# 5.14: Decimals (Exercises)

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## 5.1 - Decimals

### Name Decimals

In the following exercises, name each decimal.

- 0.8
- 0.375
- 0.007
- 5.24
- −12.5632
- −4.09

### Write Decimals

In the following exercises, write as a decimal.

- three tenths
- nine hundredths
- twenty-seven hundredths
- ten and thirty-five thousandths
- negative twenty and three tenths
- negative five hundredths

### Convert Decimals to Fractions or Mixed Numbers

In the following exercises, convert each decimal to a fraction. Simplify the answer if possible.

- 0.43
- 0.825
- 9.7
- 3.64

### Locate Decimals on the Number Line

- (a) 0.6 (b) −0.9 (c) 2.2 (d) −1.3

### Order Decimals

In the following exercises, order each of the following pairs of numbers, using < or >.

- 0.6___0.8
- 0.2___0.15
- 0.803____0.83
- −0.56____−0.562

### Round Decimals

In the following exercises, round each number to the nearest: (a) hundredth (b) tenth (c) whole number.

- 12.529
- 4.8447
- 5.897

## 5.2 - Decimal Operations

### Add and Subtract Decimals

In the following exercises, add or subtract.

- 5.75 + 8.46
- 32.89 − 8.22
- 24 − 19.31
- 10.2 + 14.631
- −6.4 + (−2.9)
- 1.83 − 4.2

### Multiply Decimals

In the following exercises, multiply.

- (0.3)(0.7)
- (−6.4)(0.25)
- (−3.35)(−12.7)
- (15.4)(1000)

### Divide Decimals

In the following exercises, divide.

- 0.48 ÷ 6
- 4.32 ÷ 24
- $6.29 ÷ 12
- (−0.8) ÷ (−0.2)
- 1.65 ÷ 0.15
- 9 ÷ 0.045

### Use Decimals in Money Applications

In the following exercises, use the strategy for applications to solve.

- Miranda got $40 from her ATM. She spent $9.32 on lunch and $16.99 on a book. How much money did she have left? Round to the nearest cent if necessary.
- Jessie put 8 gallons of gas in her car. One gallon of gas costs $3.528. How much did Jessie owe for all the gas?
- A pack of 16 water bottles cost $6.72. How much did each bottle cost?
- Alice bought a roll of paper towels that cost $2.49. She had a coupon for $0.35 off, and the store doubled the coupon. How much did Alice pay for the paper towels?

## 5.3 - Decimals and Fractions

### Convert Fractions to Decimals

In the following exercises, convert each fraction to a decimal.

- \(\dfrac{3}{5}\)
- \(\dfrac{7}{8}\)
- \(- \dfrac{19}{20}\)
- \(- \dfrac{21}{4}\)
- \(\dfrac{1}{3}\)
- \(\dfrac{6}{11}\)

### Order Decimals and Fractions

In the following exercises, order each pair of numbers, using < or >.

- \(\dfrac{1}{2}\) ___0.2
- \(\dfrac{3}{5}\) ___0.
- \(- \dfrac{7}{8}\) ___−0.84
- \(- \dfrac{5}{12}\) ___−0.42
- 0.625___\(\dfrac{13}{20}\)
- 0.33___\(\dfrac{5}{16}\)

In the following exercises, write each set of numbers in order from least to greatest.

- \(\dfrac{2}{3}, \dfrac{17}{20}\), 0.65
- \(\dfrac{7}{9}\), 0.75, \(\dfrac{11}{15}\)

### Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

- 4(10.3 − 5.8)
- \(\dfrac{3}{4}\)(15.44 − 7.4)
- 30 ÷ (0.45 + 0.15)
- 1.6 + \(\dfrac{3}{8}\)
- 52(0.5) + (0.4)
^{2} - \(− \dfrac{2}{5} \cdot \dfrac{9}{10}\) + 0.14

### Find the Circumference and Area of Circles

In the following exercises, approximate the (a) circumference and (b) area of each circle.

- radius = 6 in.
- radius = 3.5 ft.
- radius = 7 33 m
- diameter = 11 cm

## 5.4 - Solve Equations with Decimals

### Determine Whether a Decimal is a Solution of an Equation

In the following exercises, determine whether the each number is a solution of the given equation.

