Question

To best estimate the quotient in scientific notation. what number should replace m?

Answer 1

Answer:

m = 4

Step-by-step explanation:

The complete question is:

Given:

6.33 x 10 ⁹ / 1.79 x 10⁵ ≈ 3 x $10^{m}$

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 $10^{m}$

Let x = 9 and y = 5 then the above equation becomes:

6.33 x $10^{x}$ / 1.79 x $10^{y}$ = 3 x $10^{m}$

Since we know that the exponent property is:

quotient $quotient \frac{z^{x} }{z^{y} } = quotient z^{x-y}$

Now converting the given equation in the form above we get:

6.33 / 1.79 x $10^{x-y}$  

6.33 / 1.79 x $10^{9-5}$

Now the quotient is 6.33/1.79 ≈  3.536313

quotient x $10^{9-5}$

3.536313 x $10^{9-5}$

Since 9-5 = 4 So

3.536313 x $10^{4}$

3.536 x $10^{4}$

Hence

6.33 x 10 ⁹ / 1.79 x 10⁵ ≈ 3.5 x $10^{4}$

Hence m = 4