Question #c7863

2 Answers
Oct 18, 2016

Answer:

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

Explanation:

Make fraction

#0.1=1/10#

Flip

#1/10rarr10/1#

Simplify

#10/1=10#

Oct 18, 2016

Answer:

#10#

Explanation:

First, note that #0.1# just has a #1# in the #10^"th"s# position. As a fraction, then, we can represent it as #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#. So, for any nonzero number #x#, the multiplicative inverse of #x# is #1/x#. This is because #x xx 1/x = x/x = 1#

So, if we want the multiplicative inverse of #0.1#, we look at #1/0.1# and get

#1/0.1 = 1/(1/10)#

#=1/(1/10) xx 10/10#

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

#=10/((1/10)xx10)#

#=10/1#

#=10#

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

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