Question

Write each decimal as a fraction or mixed number:

$0.7,1.29,12.831,0.0041$

What do the factors of denominators of the fractions you wrote have in common? Is this always true for decimal fractions?

Answer 1

Step 1: Convert given decimal numbers into fractions or mixed fraction form.

The given decimal numbers are $0.7,1.29,12.831,0.0041$

We know that to convert a decimal into a fraction, we need to first write the given decimal in the form of a fraction, by adding a denominator $1$. Then we need to multiply both numerator and denominator with the multiples of $10$, based on the number of decimal places in the given decimal number to remove decimal $(.)$ from the given number.

$0.7=\frac{0.7}{1}\times \frac{10}{10}=\frac{7}{10}$

$1.29=\frac{1.29}{1}\times \frac{100}{100}$

$$\begin{gathered} =\frac{129}{100} \\ =1\frac{29}{100} \end{gathered}$$

$12.831=\frac{12.831}{1}\times \frac{1000}{1000}$

$$\begin{gathered} =\frac{12831}{1000} \\ =12\frac{831}{1000} \end{gathered}$$

$0.0041=\frac{0.0041}{1}\times \frac{10000}{10000}$

$=\frac{41}{10000}$

Step 2: Analyze the denominators.

The denominators are $10,100,1000,10000$

And it's very clear that the denominators are multiples of $10$ or the denominators all have a common factor of $10$

This is true for every decimal fraction as for every decimal fraction $10$ is always the factor of the denominator.

Therefore, the required factions of the given decimal numbers $0.7,1.29,12.831,0.0041$ are $\frac{7}{10},1\frac{29}{100},12\frac{831}{1000},\&\frac{41}{10000}$respectively.