Question #c7863

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Question #c7863

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Answer 1 · 2016-10-18T23:56:55

To find the multiplicative inverse, convert the number to a fraction and flip it over.

Explanation:

Make fraction

$0.1 = \frac{1}{10}$ $0.1=1/10$

Flip

$\frac{1}{10} \to \frac{10}{1}$ $1/10rarr10/1$

Simplify

$\frac{10}{1} = 10$ $10/1=10$

Answer 2 · 2016-10-18T23:57:16

$10$ $10$

Explanation:

First, note that $0.1$ $0.1$ just has a $1$ $1$ in the $10^{th} s$ $10^"th"s$ position. As a fraction, then, we can represent it as $0.1 = \frac{1}{10}$ $0.1 = 1/10$

Next, remember that the multiplicative inverse of any nonzero number is the number whose product with the original number is $1$ $1$ . So, for any nonzero number $x$ $x$ , the multiplicative inverse of $x$ $x$ is $\frac{1}{x}$ $1/x$ . This is because $x \times \frac{1}{x} = \frac{x}{x} = 1$ $x xx 1/x = x/x = 1$

So, if we want the multiplicative inverse of $0.1$ $0.1$ , we look at $\frac{1}{0.1}$ $1/0.1$ and get

$\frac{1}{0.1} = \frac{1}{\frac{1}{10}}$ $1/0.1 = 1/(1/10)$

$= \frac{1}{\frac{1}{10}} \times \frac{10}{10}$ $=1/(1/10) xx 10/10$

(multiplying the numerator and denominator by the same number doesn't change our value)

$= \frac{10}{(\frac{1}{10}) \times 10}$ $=10/((1/10)xx10)$

$= \frac{10}{1}$ $=10/1$

$= 10$ $=10$

So the multiplicative inverse of $0.1$ $0.1$ is $10$ $10$ .

As a side note, it's a useful trick to remember that $\frac{1}{\frac{1}{x}} = x$ $1/(1/x) = x$ for any nonzero $x$ $x$ . Multiplying by $\frac{x}{x} = 1$ $x/x = 1$ shows it to be true, as done above.

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Question #c7863

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