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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:

0.0003728 in scientific notation is 3.728 x 10^-4

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).

To simplify a radical, factor out the perfect squares:

\( \sqrt{125} \)
\( \sqrt{25 \times 5} \)
\( \sqrt{5^2 \times 5} \)
5\( \sqrt{5} \)

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

\( \frac{7}{100} \) x 9 = \( \frac{7 \times 9}{100} \) = \( \frac{63}{100} \) = 0.63 errors per hour

So, in an average hour, the machine will produce 9 - 0.63 = 8.37 error free parts.

The machine ran for 24 - 5 = 19 hours yesterday so you would expect that 19 x 8.37 = 159 error free parts were produced yesterday.