Question

Find the multiplicative inverse of 0.9

Answer 1

Step-by-step explanation:

Given number =0.9=9/10

multiplicative inverse of 9/10 = 10/9

since a×1/a=1 then a and 1/a are multiplicative invereses to each other

(9/10)×(10/9)=90/90=1

Answer 2

Answer:

The multiplicative inverse of 0.9 is $\frac{10}{9}$

Step-by-step explanation:

Given number is 0.9.

Here we want to find multiplicative inverse .

But now question is what is multiplicative inverse?

We call $\frac{1}{a}$the multiplicative inverse of a (a not equal to 0). The reciprocal of a number is its multiplicative inverse. A number and its reciprocal multiply to 1, which is the multiplicative identity.

So,$a \times \frac{1}{a} = 1$

By one example we can understand this concept easily.

We can take 3.

Now inverse of 3 is $\frac{1}{3}$

and $(3 \times \frac{1}{3} ) = 1$

So,$\frac{1}{3}$is multiplicative inverse of 3.

Here given number is 0.9.

First we need to convert it into fraction,

So,$0.9 = \frac{9}{10}$

Now, inverse of $\frac{9}{10}$is $\frac{10}{9}$

and $( \frac{9}{10} \times \frac{10}{9} ) = 1$

Therefore $\frac{10}{9}$is the multiplicative inverse of $\frac{9}{10}$