' is ''milliard'' (10<sup>9</sup>); after a ''billion'' it is ''billiard'' (10<sup>15</sup>). Hence, a long scale ''n''-illiard equals 10<sup>6''n''+3</sup>. The following table shows the size of first few short and long scale magnitudes. Notice how billion and trillion are in both scales but have different sizes. {| class="wikitable" ! Quantity ! Short scale ! Long scale |- |10<sup>6</sup> |million |million |- | 10<sup>9</sup> | <span style="color:red">billion</span> | milliard |- | 10<sup>12</sup> | <span style="color:blue">trillion</span> | <span style="color:red">billion</span> |- | 10<sup>15</sup> | <span style="color:green">quadrillion</span> | billiard |- | 10<sup>18</sup> | quintillion | <span style="color:blue">trillion</span> |- | 10<sup>21</sup> | sextillion | trilliard |- | 10<sup>24</sup> | septillion | <span style="color:green">quadrillion</span> |- | 10<sup>27</sup> | octillion | quadrilliard |}
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