Why is it helpful to convert fractions to decimals and decimals to fractions?
why is it helpful to convert fractions to decimals?
Essense of decimal is still fraction: 3.14=3+1/10+4/100. It is a way to represent a fraction by a set of common denominators: 1/10, 1/100...
The advantage of decimals is that because all of them are in common denominators already, addition, subtraction and comparing are quite straightforward.
To convert decimal to fraction is very simple, 3.14=314/100. However, the advantage of fraction is the freedom to not use the common denominators: 314/100=157/50. In some cases, fraction can be more accurate and much simpler, for instance, 1/3=0.33333.....(forever). On a calculator, it can only display and handle so many digits of decimal and would never really compute a simple fraction like 1/3. Try it on your own calulator: 1/3=0.3333333, X3=0.9999999, it doesn't not go back to 1 and there the accuracy is lost.
That said, in real life, we mostly deal with limited number of decimal digits, whether in measuring how tall a kid is or figuring out how many dallors needed for a bill. Decimal is a great tool for day to day stuff.
Hope it helps.
It depends on the situation really and the different ways you can express numbers become handy in applications like physics and chemistry problems. If you're given a physics problem and the different numbers you're given, like the speed or how far something moves, are whole numbers, then it's best to express things as fractions.
However, sometimes its better to use decimals and specifically, scientific notation. The number 500 can be written as 5 x 100 = 5.00 x 10^2. What if you are asked to multiply 5,000 x 30,000 and you're not sure of the answer. Well, you can rewrite both numbers as
5.00 x 1,000 = 5.00 x 10^3 and
3.00 x 10,000 = 3 x 10^4
where the powers indicate the number of zeros you add after 5 and 3.
Now, 5,000 x 30,000 = 5.00 x 10^3 x 3.00 x 10^4
5.00 x 10^3 x 3.00 x 10^4 = (5.00 x 3.00) x (10^3)x(10^4)
You can use the usual rules of exponents on the 10's and you know what 5.00 x 3.00 is so
(5.00 x 3.00) x (10^3)x(10^4) = 15 x 10^7
This can make your life easier if there is a digit to the right of the decimal point. I didn't include any just to keep things simple.
Hope that helps!