Magic with Fractions and Decimals

If you’re doing middle or high school math, this one is for you. Over the years, you must have converted decimals into fractions and fractions into decimals many times. For example, it is common to do something like

$0.5 = \dfrac{5}{10} = \dfrac{1}{2}$

$0.362 = \dfrac{362}{1000} = \dfrac{181}{500}$

$\dfrac{3}{5} = 0.6$

$\dfrac{1}{8} = 0.125$

Also, you have probably learned about never-ending repeating decimals. For example:

$\dfrac{1}{3} = 0.3333\ldots$

$\dfrac{2}{9} = 0.2222\ldots$

Understand what you see so far? Good! Then we have a puzzle for you.

Puzzle

1. How do you convert 0.3333… back to 1/3 ?

2. How would you convert 0.272727… into a fraction?

Hint: For the first one, start with the equation

$x = 0.3333\ldots$

Then multiply both sides of the equation with a suitable number to get another equation. The idea is that $10\times 0.3333\ldots = 3.3333\ldots$ Give both questions a shot and then click on Page 2 below to see the solution.

Pages: 1 2

Magic with Fractions and Decimals

Puzzle

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