Question

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

6.33x 10

1.79x 103

3 x 10"

Answer 1

m = 4

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 (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