poppyandmouse2 poppyandmouse2
  • 01-11-2018
  • Mathematics
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What is the base five representation of The number 219

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jimrgrant1 jimrgrant1
  • 01-11-2018

assuming [tex]219_{10}[/tex]

Then the column values for base five here are

5³  5²  [tex]5^{1}[/tex]  [tex]5^{0}[/tex]

We can get 1 × 5³ = 125 → 219 - 125 = 94

We can get 3 × 5² = 75 → 94 - 75 = 19

We can get 3 x [tex]5^{1}[/tex] → 19 - 15 = 4

and 4 = 4 × [tex]5^{0}[/tex]

Thus [tex]219_{10}[/tex] = [tex]1334_{5}[/tex]

As a check

(1 × 125 ) + (3 × 25 ) + (3 × 5 ) + 4 = 219


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