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6.11: Exercise Supplement

Last updated

Jun 8, 2024
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- 6.10: Summary of Key Concepts
- 6.12: Proficiency Exam

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Reading and Writing Decimals

Exercise $\PageIndex{1}$

The decimal digit that appears two places to the right of the decimal point is in the position.

Answer: hundredths

Exercise $\PageIndex{2}$

The decimal digit that appears four places to the right of the decimal point is in the position.

For problems 3-8, read each decimal by writing it in words.

Exercise $\PageIndex{3}$

7.2

Answer: seven and two tenths

Exercise $\PageIndex{4}$

8.105

Exercise $\PageIndex{5}$

16.52

Answer: sixteen and fifty-two hundredths

Exercise $\PageIndex{6}$

5.9271

Exercise $\PageIndex{7}$

0.005

Answer: five thousandths

Exercise $\PageIndex{8}$

4.01701

For problems 9-13, write each decimal using digits.

Exercise $\PageIndex{9}$

Nine and twelve-hundredths.

Answer: 9.12

Exercise $\PageIndex{10}$

Two and one hundred seventy-seven thousandths.

Exercise $\PageIndex{11}$

Fifty-six and thirty-five ten-thousandths.

Answer: 56.0035

Exercise $\PageIndex{12}$

Four tenths.

Exercise $\PageIndex{13}$

Four thousand eighty-one millionths.

Answer: 0.004081

Converting a Decimal to a Fraction

For problem 14-20, convert each decimal to a proper fraction or a mixed number.

Exercise $\PageIndex{14}$

1.07

Exercise $\PageIndex{15}$

58.63

Answer: $85 \dfrac{63}{100}$

Exercise $\PageIndex{16}$

0.05

Exercise $\PageIndex{17}$

$0.14 \dfrac{2}{3}$

Answer: $\dfrac{11}{75}$

Exercise $\PageIndex{18}$

$1.09 \dfrac{1}{8}$

Exercise $\PageIndex{19}$

$4.01 \dfrac{1}{27}$

Answer: $4 \dfrac{7}{675}$

Exercise $\PageIndex{20}$

$9.11 \dfrac{1}{9}$

Rounding Decimals

For problems 21-25, round each decimal to the specified position.

Exercise $\PageIndex{21}$

4.087 to the nearest hundredth.

Answer: 4.09

Exercise $\PageIndex{22}$

4.087 to the nearest tenth.

Exercise $\PageIndex{23}$

16.5218 to the nearest one.

Answer: 17

Exercise $\PageIndex{24}$

817.42 to the nearest ten.

Exercise $\PageIndex{25}$

0.9811602 to the nearest one.

Answer: 1

Addition, Subtraction, Multiplication and Division of Decimals, and Nonterminating Divisions ([link],[link],[link],[link])

For problem 26-45, perform each operation and simplify.

Exercise $\PageIndex{26}$

$7.10 + 2.98$

Exercise $\PageIndex{27}$

$14.007 - 5.061$

Answer: 8.946

Exercise $\PageIndex{28}$

$1.2 \cdot 8.6$

Exercise $\PageIndex{29}$

$41.8 \cdot 0.19$

Answer: 7.942

Exercise $\PageIndex{30}$

$57.51 \div 2.7$

Exercise $\PageIndex{31}$

$0.54003 \div 18.001$

Answer: 0.03

Exercise $\PageIndex{32}$

$32,051.3585 \div 23,006.9999$

Exercise $\PageIndex{33}$

$100 \cdot 1,816.001$

Answer: 181,600.1

Exercise $\PageIndex{34}$

$1,000 \cdot 1,816.001$

Exercise $\PageIndex{35}$

$10.000 \cdot 0.14$

Answer: 1.4

Exercise $\PageIndex{36}$

$0.135888 \div 16.986$

Exercise $\PageIndex{37}$

$150.79 \div 100$

Answer: 1.5079

Exercise $\PageIndex{38}$

$4.119 \div 10,000$

Exercise $\PageIndex{39}$

$42.7 \div 18$

Answer: $2.37\overline{2}$

Exercise $\PageIndex{40}$

$6.9 \div 12$

Exercise $\PageIndex{41}$

$0.014 \div 47.6$ . Round to three decimal places.

Answer: 0.000

Exercise $\PageIndex{42}$

$8.8 \div 19$ . Round to one decimal place.

Exercise $\PageIndex{43}$

$1.1 \div 9$

Answer: $0.1\overline{2}$

Exercise $\PageIndex{44}$

$1.1 \div 9.9$

Exercise $\PageIndex{45}$

$30 \div 11.1$

Answer: $2.\overline{702}$

Converting a Fraction to a Decimal

For problems 46-55, convert each fraction to a decimal.

Exercise $\PageIndex{46}$

$\dfrac{3}{8}$

Exercise $\PageIndex{47}$

$\dfrac{43}{100}$

Answer: 0.43

Exercise $\PageIndex{48}$

$\dfrac{82}{1000}$

Exercise $\PageIndex{49}$

$9\dfrac{4}{7}$

Answer: $9.\overline{571428}$

Exercise $\PageIndex{50}$

$8 \dfrac{5}{16}$

Exercise $\PageIndex{51}$

$1.3 \dfrac{1}{3}$

Answer: $1.\overline{3}$

Exercise $\PageIndex{52}$

$25.6 \dfrac{2}{3}$

Exercise $\PageIndex{53}$

$125.125 \dfrac{1}{8}$

Answer: 125.125125 (not repeating)

Exercise $\PageIndex{54}$

$9.11 \dfrac{1}{9}$

Exercise $\PageIndex{55}$

$0.0\dfrac{5}{6}$

Answer: $0.08\overline{3}$

Combinations of Operations with Decimals and Fractions

For problems 56-62, perform each operation.

Exercise $\PageIndex{56}$

$\dfrac{5}{8} \cdot 0.25$

Exercise $\PageIndex{57}$

$\dfrac{3}{16} \cdot 1.36$

Answer: 0.255

Exercise $\PageIndex{58}$

$\dfrac{3}{5} \cdot (\dfrac{1}{2} + 1.75)$

Exercise $\PageIndex{59}$

$\dfrac{7}{2} \cdot (\dfrac{5}{4} + 0.30)$

Answer: 5.425

Exercise $\PageIndex{60}$

$19.375 \div (4.375 - 1 \dfrac{1}{16})$

Exercise $\PageIndex{61}$

$\dfrac{15}{602} \cdot (2. \overline{6} + 3 \dfrac{1}{4})$

Answer: 0.09343

Exercise $\PageIndex{62}$

$4 \dfrac{13}{18} \div (5 \dfrac{3}{14} + 3 \dfrac{5}{21})$