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:

8,011,000 in scientific notation is 8.011 x 10⁶

The equation for this sequence is:

a_n = a_n-1 + 3

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 3
a₆ = 13 + 3
a₆ = 16

The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [40, 80] making 40 the smallest multiple 8 and 10 have in common.

To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.

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

\( \frac{2}{100} \) x 9 = \( \frac{2 \times 9}{100} \) = \( \frac{18}{100} \) = 0.18 errors per hour

So, in an average hour, the machine will produce 9 - 0.18 = 8.82 error free parts.

The machine ran for 24 - 9 = 15 hours yesterday so you would expect that 15 x 8.82 = 132.3 error free parts were produced yesterday.