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:

0.0001461 in scientific notation is 1.461 x 10^-4

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $100
i = 0.08 x $100
i = $8

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

-5y⁷ - 1y⁷
(-5 - 1)y⁷
-6y⁷

The number of students taking German or Spanish is 5 + 7 = 12. Of that group of 12, 3 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 12 - 3 = 9 who are taking at least one language. 23 - 9 = 14 students who are not taking either language.

If 47% of the town's 37,000 voters cast ballots the number of votes cast is:

(\( \frac{47}{100} \)) x 37,000 = \( \frac{1,739,000}{100} \) = 17,390

The mayor got 72% of the votes cast which is:

(\( \frac{72}{100} \)) x 17,390 = \( \frac{1,252,080}{100} \) = 12,521 votes.