- x − 0.4 = 2.1
- x = 1.7
- x = 2.5

- y + 3.2 = −1.5
- y = 1.7
- y = −4.7

- \(\dfrac{u}{2.5}\) = −12.5
- u = −5
- u = −31.25

- 0.45v = −40.5
- v = −18.225
- v = −90

### Solve Equations with Decimals

In the following exercises, solve.

- m + 3.8 = 7.5
- h + 5.91 = 2.4
- a + 2.26 = −1.1
- p − 4.3 = −1.65
- x − 0.24 = −8.6
- j − 7.42 = −3.7
- 0.6p = 13.2
- −8.6x = 34.4
- −22.32 = −2.4z
- \(\dfrac{a}{0.3}\) = −24
- \(\dfrac{p}{−7}\) = −4.2
- \(\dfrac{s}{−2.5}\) = −10

### Translate to an Equation and Solve

In the following exercises, translate and solve.

- The difference of n and 15.2 is 4.4.
- The product of −5.9 and x is −3.54.
- The quotient of y and −1.8 is −9.
- The sum of m and −4.03 is 6.8.

## 5.5 - Averages and Probability

### Find the Mean of a Set of Numbers

In the following exercises, find the mean of the numbers.

- 2, 4, 1, 0, 1, and 1
- $270, $310.50, $243.75, and $252.15
- Each workday last week, Yoshie kept track of the number of minutes she had to wait for the bus. She waited 3, 0, 8, 1, and 8 minutes. Find the mean
- In the last three months, Raul’s water bills were $31.45, $48.76, and $42.60. Find the mean.

### Find the Median of a Set of Numbers

In the following exercises, find the median.

- 41, 45, 32, 60, 58
- 25, 23, 24, 26, 29, 19, 18, 32
- The ages of the eight men in Jerry’s model train club are 52, 63, 45, 51, 55, 75, 60, and 59. Find the median age.
- The number of clients at Miranda’s beauty salon each weekday last week were 18, 7, 12, 16, and 20. Find the median number of clients.

### Find the Mode of a Set of Numbers

In the following exercises, identify the mode of the numbers.

- 6, 4, 4, 5, 6, 6, 4, 4, 4, 3, 5
- The number of siblings of a group of students: 2, 0, 3, 2, 4, 1, 6, 5, 4, 1, 2, 3

### Use the Basic Definition of Probability

In the following exercises, solve. (Round decimals to three places.)

- The Sustainability Club sells 200 tickets to a raffle, and Albert buys one ticket. One ticket will be selected at random to win the grand prize. Find the probability Albert will win the grand prize. Express your answer as a fraction and as a decimal.
- Luc has to read 3 novels and 12 short stories for his literature class. The professor will choose one reading at random for the final exam. Find the probability that the professor will choose a novel for the final exam. Express your answer as a fraction and as a decimal.

## 5.6 - Ratios and Rate

### Write a Ratio as a Fraction

In the following exercises, write each ratio as a fraction. Simplify the answer if possible.

- 28 to 40
- 56 to 32
- 3.5 to 0.5
- 1.2 to 1.8
- \(1 \dfrac{3}{4}\) to \(1 \dfrac{5}{8}\)
- \(2 \dfrac{1}{3}\) to \(5 \dfrac{1}{4}\)
- 64 ounces to 30 ounces
- 28 inches to 3 feet

### Write a Rate as a Fraction

In the following exercises, write each rate as a fraction. Simplify the answer if possible.

- 180 calories per 8 ounces 643. 90 pounds per 7.5 square inches
- 126 miles in 4 hours 645. $612.50 for 35 hours

### Find Unit Rates

In the following exercises, find the unit rate.

- 180 calories per 8 ounces
- 90 pounds per 7.5 square inches
- 126 miles in 4 hours
- $612.50 for 35 hours

### Find Unit Price

In the following exercises, find the unit price.

- T-shirts: 3 for $8.97
- Highlighters: 6 for $2.52
- An office supply store sells a box of pens for $11. The box contains 12 pens. How much does each pen cost?
- Anna bought a pack of 8 kitchen towels for $13.20. How much did each towel cost? Round to the nearest cent if necessary.

In the following exercises, find each unit price and then determine the better buy.

- Shampoo: 12 ounces for $4.29 or 22 ounces for $7.29?
- Vitamins: 60 tablets for $6.49 or 100 for $11.99?

### Translate Phrases to Expressions with Fractions

In the following exercises, translate the English phrase into an algebraic expression.

