Section 1
Decimal Notation and Rounding
Define the key terms.a. Decimal fractionb. Decimal notation
State the first five place positions to the right of the decimal point in order from left to right.
For Exercises $3-10$, expand the powers of 10 or $\frac{1}{10}$.$$10^{2}$$
Expand the powers of 10 or $\frac{1}{10}$.$$10^{3}$$
Expand the powers of 10 or $\frac{1}{10}$.$$10^{4}$$
Expand the powers of 10 or $\frac{1}{10}$.$$10^{5}$$
Expand the powers of 10 or $\frac{1}{10}$.$$\left(\frac{1}{10}\right)^{2}$$
Expand the powers of 10 or $\frac{1}{10}$.$$\left(\frac{1}{10}\right)^{3}$$
Expand the powers of 10 or $\frac{1}{10}$.$$\left(\frac{1}{10}\right)^{4}$$
Expand the powers of 10 or $\frac{1}{10}$.$$\left(\frac{1}{10}\right)^{5}$$
For Exercises 11–22, identify the place value of each underlined digit. (See Example 1.)$$3. {\underline{9}}83$$
Identify the place value of each underlined digit. (See Example 1.)$$34.8{\underline{2}}$$
Identify the place value of each underlined digit. (See Example 1.)$$440.3{\underline{9}}$$
Identify the place value of each underlined digit. (See Example 1.)$$2{\underline{4}}8.94$$
Identify the place value of each underlined digit. (See Example 1.)$$4{\underline{8}}9.02$$
Identify the place value of each underlined digit. (See Example 1.)$$4.092{\underline{8}}4$$
Identify the place value of each underlined digit. (See Example 1.)$$-9.283{\underline{4}}5$$
Identify the place value of each underlined digit. (See Example 1.)$$-0.32{\underline{1}}$$
Identify the place value of each underlined digit. (See Example 1.)$$0.48{\underline{9}}$$
Identify the place value of each underlined digit. (See Example 1.)$$5{\underline{8}}.211$$
Identify the place value of each underlined digit. (See Example 1.)$$-9 \underline{3} .834$$
Identify the place value of each underlined digit. (See Example 1.)$$-5.00000\underline{1}$$
For Exercises 23–30, write the word name for each decimal fraction.$$\frac{9}{10}$$
Write the word name for each decimal fraction.$$\frac{7}{10}$$
Write the word name for each decimal fraction.$$\frac{23}{100}$$
Write the word name for each decimal fraction.$$\frac{19}{100}$$
Write the word name for each decimal fraction.$$-\frac{33}{1000}$$
Write the word name for each decimal fraction.$$-\frac{51}{1000}$$
Write the word name for each decimal fraction.$$\frac{407}{10,000}$$
Write the word name for each decimal fraction.$$\frac{20}{10,000}$$
For Exercises 31–38, write the word name for the decimal. (See Example 2.)$$3.24$$
Write the word name for the decimal. (See Example 2.)$$4.26$$
Write the word name for the decimal. (See Example 2.)$$-5.9$$
Write the word name for the decimal. (See Example 2.)$$-3.4$$
Write the word name for the decimal. (See Example 2.)$$52.3$$
Write the word name for the decimal. (See Example 2.)$$21.5$$
Write the word name for the decimal. (See Example 2.)$$6.219$$
Write the word name for the decimal. (See Example 2.)$$7.338$$
For Exercises 39–44, write the word name as a numeral. (See Example 3.)Negative eight thousand, four hundred seventy-two and fourteen thousandths
Write the word name as a numeral. (See Example 3.)Negative sixty thousand, twenty-five and four hundred one ten-thousandths
Write the word name as a numeral. (See Example 3.)Seven hundred and seven hundredths
Write the word name as a numeral. (See Example 3.)Nine thousand and nine thousandths
Write the word name as a numeral. (See Example 3.)Negative two million, four hundred sixty-nine thousand and five hundred six thousandths
Write the word name as a numeral. (See Example 3.)Negative eighty-two million, six hundred fourteen and ninety-seven ten-thousandths
For Exercises 45–56, write the decimal as a proper fraction or as a mixed number and simplify. (See Example 4.)$$3.7$$
Write the decimal as a proper fraction or as a mixed number and simplify. (See Example 4.)$$1.9$$
