Integers

[dagr8est]

If x is an integer, which of the following could be x^3?

i) 1.25(10^17)
ii) 12.5(10^-12)
iii) 0.125(10^-12)


This is what I did.

i) 1.25(10^17) = 125(10^15) = [5(10^5)]^3, then x = 500000

ii) 12.5(10^-12) = 125(10^-13) = [5(10^-13/3)]^3, then x = 0.00023207...

iii) 0.125(10^-12) = 125(10^-15) = [5(10^-5)]^3, then x = 0.00005

I answered only i since 0.00005 is not an integer, but the answer key says it is i and iii. Is the answer key wrong or am I missing something?

 

[soroban]

Hello, dagr8est!

If x is an integer, which of the following could be x³ ?

i) 1.25 x 10¹⁷
ii) 12.5 x 10^-12
iii) 0.125 x 10^-12


This is what I did.

i) 1.25(10¹⁷) = 125(10¹⁵) = [5(10⁵)]³, then x = 500000

ii) 12.5(10^-12) = 125(10^-13) = [5(10^-13/3)]³, then x = 0.00023207...

iii) 0.125(10^-12) = 125(10^-15) = [5(10^-5)]³, then x = 0.00005

I answered only i since 0.00005 is not an integer, but the answer key says it is i and iii.
Is the answer key wrong or am I missing something?

I see absolutely nothing wrong with your work.
Could there be a typo? .Did you copy the problem incorrectly?