- 535 miles per h hours
- a adults to 45 children
- the ratio of 4y and the difference of x and 10
- the ratio of 19 and the sum of 3 and n

## 5.7 - Simplify and Use Square Roots

### Simplify Expressions with Square Roots

In the following exercises, simplify.

- \(\sqrt{64}\)
- \(\sqrt{144}\)
- \(- \sqrt{25}\)
- \(- \sqrt{81}\)
- \(- \sqrt{9}\)
- \(\sqrt{-36}\)
- \(\sqrt{64}\ + \sqrt{225}\)
- \(\sqrt{64+225}\)

### Estimate Square Roots

In the following exercises, estimate each square root between two consecutive whole numbers.

- \(\sqrt{28}\)
- \(\sqrt{155}\)

### Approximate Square Roots

In the following exercises, approximate each square root and round to two decimal places.

- \(\sqrt{15}\)
- \(\sqrt{57}\)

### Simplify Variable Expressions with Square Roots

In the following exercises, simplify. (Assume all variables are greater than or equal to zero.)

- \(\sqrt{q^{2}}\)
- \(\sqrt{64b^{2}}\)
- \(- \sqrt{121a^{2}}\)
- \(\sqrt{225m^{2} n^{2}}\)
- \(- \sqrt{100q^{2}}\)
- \(\sqrt{49y^{2}}\)
- \(\sqrt{4a^{2} b^{2}}\)
- \(\sqrt{121c^{2} d^{2}}\)

### Use Square Roots in Applications

In the following exercises, solve. Round to one decimal place.

**Art**Diego has 225 square inch tiles. He wants to use them to make a square mosaic. How long can each side of the mosaic be?**Landscaping**Janet wants to plant a square flower garden in her yard. She has enough topsoil to cover an area of 30 square feet. How long can a side of the flower garden be?**Gravity**A hiker dropped a granola bar from a lookout spot 576 feet above a valley. How long did it take the granola bar to reach the valley floor?**Accident investigation**The skid marks of a car involved in an accident were 216 feet. How fast had the car been going before applying the brakes?

## PRACTICE TEST

- Write six and thirty-four thousandths as a decimal.
- Write 1.73 as a fraction.
- Write 5 8 as a decimal.
- Round 16.749 to the nearest (a) tenth (b) hundredth (c) whole number
- Write the numbers \(\dfrac{4}{5}\), −0.1, 0.804, \(\dfrac{2}{9}\), −7.4, 0.21 in order from smallest to largest.

In the following exercises, simplify each expression.

- 15.4 + 3.02
- 20 − 5.71
- (0.64)(0.3)
- (−4.2)(100)
- 0.96 ÷ (−12)
- −5 ÷ 0.025
- −0.6 ÷ (−0.3)
- (0.7) 2
- 24 ÷ (0.1 + 0.02)
- 4(10.3 − 5.8)
- 1.6 + \(\dfrac{3}{8}\)
- \(\dfrac{2}{3}\)(14.65 − 4.6)

In the following exercises, solve.

- m + 3.7 = 2.5
- \(\dfrac{h}{0.5}\) = 4.38
- −6.5y = −57.2
- 1.94 = a − 2.6
- Three friends went out to dinner and agreed to split the bill evenly. The bill was $79.35. How much should each person pay?
- A circle has radius 12. Find the (a) circumference and (b) area. [Use 3.14 for \(\pi\).]
- The ages, in months, of 10 children in a preschool class are: 55, 55, 50, 51, 52, 50, 53, 51, 55, 49. Find the (a) mean (b) median (c) mode
- Of the 16 nurses in Doreen’s department, 12 are women and 4 are men. One of the nurses will be assigned at random to work an extra shift next week. (a) Find the probability a woman nurse will be assigned the extra shift. (b) Convert the fraction to a decimal.
- Find each unit price and then the better buy. Laundry detergent: 64 ounces for $10.99 or 48 ounces for $8.49

In the following exercises, simplify.

- \(\sqrt{36 + 64}\)
- \(\sqrt{144n^{2}}\)
- Estimate \(\sqrt{54}\) to between two whole numbers.
- Yanet wants a square patio in her backyard. She has 225 square feet of tile. How long can a side of the patio be?

## Contributors and Attributions

Lynn Marecek (Santa Ana College) and MaryAnne Anthony-Smith (Formerly of Santa Ana College). This content is licensed under Creative Commons Attribution License v4.0 "Download for free at http://cnx.org/contents/fd53eae1-fa2...49835c3c@5.191."