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math problems

S

simonbellfi

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Guys, I need some math assistance, and I would appreciate any help. My skills are not that bad, but I haven't figured out how to solve decimals. Here is the task - Show that the decimals 0.5, 0.1, 0.2, and 0.525 are positive rational numbers.
 
.5 is 5 tenths or 5/10
.1 is 1 tenth or 1/10
.525 is 525 thousandths or 525/1000
All those denominators and numerators are integers so they're rational and the 3 values are all positive, so they're positive rational numbers…no?
 
All decimals by default are rational
As P45cal pointed out, sinmply coun t the number of digits in a decimal and put a 1 in from of that many zero's as the denominator and remove the decimal

eg:
.5, 1 number after the decimal = 1 zero, add a 1 and remove "." = 0.5 -> 5/10
.15, 2 number after the decimal = 2 zero's, add a 1 and remove "." = 0.15 -> 15/100
1.5. 1 number after the decimal = 1 zero, add a 1 and remove "." = 1.5 -> 15/10

It is only non-decmals that are irrational, eg:
1/9 = 0.1111111 and that keeps going on forever
But the representation of 0.1111111 using the above logic, with 7 numbers after the decimal =
0.1111111 = 1111111/10000000
 
Thanks for your help. I'd been trying to solve it for a long time and didn't succeed. I posted the decimals I had to solve on https:/ /plainmath.net/post-secondary/calculus-and-analysis/integral-calculus/decimals, and in some time, it was solved. Now when I see step-by-step solutions, I understand where I made a mistake.
 
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