What's the exact/closest approximate to the inverse of getting 70%?

Question

To clarify: I'm creating a computer program and I'm trying to find the actual mathematical way of approaching my problem. Given a number x, a is 0.7x. After doing some testing, it seems that to get back up to x from a, I can multiply by 1.42857143, but sometimes this isn't enough precision and gets a number that is very wrong.

Is there a blatantly obvious solution to this that I can't see? I want to find a better way to solve this without repeatedly adding 1 until it's right.

Thanks!

what are the restraints of your program? could you simply divide by $.7$? — shai horowitz, Dec 28 '20 at 02:34
With finite precision it may actually be impossible to recover $x$ exactly, depending on what gets rounded when. — Qiaochu Yuan, Dec 28 '20 at 02:50
I can't divide by .7 as it's horribly off. And It's ok with me if it's off slightly, by at most 1. — Emily, Dec 28 '20 at 04:41
What language are you using? You may try Newton Rhapson division but the accuracy depends on multiplication accuracy. — Anvit, Dec 28 '20 at 16:31

score 1 · Answer 1 · answered Dec 28 '20 at 06:31

1

Precision of operations is limited on computers.

What data type do you use? Float? Double?

To get better precision, you may want to use the types like BigDecimal.

If this is not sufficient, use other tools for programming like Mathematica.

answered Dec 28 '20 at 06:31

mentallurg

354

score 1 · Accepted Answer · answered Dec 28 '20 at 09:46

1

Ooooookay so it looks like I'm an idiot. 1.42857143 is 10÷7, and somehow I didn't notice that. I can simply just repeat the value if I want more precision.

answered Dec 28 '20 at 09:46

Emily

11

What's the exact/closest approximate to the inverse of getting 70%?

2 Answers2