Answer:
m = 4
Step-by-step explanation:
The complete question is:
Given:
6.33 x 10 ⁹ / 1.79 x 10⁵ ≈ 3 x [tex]10^{m}[/tex]
To find:
To best estimate the quotient in scientific notation. what number should replace m?
Solution:
The equation is:
6.33 x 10 ⁹ / 1.79 x 10⁵ = 3 x [tex]10^{m}[/tex]
Let x = 9 and y = 5 then the above equation becomes:
6.33 x [tex]10^{x}[/tex] / 1.79 x [tex]10^{y}[/tex] = 3 x [tex]10^{m}[/tex]
Since we know that the exponent property is:
quotient [tex]quotient \frac{z^{x} }{z^{y} } = quotient z^{x-y}[/tex]
Now converting the given equation in the form above we get:
6.33 / 1.79 x [tex]10^{x-y}[/tex]
6.33 / 1.79 x [tex]10^{9-5}[/tex]
Now the quotient is 6.33/1.79 ≈ 3.536313
quotient x [tex]10^{9-5}[/tex]
3.536313 x [tex]10^{9-5}[/tex]
Since 9-5 = 4 So
3.536313 x [tex]10^{4}[/tex]
3.536 x [tex]10^{4}[/tex]
Hence
6.33 x 10 ⁹ / 1.79 x 10⁵ ≈ 3.5 x [tex]10^{4}[/tex]
Hence m = 4
