5.14: Decimals (Exercises)

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5.1 - Decimals

Name Decimals

In the following exercises, name each decimal.

1. 0.8
2. 0.375
3. 0.007
4. 5.24
5. −12.5632
6. −4.09

Write Decimals

In the following exercises, write as a decimal.

1. three tenths
2. nine hundredths
3. twenty-seven hundredths
4. ten and thirty-five thousandths
5. negative twenty and three tenths
6. 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.

1. 0.43
2. 0.825
3. 9.7
4. 3.64

Locate Decimals on the Number Line

1. (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 >.

1. 0.6___0.8
2. 0.2___0.15
3. 0.803____0.83
4. −0.56____−0.562

Round Decimals

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

1. 12.529
2. 4.8447
3. 5.897

5.2 - Decimal Operations

In the following exercises, add or subtract.

1. 5.75 + 8.46
2. 32.89 − 8.22
3. 24 − 19.31
4. 10.2 + 14.631
5. −6.4 + (−2.9)
6. 1.83 − 4.2

Multiply Decimals

In the following exercises, multiply.

1. (0.3)(0.7)
2. (−6.4)(0.25)
3. (−3.35)(−12.7)
4. (15.4)(1000)

Divide Decimals

In the following exercises, divide.

1. 0.48 ÷ 6
2. 4.32 ÷ 24
3. $6.29 ÷ 12 4. (−0.8) ÷ (−0.2) 5. 1.65 ÷ 0.15 6. 9 ÷ 0.045 Use Decimals in Money Applications In the following exercises, use the strategy for applications to solve. 1. 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.
2. 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? 3. A pack of 16 water bottles cost$6.72. How much did each bottle cost?
4. 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.

1. $$\dfrac{3}{5}$$
2. $$\dfrac{7}{8}$$
3. $$- \dfrac{19}{20}$$
4. $$- \dfrac{21}{4}$$
5. $$\dfrac{1}{3}$$
6. $$\dfrac{6}{11}$$

Order Decimals and Fractions

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

1. $$\dfrac{1}{2}$$ ___0.2
2. $$\dfrac{3}{5}$$ ___0.
3. $$- \dfrac{7}{8}$$ ___−0.84
4. $$- \dfrac{5}{12}$$ ___−0.42
5. 0.625___$$\dfrac{13}{20}$$
6. 0.33___$$\dfrac{5}{16}$$

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

1. $$\dfrac{2}{3}, \dfrac{17}{20}$$, 0.65
2. $$\dfrac{7}{9}$$, 0.75, $$\dfrac{11}{15}$$

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

1. 4(10.3 − 5.8)
2. $$\dfrac{3}{4}$$(15.44 − 7.4)
3. 30 ÷ (0.45 + 0.15)
4. 1.6 + $$\dfrac{3}{8}$$
5. 52(0.5) + (0.4)2
6. $$− \dfrac{2}{5} \cdot \dfrac{9}{10}$$ + 0.14

Find the Circumference and Area of Circles

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

3. radius = 7 33 m
4. 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.

1. x − 0.4 = 2.1
1. x = 1.7
2. x = 2.5
2. y + 3.2 = −1.5
1. y = 1.7
2. y = −4.7
3. $$\dfrac{u}{2.5}$$ = −12.5
1. u = −5
2. u = −31.25
4. 0.45v = −40.5
1. v = −18.225
2. v = −90

Solve Equations with Decimals

In the following exercises, solve.

1. m + 3.8 = 7.5
2. h + 5.91 = 2.4
3. a + 2.26 = −1.1
4. p − 4.3 = −1.65
5. x − 0.24 = −8.6
6. j − 7.42 = −3.7
7. 0.6p = 13.2
8. −8.6x = 34.4
9. −22.32 = −2.4z
10. $$\dfrac{a}{0.3}$$ = −24
11. $$\dfrac{p}{−7}$$ = −4.2
12. $$\dfrac{s}{−2.5}$$ = −10

Translate to an Equation and Solve

In the following exercises, translate and solve.

1. The difference of n and 15.2 is 4.4.
2. The product of −5.9 and x is −3.54.
3. The quotient of y and −1.8 is −9.
4. 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.

1. 2, 4, 1, 0, 1, and 1
2. $270,$310.50, $243.75, and$252.15
3. 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

Find Unit Rates

In the following exercises, find the unit rate.

1. 180 calories per 8 ounces
2. 90 pounds per 7.5 square inches
3. 126 miles in 4 hours
4. $612.50 for 35 hours Find Unit Price In the following exercises, find the unit price. 1. T-shirts: 3 for$8.97
2. Highlighters: 6 for $2.52 3. An office supply store sells a box of pens for$11. The box contains 12 pens. How much does each pen cost?
4. 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. 1. Shampoo: 12 ounces for$4.29 or 22 ounces for $7.29? 2. 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. 1. 535 miles per h hours 2. a adults to 45 children 3. the ratio of 4y and the difference of x and 10 4. 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. 1. $$\sqrt{64}$$ 2. $$\sqrt{144}$$ 3. $$- \sqrt{25}$$ 4. $$- \sqrt{81}$$ 5. $$- \sqrt{9}$$ 6. $$\sqrt{-36}$$ 7. $$\sqrt{64}\ + \sqrt{225}$$ 8. $$\sqrt{64+225}$$ Estimate Square Roots In the following exercises, estimate each square root between two consecutive whole numbers. 1. $$\sqrt{28}$$ 2. $$\sqrt{155}$$ Approximate Square Roots In the following exercises, approximate each square root and round to two decimal places. 1. $$\sqrt{15}$$ 2. $$\sqrt{57}$$ Simplify Variable Expressions with Square Roots In the following exercises, simplify. (Assume all variables are greater than or equal to zero.) 1. $$\sqrt{q^{2}}$$ 2. $$\sqrt{64b^{2}}$$ 3. $$- \sqrt{121a^{2}}$$ 4. $$\sqrt{225m^{2} n^{2}}$$ 5. $$- \sqrt{100q^{2}}$$ 6. $$\sqrt{49y^{2}}$$ 7. $$\sqrt{4a^{2} b^{2}}$$ 8. $$\sqrt{121c^{2} d^{2}}$$ Use Square Roots in Applications In the following exercises, solve. Round to one decimal place. 1. 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? 2. 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? 3. 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? 4. 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 1. Write six and thirty-four thousandths as a decimal. 2. Write 1.73 as a fraction. 3. Write 5 8 as a decimal. 4. Round 16.749 to the nearest (a) tenth (b) hundredth (c) whole number 5. 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. 1. 15.4 + 3.02 2. 20 − 5.71 3. (0.64)(0.3) 4. (−4.2)(100) 5. 0.96 ÷ (−12) 6. −5 ÷ 0.025 7. −0.6 ÷ (−0.3) 8. (0.7) 2 9. 24 ÷ (0.1 + 0.02) 10. 4(10.3 − 5.8) 11. 1.6 + $$\dfrac{3}{8}$$ 12. $$\dfrac{2}{3}$$(14.65 − 4.6) In the following exercises, solve. 1. m + 3.7 = 2.5 2. $$\dfrac{h}{0.5}$$ = 4.38 3. −6.5y = −57.2 4. 1.94 = a − 2.6 5. Three friends went out to dinner and agreed to split the bill evenly. The bill was$79.35. How much should each person pay?
6. A circle has radius 12. Find the (a) circumference and (b) area. [Use 3.14 for $$\pi$$.]
7. 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
8. 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.
9. 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.

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