Question

Yara multiplies and divides a certain number by the same

power of 10. The product she gets is 40,000 and the
quotient she gets is 0.000004. Find Yara's number and
the power of 10 she used. Explain your reasoning.

Answer 1

0.4 and 10.5

Explanation:

Answer 2

For this case we have to:

x: Represents the unknown number

y: Represents the exponent of base 10

So, considering a system of equations we have:

`x * 10 ^ y = 40,000\\\frac {x} {10 ^ y} = 0.000004`

From the first equation we have:

`10 ^ y = \frac {40,000} {x}`

Substituting in the second equation:

`\frac {x} {\frac {40,000} {x}} = 0.000004\\\frac {x ^ 2} {40,000} = 0.000004\\x ^ 2 = 40,000 * 0.000004\\x ^ 2 = 0.16\\x = \pm \sqrt {0.16}`

We choose the positive value:

`x = 0.4`

So, the number is 0.4.

So:

`10 ^ y = \frac {40,000} {0.4}\\10 ^ y = 100,000\\y = 5`

Thus, the exponent is 5.

Answer:

Yara use 0.4 and
`10 ^ 5`