The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:

\( \frac{3}{100} \) x 9 = \( \frac{3 \times 9}{100} \) = \( \frac{27}{100} \) = 0.27 errors per hour

So, in an average hour, the machine will produce 9 - 0.27 = 8.73 error free parts.

The machine ran for 24 - 3 = 21 hours yesterday so you would expect that 21 x 8.73 = 183.3 error free parts were produced yesterday.

A number in scientific notation has the format 0.000 x 10^exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:

0.0004686 in scientific notation is 4.686 x 10^-4

To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{-8c^9}{9c^3} \)
\( \frac{-8}{9} \) c^{(9 - 3)}
-\(\frac{8}{9}\)c⁶

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.