A lot of people are going the hard way when converting decimals. That is because they usually follow the mainstream version of converting decimals to fractions. In this way, they were not able to appreciate the art of mathematics, which is totally a beautiful one like poetry. At the same time, knowing the techniques in computing fractions easily will give you a better grasp of the concepts of numbers other than making a pointless computation of the fraction. This will also let you derive some quick steps of computing by going through different patterns of computation that can be easily determined around.
Most teachers failed to teach their students some valuable lessons in computation. Every computation is just related with each other and all you have to do is to supply the missing pieces to create relationships. Now, we are already talking calculus here. However, calculus can be made easier if students were taught about the relationships of numbers before they will be taught on how to compute. This is where the beauty of math can be appreciated by people.
They say that geniuses could distinguish patterns the way some people could not. Well, that is true and the secrets of being a genius are that you will be able to determine patterns first instead of going through computation. In this way, your intuition is very important. Intuition in the sense, you will be able to derive from your observations, a grasp of the relations of things by yourself.
But, the article is not about intuition and how genius computes. It is about teaching you to master the computation of decimals to fraction by looking at the patterns and forming those important skills to make computation sensible. Now, let us check the patterns between 0.1 and 0.9. Here are the conversion equivalents from fraction to decimals.
- 0.1 = 1/10
- 0.2 = 1/5
- 0.3 = 3/10
- 0.4 = 2/5
- 0.5 = ½
- 0.6= 3/5
- 0.7= 7/10
- 0.8= 4/5
- 0.9= 9/10
As you notice, there are only two repeating denominators. The first one is 10, the other one is 5. The decimal 0.5 is a special status because it represents half. Now, this is very important as decimal numbers will keep on repeating the same type of conversion if you will take them closely.
For those which have a decimal place with its integer is an odd number, you can automatically put on 10 as its denominator and copy the number to make it as its numerator. This is true in case of 0.1 which has been converted into 1/10 and so on. With exception to 5, because it always has a value of 2 in its denominator.
For even numbers, it is just way too easy. All you have to do is to put number 5 as denominator and then divide the integer by two and you have a product in its simplest form. Suppose we have 0.4, we put 5 as denominator and since 4 divided 2 equals to 2, we have 2/5 as the simplest form of fraction.
Now, you already have a pattern in mind. You can derive more patterns of this once we moved on.
Suppose we have 0.01, it is a little bit difficult for us to move on. However, with the pattern on mind, we only have to change the denominator by adding zeros to it. Now, we have 1/100 as the equivalent. That can be true with 0.2 which we now have as 1/50.
Isn’t it great? As you can see, you will be able to get the fraction equivalent in just 10 seconds.