ACT Math - Decimals and Percentage

1

A high school senior takes a survey of the entire senior class for a project. She's interested in seeing the distribution of what her peers decide to pursue in college. She came up with the following data:

Majors_and_percents

The rest of the students stated an interest in Linguistics. How many students in total were surveyed?

Explanation

Majors_and_percents

In this question, information about 5 groups of students is included but isn't expressed in the table nor is it expressed in terms of a percentage.

The sample the student took, despite how many students were interviewed, will have all the percents add up to 100% - as in the case with any study with percent breakdowns. The number of prospective Linguistic students is given (37), and it's know they're a part of the 100% the sample provides. To determine their percent, all the other intended majors percents must be subtracted from the total (100%).

Once this information has been uncovered, this problem becomes a matter of being able to calculate what 37 is 6% of. This can be uncovered through the use of $\frac{percent}{100}=\frac{is}{of}$ . In this question, the percent and "is" is known. The goal is to find what the "of" is. The of will provide the total number of students surveyed. Denoting the "of" as x, substituting all information in, and undergoing cross multiplication will provide the final answer.

$\frac{6}{100}=\frac{37}{x}$

${\color{Blue} x=616.67}$

Given that fractions of a person cannot be surveyed, the final answer must be rounded to the nearest whole number.

2

A high school senior takes a survey of the entire senior class for a project. She's interested in seeing the distribution of what her peers decide to pursue in college. She came up with the following data:

Majors_and_percents

The rest of the students stated an interest in Linguistics. How many students in total were surveyed?

Explanation

Majors_and_percents

In this question, information about 5 groups of students is included but isn't expressed in the table nor is it expressed in terms of a percentage.

The sample the student took, despite how many students were interviewed, will have all the percents add up to 100% - as in the case with any study with percent breakdowns. The number of prospective Linguistic students is given (37), and it's know they're a part of the 100% the sample provides. To determine their percent, all the other intended majors percents must be subtracted from the total (100%).

Once this information has been uncovered, this problem becomes a matter of being able to calculate what 37 is 6% of. This can be uncovered through the use of $\frac{percent}{100}=\frac{is}{of}$ . In this question, the percent and "is" is known. The goal is to find what the "of" is. The of will provide the total number of students surveyed. Denoting the "of" as x, substituting all information in, and undergoing cross multiplication will provide the final answer.

$\frac{6}{100}=\frac{37}{x}$

${\color{Blue} x=616.67}$

Given that fractions of a person cannot be surveyed, the final answer must be rounded to the nearest whole number.

3

Express the following as a decimal:

Explanation

To convert a percentage to a decimal, you must add a decimal two points to the left from the right hand side. Thus,

$143%\rightarrow 1.43$

4

Express the following as a decimal:

Explanation

To convert a percentage to a decimal, you must add a decimal two points to the left from the right hand side. Thus,

$143%\rightarrow 1.43$

5

Which of the following is equivalent to $19 \frac{3}{4} %$ ?

Explanation

To find a decimal from a percentage, divide the percentage value by . In this case, convert the fraction to a decimal first:

$19 \frac{3}{4}% = 19.75 % = 0.1975$

6

Which of the following is equivalent to $19 \frac{3}{4} %$ ?

Explanation

To find a decimal from a percentage, divide the percentage value by . In this case, convert the fraction to a decimal first:

$19 \frac{3}{4}% = 19.75 % = 0.1975$

7

Students at a country fair typically spend \$40. The students have agreed to spend 40% less at this year's fair. Assuming all the students follow their new agreement, what is the most that could be spent by a student at this year's fair?

\$24

\$10

\$30

\$16

\$20

Explanation

This is a percentage problem, so it is important to know that 40% of some value is equal to 0.4 of said value. So to find 40% of \$40, we multiply 40 * 0.40, which equals 16. This 16 represents 40% of the original value of \$40. So if a student was to spend 40% less than they usually spend, we would subtract \$16, which is 40% of the original value, from \$40, giving us an answer of \$24.

8

Students at a country fair typically spend \$40. The students have agreed to spend 40% less at this year's fair. Assuming all the students follow their new agreement, what is the most that could be spent by a student at this year's fair?

\$24

\$10

\$30

\$16

\$20

Explanation

This is a percentage problem, so it is important to know that 40% of some value is equal to 0.4 of said value. So to find 40% of \$40, we multiply 40 * 0.40, which equals 16. This 16 represents 40% of the original value of \$40. So if a student was to spend 40% less than they usually spend, we would subtract \$16, which is 40% of the original value, from \$40, giving us an answer of \$24.

9

A share in a stock is added to a share by speculators. What is the decimal equivalent of the combined shares?