6.11: Exercise Supplement

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 \(\PageIndex{62}\)

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