How to simplify this fraction ?

[Zulgok]

Ive got a fraction (6 * 10^24) / (4.19 * 6400^3). I was only able to simplify it to (6 * 2^12 * 5^15) / (4.19 * 3.2^3) , but I know it can be simplified further, maybe even get rid of denominator. What are the next steps I should do ? What I did was :

(6 * 10^24) / (4.19 * 6400^3)

(6 * 10^24) / (4.19 * 6.4^3 * 10^9)

(6 * 10^15) / (4.19 * 6.4^3)

(6 * 2^15 * 5^15) / (4.19 * 2^3 * 3.2^3)

(6 * 2^12 * 5^15) / (4.19 * 3.2^3)

 

[Ishuda]

Ive got a fraction (6 * 10^24) / (4.19 * 6400^3). I was only able to simplify it to (6 * 2^12 * 5^15) / (4.19 * 3.2^3) , but I know it can be simplified further, maybe even get rid of denominator. What are the next steps I should do ? What I did was :

(6 * 10^24) / (4.19 * 6400^3)

(6 * 10^24) / (4.19 * 6.4^3 * 10^9)

(6 * 10^15) / (4.19 * 6.4^3)

(6 * 2^15 * 5^15) / (4.19 * 2^3 * 3.2^3)

(6 * 2^12 * 5^15) / (4.19 * 3.2^3)

Were I given this problem I would proceed in the following manner: Since there seems to be decimals, as opposed to whole numbers, in the question, I would assume a decimal answer would suffice. Since the accuracy of the decimal (4.19) is two decimal places, I would present my final answer to two decimal places. So, continuing from your
(6 * 10^15) / (4.19 * 6.4^3)
we have
(6 * 10¹⁵) / 1098.383 = 5.46 * 10¹²
or, in more detail,
(6 * 10¹⁵) / (4.19 * 262.144) = (6 * 10¹⁵) / 1098.383
= (6 * 10¹⁵) / 1.098383 10³) = 5.46257365005966 * 10¹²
or, to two decimal places
5.46 * 10¹²

 

[Zulgok]

So, I see there are a lot of ways to do this and more than just one answer. Thanks for support.

 

[Deleted member 4993]

So, I see there are a lot of ways to do this and more than just one answer. Thanks for support.

Yes ... there are many apparently different ways to solve the same problem.

However - there is only one EXACT answer - which we may NOT be able to calculate numerically.

There may be many APPROXIMATE answers.