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# Which of the following is the value

Which of the following is the value of 0.000064?

### 4 Explanations

2

Why was 0.000064 converted to 1,000,000?

Jan 24, 2017 • Comment

Sam Kinsman, Magoosh Tutor

Happy to help! We converted 0.000064 to 64 / 1,000,000 because in this situation, a fraction is easier to work with than a decimal. Once Mike had 64 / 1,000,000, he was able to simplify things by taking the cubed root of both the top and the bottom of the fraction.

If you're having a hard to time visualizing this conversion, let's say we have 0.6. We can also write this as 6/10. Similarly, if we have 0.64, we can write that as 64/100. And 0.064 would be 64/1000. So if we have 0.000064, we can write that as 64 / 1,000,000. The result of the division would be 0.000064

1

Daniel Castelli

converting the decimals to fractions was essential. Also, for numbers with just one and zero, I didn't not know you could simply divide the number of zeros by the exponent. Very helpful.

Jan 3, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

1

6th root of (2^6 * 10^-6)
2 * 10^-1
0.2

Jan 25, 2015 • Comment

SONIKA VASANTH

Hi
Can u explain this in detail?

Cydney Seigerman, Magoosh Tutor

Hi Sonika :)

In his explanation, José is finding the 6th root of the product mentioned:

(2^6 * 10^-6)^(1/6)

One way to find this value is to distribute the ^(1/6) across the two terms connected by multiplication in parenthesis:

(2^6 * 10^-6)^(1/6) = (2^6)^(1/6)*(10^-6)^(1/6)
--> (2^6)^(1/6) = 2^(6/6) = 2^1 = 2
--> (10^-6)^(1/6) = 10^(-6/6) = 10^-1 = 0.1
(2^6 * 10^-6)^(1/6) = 2*0.1 = 0.2

Hope this clarifies things! :)

2 Mike McGarry, Magoosh Tutor

Dec 26, 2013 • Comment

SONIKA VASANTH

When we divide 1000000 by three zeros it should be 1000 but in the explanation u have mentioned 100?

Cydney Seigerman, Magoosh Tutor

Hi Sonika,

Happy to clarify :) Here, we're not dividing per se but rather finding the cube root of 1000000 (= 10^6). The cube root of 10^6 is equal to

(10^6)^(1/3) = 10^(6/3) = 10^2 = 100

That's how we get 100 in that part of the solution :)

Hope this helps!