What to choose for calculations fractions or decimals?
What are fractions and decimals pros and cons?
Both fractions and decimals are heavily used in engineering, finance, science, medicine, construction, and other industries. So, the question is when to use fractions and when decimals?
In some cases, it’s much easier to use fractions.
Let’s say you need to multiply 1/8 by 5. If you calculate using fractions, you can easily get the result 5/8. In case you work with the same value in the decimal format, multiplying 0.125 by 5 will take a bit more time and efforts. Another example is if you multiply 4/5, 5/6 and 3/4. Sines you can cancel numerators and denominators of these fractions, you even don’t have to multiply. The result you get is 3/6 that can be reduced to ½. If you write down this problem in the decimal format, it will look 0.8 *0.83333333 * 0.75 = 0.5
The same situation is when you add or subtract fractions with the same denominators. For example, to calculate 1/7 + 3/7 = 4/8 is much easier than 0.14285714 + 0.42857143 = 0.57142857.
Sometimes fractions are quicker to write down than decimals. For example, let’s compare 1/7 and its decimal alternative 0.14285714.
Fractions are also used over decimals when you want a precise result.
Some fractions and decimals have equal precision such as ¾ and 0.75 it does not work in 100% cases. For example, while 1/3 is an exact number, it’s decimal equivalent 0,33333… rounded to a certain number of decimal places is not. That can be easily seen if you solve 1/3 – 0.333 = 1/3 – 333/1000 = 1000/3000 – 999/3000 = 1/3000. Note: However, it’s important to mention that for some operations, the result can’t be always represented by a precise fraction. For example, the square root of ½.
In many situations, especially when you have to add, subtract or compare values, using decimal numbers is a better choice as all decimals have common denominators such as 1/10, 1/100, 1/1000.
Decimals are easier to compare and calculate as they put numbers on a common platform, so you don’t need to think about different denominators. What is easier to compare or add 2/5 and ¾ or their decimal representation 0.4 and 0.75? Of course, the decimal alternative is easier to work with.
Using fractions is less convenient to calculate large numbers or numbers with many decimal places. It’s easier to write down 0.2532 + 0.383 than 2532/10000 + 383/1000 that looks clumsy.
Many calculators don’t provide an intuitive the interface to enter fractions
Fraction to decimal conversion FAQ
What are the ways to convert fractions to decimals?
There are two ways to convert a fraction into a decimal – the long division method and Conversion of the denominator to powers of 10
How to convert a mixed fraction to a decimal?
To convert a mixed fraction to a decimal, divide the numerator by the denominator and add it to the whole number.
How to convert a negative fraction into a decimal?
In case you need to convert a negative fraction to a decimal, remove the negative sign first, perform the fraction to decimal conversion on the positive value and add the negative sign to the decimal result.
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