Question

find the reciprocal of 0.3.
select the correct choice below and, if necessary, fill in the answer box within your choice.
a. the reciprocal of 0.3 is . (do not simplify.)
b. the reciprocal does not exist.

Explanation:

Step1: Recall the definition of reciprocal

The reciprocal of a number \( x \) (where \( x
eq0 \)) is \( \frac{1}{x} \), because the product of a number and its reciprocal is 1.

Step2: Apply the definition to 0.3

First, we can write 0.3 as a fraction. \( 0.3=\frac{3}{10} \). Then, the reciprocal of \( \frac{3}{10} \) is \( \frac{1}{\frac{3}{10}} \). Using the rule for dividing by a fraction (\( \frac{1}{\frac{a}{b}}=\frac{b}{a} \) for \( a
eq0,b
eq0 \)), we get \( \frac{10}{3} \). Alternatively, directly using the decimal, the reciprocal of 0.3 is \( \frac{1}{0.3} \). If we don't simplify, we can keep it as \( \frac{1}{0.3} \) or convert 0.3 to a fraction first and then take the reciprocal. Since 0.3 is not zero, its reciprocal exists.

Answer:

A. The reciprocal of 0.3 is \(\frac{1}{0.3}\) (or \(\frac{10}{3}\) but as per instruction not to simplify, \(\frac{1}{0.3}\) is also correct).