Learn Decimals with Plainmath's In-Depth Explanations and Real-World Examples

What is 7/8 as a decimal rounded to the nearest hundredth?

Solve
a) ${\displaystyle 7.456\times 8}$
b) ${\displaystyle 56\times 35}$

How would you convert a repeating decimal like 1.27 or 0.6 into a fraction?

How do you write 3/7 as a terminating or repeating decimal?

How do you write 0.4747... as a fraction?

How do you express the repeating decimal 0.244 as a fraction?

What is ${\displaystyle \frac{1}{3}}$ as a percent?

$$\begin{array}{|cccccc|}\hline \text{Year}& 1970& 1980& 1990& 2000& 2010\\ \text{Hours}& 2020& 1880& 1730& 1690& 1570\\ \hline\end{array}$$
The table to the right lists the annual hours worked by the average worker in a country for selected years.
a) Let x represent the number of years after 1970. Find a formula in slope-intercept form for a linear function f that models the data.
b) Interpret the slope of graph of ${\displaystyle y=f\left(x\right)}$.
c) Estimate the annual hours worked in 2018.

The exponential models describe the population of the indicated country. A, in millions, t years after 2010. Which countries have a decreasing population? By what percentage is the population of these countries decreasing each year?
Country B: ${\displaystyle A=1173.3e^{0.008t}}$
Country C: ${\displaystyle A=33.5e^{0.017t}}$
Country D: ${\displaystyle A=121.7e^{-0.004t}}$
Country E: ${\displaystyle A=145.7e^{0.002t}}$

Compute the product AB by the definition of the product of matrices, where ${\displaystyle A{b}_1\text{and}A{b}_2}$ are computed separately, and by the row-comumn rule for computing AB.
$$A=\left[\begin{array}{cc}-2& 3\\ 3& 5\\ 6& -2\end{array}\right]$$,
$$B=\left[\begin{array}{cc}5& -1\\ -1& 4\end{array}\right]$$
Set up the product ${\displaystyle A{b}_1}$, where ${\displaystyle b_1}$ is the first column of B.
${\displaystyle A{b}_1=??}$ where b1 is the first column of B.
Calculate ${\displaystyle A{b}_1\text{where}{b}_1}$ is the first column of of B.
${\displaystyle A{b}_1=?}$
Set up the product ${\displaystyle A{b}_2\text{where}{b}_2}$ is the second column of B
${\displaystyle A{b}_2=?}$
Calculate ${\displaystyle A{b}_2\text{where}{b}_2}$ is the second column of B.
${\displaystyle A{b}_2=?}$
Determine the numerical expression for the first entry in the first column of AB using the​ row-column rule.

At a certain school, the number of student tickets sold for a home football game can be modeled by ${\displaystyle S\left(p\right)=59p+8100}$, where p is the winning percent of the home team. The number of nonstudent tickets sold for these home games is given by ${\displaystyle N\left(p\right)=0.2p^2+12p+4100}$.
a. Write an equation T(p) for the total number of tickets sold for a home football game at this school as a function of the winning percent p.
b. What is the domain for the function in part a. in this context?
c. Assuming that the football stadium is filled to capacity when the team wins 90% of its home games, what is the capacity of the school's stadium?

How wide is the chasm between what men and women earn in the workplace? According to a 2015 analysis from a national women's group, women lose $435,049 over the course of a career because of the pay gap. The bar graph to the right shows the average earnings in the United States for men and women at ages 24 and 60. This exercise involves the graphs of models for the data shown in the rectangular coordinate system to the right. Complete parts (a) through (c) below.
a. Use the two points for men shown on the graph to find a function in the form ${\displaystyle M\left(x\right)=mx+b}$ that models average yearly earnings for men x years after age 24.
${\displaystyle M\left(x\right)=?}$

Gabriela bought a new pair of glasses at the store when they were having a 30% off sale.
If the regular price of the pair of glasses was $72, how much did Gabriela pay with the discount?

The chart to the right shows a country's annual egg production. Model the data in the chart with a linear function, using the points (0,52.7) and (4,61.4). Let ${\displaystyle x=0}$ represent 1994, ${\displaystyle x=1}$ represent 1995, and so on, and let y represent the egg production (in billions). Predict egg production in 2000. How does the result compare to the actual data given in hte table, 70.7?
$$\begin{array}{|cc|}\hline \text{Year}& \text{Egg production (in billions)}\\ 1994& 52.7\\ 1995& 53.6\\ 1996& 55.4\\ 1997& 58.3\\ 1998& 61.4\\ 1999& 65\\ 2000& 70.7\\ \hline\end{array}$$

If an employee purchases a dishwasher during a 15 percent off sale, how much will he pay if the dishwasher originally cost $450?

If the lengths of the radii of two circles are 1 and 4 respectively, what is the ratio of their circumference and of their areas?

Tavon has a gift card for $95 that loses $2 for each 30-day period it is not used. He has another gift card for $75 that loses $1.50 for each 30-day period it is not used.
A. Write and solve an equation for the number of 30-day periods until the value of the gift cards will be equal.
B. What will the value of each card be when they have equal value?

How can you change a repeating decimal 0.25 into a percent?

A ball is thrown upward and outward from a height of 6 feet. The table shows four measurements indicating the ball's height at various horizontal distances from where it was thrown. A graphing calculator displays a quadratic function that models the ball's height, y, in feet, in terms of its horizontal distance, x, in feet. Answer
$$\begin{array}{|cc|}\hline x,\text{Ball's Horizontal Distance (feet)}& y,\text{Ball's Height (feet)}\\ 0& 6\\ 1& 8.1\\ 3& 6\\ 4& 2.9\\ \hline\end{array}$$
a. Explain why a quadratic function was used to model the data.
In the quadratic regression screen shown in the problem statement, why is the value of the coefficient a negative?
b. Use the graphing calculator screen (shown in the box above) to express the model in function notation.
${\displaystyle f\left(x\right)=?}$
c. Use the model from part (b) to determine the k-coordinate of the quadratic function's vertex.
The x-coordinate of the vertex is ?

A person invests $2500 in an account at 6% interest compounded annually. Let ${\displaystyle V=f\left(t\right)}$ be the value (in dollars) of the account after t years or any fraction thereof.
a. Find an equation of f.
b. What is the V-intercept? What does it mean in this situation?
c. What will be the value of the investment in six years?
d. When will the value of the investment be $7000?