If we’re measuring a length of pi centimeters, why does it look finite but the number of digits is going on forever? It looks like that it’s moving small amount of time every time. Same with 0.5555555… or any number with infinite decimal places. I can’t wrap my head around it.
In: 0
We write decimals in base 10. That means any number you write down is being represented as the sum of a bunch of powers of 10. For example, 0.426 is 4 x 1/10 + 2 x 1/100 + 6 x 1/1000.
Some (in fact most) numbers can’t be written exactly as the sum of powers of 10.
Someone else here mentioned 1/3. It’s a finite quantity, but you can never quite get there with powers of 10. If you try to estimate it with one decimal place, it’s bigger than 0.3 but smaller than 0.4. Likewise, it’s bigger than 0.33 but smaller than 0.34. It’s bigger than 0.3333333 but smaller than 0.3333334. In fact, no matter how many decimal places you take, 1/3 is always “in the crack” between the last digit being a 3 and a 4. That’s why you have to have infinite 3s in the decimal. The more places, the closer it gets… but it never reaches it in a finite number of places.
Latest Answers