Question

Can someone help explain this?

Answer 1

How do you change a rational number to a decimal? can you give an example for me?

Answer 2

Rational numbers are whole numbers, fractions, and decimals - the numbers we use in our daily lives. They can be written as a ratio of two integers. Rational numbers are contrasted with irrational numbers - numbers such as Pi, √2, √7, other roots, sines, cosines, and logarithms of numbers. This article concentrates on rational numbers.

The definition says that a number is rational if you can write it in a form a/b where a and b are integers, and b is not zero. Clearly all fractions are of that form, so fractions are rational numbers. Terminating decimal numbers can also easily be written in that form: for example 0.67 = 67/100, 3.40938 = 340938/100000, and so on.

Answer 3

Huh? do you mind breaking it down and explaining it a little more detailed?

Answer 4

Let's name our number a = 0.135135135... and multiply it by a power of 10, then subtract the original a and the new number so that the repeating decimal parts cancel each other in the subtraction.

a = 0. 135135135...
10a = 1. 35135135135...
100a = 13. 5135135135...
1000a = 135. 135135135...
Okay, using 1000a and a will work, the decimals will line up! So now we subtract 1000a and a:

1000a = 135. 135135135...
- a = 0. 135135135...

999a = 135 ,
from which a = 135/999.


Another example of writing a repeating decimal as a fraction

Sometimes the first couple decimal digits are not part of the repeating pattern. For example, b = 5.65787878787... is such a number. The same trick works though: we multiply b by such power of ten that the repeating parts cancel each other in the subtraction.

b = 5. 65787878787...
10b = 56. 578787878...
100b = 565. 7878787...
As you can see, the decimal parts of b and 100b are identical! So we can subtract them:

100b = 565. 78787878...
− b = − 5. 65787878...

99b = 560. 13
from which b = 560.13/99 = 56013/9900.

Answer 5

Does that explain it

Answer 6

Not really i still don't understand it..

Answer 7

I dont kno how get anymore detailed than that im sorry if i wasnt any help