Question 7
Find the fraction which is equivalent to

To convert the repeating decimal into a fraction, let’s break it down. The decimal can be expressed as .

For , we can set . This gives us:

Now, adding or we have:

Now we need a common denominator, which is 990. Therefore, we can rewrite:

Now combine the two fractions:

So, the fraction equivalent to is .

Fun Fact: The concept of repeating decimals has been around for centuries! Mathematicians way back in the 9th century were already playing with the ideas of fractions and decimals, though it took a long time for people to actually use decimals as we do today.

If you’re trying to avoid confusion with repeating decimals, a handy tip is to always identify the repeating part and get a clear plan for writing it as a fraction. Common mistakes include skipping the steps in combining like fractions or misidentifying the repeating part’s length, so keep an eye out!