Question

What strategy do you use to write the decimal expansion of a fraction? What strategy do you use to write the decimal expansion of square and cube roots?

Answer 1

Supose you have the number 1.2345

Here you have 4 numbers afther the decimal point, if you want to write this as a fraction, you can multiply it and divide it by 10^n

where n is the number of decimals afther the decimal point, in this 4 = 30

10^4 = 10*10*10*10 = 10,000

Then we have:

1.2345 = (10,000/10,000)*1.2345 = (12,345/10,000)

Now you have the initial number as a fraction.

You can use this in the next step.

if you have
`\sqrt[n]{1.23}`

where if n= 2 you have a square root and if n = 3 you have a cubic root.

You can convert 1.23 by using the time we view befor, we divide and multiply by 10^2 (because we have two decimals after the decimal point)

1.23 = (100/100)*1.23 = 123/100

and now you have:

`\sqrt[n]{1.23} = \frac{\sqrt[n]{123} }{\sqrt[n]{100} }`

And now you calculate the roots as ussual.