Dividing small number by large number: How can you just keep adding 0s ?

[Pomoverlord]

Hi,

When dividing 3 into 451, 3 goes into 45 15 times and into 1 0 times. Then you add a zero and 3 goes into 10 3 times with 1 remainder, and so on and so on. How can you just keep adding 0s. What exactly are we doing here? This could go on forever!

Please explain.

Thankyou.

 

[Denis]

What grade are you in?

Have a look here:
https://www.mathsisfun.com/numbers/long-division-index.html

 

[Dr.Peterson]

Hi,

When dividing 3 into 451, 3 goes into 45 15 times and into 1 0 times. Then you add a zero and 3 goes into 10 3 times with 1 remainder, and so on and so on. How can you just keep adding 0s. What exactly are we doing here? This could go on forever!

Please explain.

Thankyou.

Are you talking about adding a decimal point followed by zeros, so that your quotient is 150.333... ?

If so, that is correct. For a simpler example, you can divide 1 by 3 to get 0.333... ; this is called a non-terminating decimal, and will happen whenever the denominator of a fraction has any factors other than 2 and 5.

The result of dividing will always be a repeating decimal like these; but some numbers, like pi and the square root of 2, never end, and also never repeat.

This is one of the reasons fractions are preferred when you need an exact answer: decimals can't always give you an exact result, because they don't always end.

In practice, you just keep going until the result is as accurate as you need it (say, to the nearest hundredth), and then you stop with the resulting approximate value.

 

[Steven G]

Hi,

When dividing 3 into 451, 3 goes into 45 15 times and into 1 0 times. Then you add a zero and 3 goes into 10 3 times with 1 remainder, and so on and so on. How can you just keep adding 0s. What exactly are we doing here? This could go on forever!

Please explain.

Thankyou.

You can keep adding 0s since they do NOT change the value of the number. That is 451=451.0 = 451.00 = 451.000 = 451.0000 = ...
Do you see that? If not, then please subtract two of the numbers. If you get 0, then the numbers are the same.

In 451.0 what is the value in the 1000th place? In 451.0000 what is the value in the 1000th place. For all the numbers I listed you should find the value of the hundreds place, the tens place, the ones place, the tenth place, the hundredth place, the thousandth place and so on until you see that the same position place of each number has the same digit making the numbers all equal to one another.

 

[JeffM]

Hi,

When dividing 3 into 451, 3 goes into 45 15 times and into 1 0 times. Then you add a zero and 3 goes into 10 3 times with 1 remainder, and so on and so on. How can you just keep adding 0s. What exactly are we doing here? This could go on forever!

Please explain.

Thankyou.

Decimal representations of fractions are easy to work with, but are frequently only approximations.

\(\displaystyle 451 \div 3 = \dfrac{451}{3} = \dfrac{450}{3} + \dfrac{1}{3} = 150 + \dfrac{1}{3}.\)

That is an exact answer, but it is not in decimal form. If you want to express it in decimal form exactly, you must use an infinite number of digits, which goes beyond the impractical and becomes the impossible.

 

[Pomoverlord]

Thank you very much. That was very helpful. And thanks for the black cat quote. Love it!