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Why is there no real number equal to $\sqrt{\mathrm{-64}}?$
What is the difference between ${9}^{2}$ and $\sqrt{9}?$
Answers will vary. 9 ^{2} reads: “nine squared” and means nine times itself. The expression $\sqrt{9}$ reads: “the square root of nine” which gives us the number such that if it were multiplied by itself would give you the number inside of the square root.
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
ⓑ Overall, after looking at the checklist, do you think you are well-prepared for the next Chapter? Why or why not?
Name Decimals
In the following exercises, name each decimal.
$\mathrm{-12.5632}$
Write Decimals
In the following exercises, write as a decimal.
three tenths
twenty-seven hundredths
negative twenty and three tenths
Convert Decimals to Fractions or Mixed Numbers
In the following exercises, convert each decimal to a fraction. Simplify the answer if possible.
Locate Decimals on the Number Line
Locate the following decimals on a number line.
ⓐ $\phantom{\rule{0.2em}{0ex}}0.6$
ⓑ $\phantom{\rule{0.2em}{0ex}}\mathrm{-0.9}$
ⓒ $\phantom{\rule{0.2em}{0ex}}2.2$
ⓓ $\phantom{\rule{0.2em}{0ex}}\mathrm{-1.3}$
Order Decimals
In the following exercises, order each of the following pairs of numbers, using $<$ or $\text{>.}$
$0.2\_\_\_0.15$
$\mathrm{-0.56}\_\_\_\_\mathrm{-0.562}$
Round Decimals
In the following exercises, round each number to the nearest:
ⓐ hundredth
ⓑ tenth
ⓒ whole number.
Add and Subtract Decimals
In the following exercises, add or subtract.
$5.75+8.46$
$24-19.31$
$\mathrm{-6.4}+(\mathrm{-2.9})$
Multiply Decimals
In the following exercises, multiply.
$(0.3)(0.7)$
$(\mathrm{-3.35})(\mathrm{-12.7})$
Divide Decimals
In the following exercises, divide.
$0.48\xf76$
$\text{\$6.29}\xf712$
$1.65\xf70.15$
Use Decimals in Money Applications
In the following exercises, use the strategy for applications to solve.
Miranda got $\text{\$40}$ from her ATM. She spent $\text{\$9.32}$ on lunch and $\text{\$16.99}$ on a book. How much money did she have left? Round to the nearest cent if necessary.
Jessie put $8$ gallons of gas in her car. One gallon of gas costs $\text{\$3.528.}$ How much did Jessie owe for all the gas?
$28.22
A pack of $16$ water bottles cost $\text{\$6.72.}$ How much did each bottle cost?
Alice bought a roll of paper towels that cost $\text{\$2.49.}$ She had a coupon for $\text{\$0.35}$ off, and the store doubled the coupon. How much did Alice pay for the paper towels?
$1.79
Convert Fractions to Decimals
In the following exercises, convert each fraction to a decimal.
$\frac{3}{5}$
$-\frac{19}{20}$
$\frac{1}{3}$
Order Decimals and Fractions
In the following exercises, order each pair of numbers, using $<$ or $\text{>.}$
$\frac{1}{2}\_\_\_0.2$
$-\frac{7}{8}\_\_\_\mathrm{-0.84}$
$0.625\_\_\_\frac{13}{20}$
In the following exercises, write each set of numbers in order from least to greatest.
$\frac{2}{3},\frac{17}{20},0.65$
$\frac{7}{9},0.75,\frac{11}{15}$
$\frac{11}{15},0.75,\frac{7}{9}$
Simplify Expressions Using the Order of Operations
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