6.11: Exercise Supplement
- Page ID
- 53019
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)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 \(\PageIndex{62}\)
\(4 \dfrac{13}{18} \div (5 \dfrac{3}{14} + 3 \dfrac{5}{21})\)