Write the decimal as a proper fraction or as a mixed number and simplify. (See Example 4.)$$2.8$$
Write the decimal as a proper fraction or as a mixed number and simplify. (See Example 4.)$$4.2$$
Write the decimal as a proper fraction or as a mixed number and simplify. (See Example 4.)$$0.25$$
Write the decimal as a proper fraction or as a mixed number and simplify. (See Example 4.)$$0.75$$
Write the decimal as a proper fraction or as a mixed number and simplify. (See Example 4.)$$-0.55$$
Write the decimal as a proper fraction or as a mixed number and simplify. (See Example 4.)$$-0.45$$
Write the decimal as a proper fraction or as a mixed number and simplify. (See Example 4.)$$20.812$$
Write the decimal as a proper fraction or as a mixed number and simplify. (See Example 4.)$$32.905$$
Write the decimal as a proper fraction or as a mixed number and simplify. (See Example 4.)$$-15.0005$$
Write the decimal as a proper fraction or as a mixed number and simplify. (See Example 4.)$$-4.0015$$
For Exercises 57–64, write the decimal as an improper fraction and simplify. (See Example 5.)$$8.4$$
Write the decimal as an improper fraction and simplify. (See Example 5.)$$2.5$$
Write the decimal as an improper fraction and simplify. (See Example 5.)$$3.14$$
Write the decimal as an improper fraction and simplify. (See Example 5.)$$5.65$$
Write the decimal as an improper fraction and simplify. (See Example 5.)$$-23.5$$
Write the decimal as an improper fraction and simplify. (See Example 5.)$$-14.6$$
Write the decimal as an improper fraction and simplify. (See Example 5.)$$11.91$$
Write the decimal as an improper fraction and simplify. (See Example 5.)$$21.33$$
For Exercises 65–72, fill in the blank with $<$ or $>$ . (See Examples 6–7.)$$6.312 \square 6.321$$
Fill in the blank with $<$ or $>$ . (See Examples 6–7.)$$8.503 \square 8.530$$
Fill in the blank with $<$ or $>$ . (See Examples 6–7.)$$11.21 \square 11.2099$$
Fill in the blank with $<$ or $>$ . (See Examples 6–7.)$$10.51 \square 10.5098$$
Fill in the blank with $<$ or $>$ . (See Examples 6–7.)$$-0.762 \square -0.76$$
Fill in the blank with $<$ or $>$ . (See Examples 6–7.)$$-0.1291 \square -0.129$$
Fill in the blank with $<$ or $>$ . (See Examples 6–7.)$$-51.72 \square -51.721$$
Fill in the blank with $<$ or $>$ . (See Examples 6–7.)$$-49.06 \square -49.062$$
Which number is between 3.12 and 3.13? Circle all that apply.a. 3.127b. 3.129c. 3.134d. 3.139
Which number is between 42.73 and 42.86? Circle all that apply.a. 42.81b. 42.64c. 42.79d. 42.85
The batting averages for five legends are given in the table. Rank the players' batting averages from lowest to highest. (Source: Baseball Almanac)$$\begin{array}{|l|l|}\hline \text { Player } & \text { Average } \\\hline \text { Joe Jackson } & 0.3558 \\\hline \text { Ty Cobb } & 0.3664 \\\hline \text { Lefty O'Doul } & 0.3493 \\\hline \text { Ted Williams } & 0.3444 \\\hline \text { Rogers Hornsby } & 0.3585 \\ \hline\end{array}$$
The average speed, in miles per hour (mph), of the Daytona 500 for selected years is given in the table. Rank the speeds from slowest to fastest. (Source: NASCAR)$$\begin{array}{|l|l|l|} \hline\text { Year } & \text { Driver } & \text { Speed (mph) } \\\hline 1989 & \text { Darrell Waltrip } & 148.466 \\\hline 1991 & \text { Ernie Irvan } & 148.148 \\\hline 1997 & \text { Jeff Gordon } & 148.295 \\\hline 2007 & \text { Kevin Harvick } & 149.333 \\ \hline\end{array}$$
The numbers given all have equivalent value. However, suppose they represent measured values from a scale. Explain the difference in the interpretation of these numbers.$$0.25, \quad 0.250, \quad 0.2500, \quad 0.25000$$
Which number properly represents 3.499999 rounded to the thousandths place?a. 3.500b. 3.5c. 3.500000d. 3.499
Which value is rounded to the nearest tenth, 7.1 or 7.10?
