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:
[tex]x * 10 ^ y = 40,000\\\frac {x} {10 ^ y} = 0.000004[/tex]
From the first equation we have:
[tex]10 ^ y = \frac {40,000} {x}[/tex]
Substituting in the second equation:
[tex]\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}[/tex]
We choose the positive value:
[tex]x = 0.4[/tex]
So, the number is 0.4.
So:
[tex]10 ^ y = \frac {40,000} {0.4}\\10 ^ y = 100,000\\y = 5[/tex]
Thus, the exponent is 5.
Answer:
Yara use 0.4 and[tex]10 ^ 5[/tex]
