If 1,600 people live 25% of the population how many people need to leave

Mathematics

1 answer:

Zolol [24]2 years ago

7 0

Please, proofread your problem statements before posting them. Your "If 1,600 people live 25% of the population how many people need to leave" should be written as "<span>If the whole population is 1,600 and 25% of them need to leave, how many must leave?"

0.25(1600) = 400

400 people need to leave. This is 25% of the entire population, or 25% of 1600 people. Please note: it's "leave," not "live."</span>

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.<br> Evaluate the series 1 + 0.1 + 0.01 + . . .

EastWind [94]

We can employ a simple repeated decimal trick:

$x=1.111\ldots$

$0.1x=0.111\ldots$

$\implies x-0.1x=1\implies0.9x=1\implies x=\dfrac1{0.9}=\dfrac{10}9$

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Alternatively, we can compute the partial sum of the series.

$\displaystyle S_n=\sum_{k=0}^n\dfrac1{10^k}$

$S_n=1+0.1+0.01+\cdots+\dfrac1{10^n}$

$0.1S_n=0.1+0.01+0.001+\cdots+\dfrac1{10^{n+1}}$

$\implies S_n-0.1S_n=0.9S_n=1-\dfrac1{10^{n+1}}$

$\implies S_n=\dfrac{10}9-\dfrac9{10^n}$

As $n\to\infty$ , the second term vanishes and we're left with $\dfrac{10}9$ . Notice that this is really just a more formal version of the earlier trick.