Which value is rounded to the nearest hundredth, 34.50 or 34.5?
For Exercises 81–92, round the decimals to the indicated place values. (See Examples 8–9.)$49.943 ;$ tenths
Round the decimals to the indicated place values. (See Examples 8–9.)$12.7483 ;$ tenths
Round the decimals to the indicated place values. (See Examples 8–9.)$33.416 ;$ hundredths
Round the decimals to the indicated place values. (See Examples 8–9.)$4.359 ;$ hundredths
Round the decimals to the indicated place values. (See Examples 8–9.)$-9.0955 ;$ thousandths
Round the decimals to the indicated place values. (See Examples 8–9.)$-2.9592 ;$ thousandths
Round the decimals to the indicated place values. (See Examples 8–9.)$21.0239 ;$ tenths
Round the decimals to the indicated place values. (See Examples 8–9.)$16.804 ;$ hundredths
Round the decimals to the indicated place values. (See Examples 8–9.)$6.9995 ;$ thousandths
Round the decimals to the indicated place values. (See Examples 8–9.)$21.9997 ;$ thousandths
Round the decimals to the indicated place values. (See Examples 8–9.)$0.0079499 ;$ ten-thousandths
Round the decimals to the indicated place values. (See Examples 8–9.)$0.00084985 ;$ ten-thousandths
A snail moves at a rate of about 0.00362005 miles per hour. Round the decimal value to the ten-thousandthsplace.
For Exercises 94–97, round the number to the indicated place value.$$\begin{array}{|l|l|l|l|l|l|} \hline &\text { Number } & \text { Hundreds } & \text { Tens } & \text { Tenths } & \text { Hundredths } & \text { Thousandths } \\\hline & 349.2395 & & & & & \\\hline& {} & & & & & \\\hline & {} & & & & & \\\hline & {} & & & & & \\\hline\end{array}$$
Round the number to the indicated place value.$$\begin{array}{|l|l|l|l|l|l|} \hline &\text { Number } & \text { Hundreds } & \text { Tens } & \text { Tenths } & \text { Hundredths } & \text { Thousandths } \\\hline& 971.0948 & & & & & \\\hline & {} & & & & & \\\hline & {} & & & & & \\\hline\end{array}$$
Round the number to the indicated place value.$$\begin{array}{|l|l|l|l|l|l|} \hline &\text { Number } & \text { Hundreds } & \text { Tens } & \text { Tenths } & \text { Hundredths } & \text { Thousandths } \\\hline & 79.0046 & & & & & \\\hline & {} & & & & & \\\hline\end{array}$$
Round the number to the indicated place value.$$\begin{array}{|l|l|l|l|l|l|} \hline &\text { Number } & \text { Hundreds } & \text { Tens } & \text { Tenths } & \text { Hundredths } & \text { Thousandths } \\\hline & 21.9754 & & & & & \\\hline & {} & & & & & \\\hline\end{array}$$
What is the least number with three places to the right of the decimal that can be created with the digits 2, 9, and 7? Assume that the digits cannot be repeated.
What is the greatest number with three places to the right of the decimal that can be created from the digits 2, 9, and 7? Assume that the digits cannot be repeated.