is 1.0227 a rational number

Answer 1

Rational numbers are any numbers that are Terminating and Not repeating

Terminating meaning a decimal that simply has an end, repeating decimals while still having an infinite amount of digits can actually be simplified to a fraction.

Therefore 1.0227 IS Rational

But for example,

0.888888888888... isn't terminating, but it

IS repeating since there is a predictable sequence of numbers.

For this simple repeating decimal we can just use the nine's trick and say that 0.8 repeating is equal to 8/9

But to solve it we first have to fit this number into a writable variable, so let's say that X = 0.8 R (Repeating) so now we have to add a power to 10 for each number in the pattern/sequence that is repeating and multiply 0.8 R and the value of X by it, so in this case (0.8) there is only one number in this sequence, therefore we would do,

10X = 100.88 R (an asterisk or * means multiplication)

Which is,

10x = 8.88 R

Therefore we take each side of the expression and subtract the value of X (Which is still 0.8 R) from them. So,

10x - x = 9x (since ten 0.8's minus one is nine 0.8's) and,

8.88 R - X (0.88) is 8 (since X cancels out the infinity of eights, leaving you with a difference of 8)

Which in conclusion means 9x = 8

So X = 8/9 (eight ninths, or eight over nine)

Hope this was useful :)

Answer 2

The decimal 1.0227 is a rational number. First of all, it is a terminating decimal, which means that the decimal has a definite ending point.

Answer 3

Yes

Answer 4

yes