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Prealgebra
Decimals

1
Decimal Notation, Place Value, and Rounding

Problem 1

Write \(423.576\) in expanded form.

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Stephanie cc
Stephanie
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 2

Write each in words:

  1. \(0.4\)

  2. \(0.04\)

  3. \(0.004\)

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Stephanie cc
Stephanie
Preston cc
Preston
Cynthia cc spanish language icon
Cynthia
Problem 3

Write each in words:

  1. \(5.4\)

  2. \(5.04\)

  3. \(5.004\)

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Stephanie cc
Stephanie
Preston cc
Preston
Edwin cc spanish language icon
Edwin
Problem 4

Write \(3.64\) in words.

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Stephanie cc
Stephanie
Aaron cc
Aaron
Cynthia cc spanish language icon
Cynthia
Problem 5

Write \(25.4936\) in words.

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Stephanie cc
Stephanie
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 6

Write each number as a fraction or a mixed number. Do not reduce to lowest terms.

  1. \(0.004\)

  2. \(3.64\)

  3. \(25.4936\)

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Stephanie cc
Stephanie
Aaron cc
Aaron
Julieta cc spanish language icon
Julieta
Problem 7

Round \(9,235.492\) to the nearest hundred.

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Stephanie cc
Stephanie
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 8

Round \(0.00346\) to the nearest ten-thousandth.

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Stephanie cc
Stephanie
Aaron cc
Aaron
Cynthia cc spanish language icon
Cynthia
Problem 9

Determine which is larger: \(0.7\) or \(0.83\)

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Julieta cc
Julieta
Julieta cc spanish language icon
Julieta
Problem 10

Order \(10.02\), \(10.002\), \(10\), and \(9.8\) from least to greatest.

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Julieta cc
Julieta
Julieta cc spanish language icon
Julieta

2
Addition and Subtraction with Decimals

Problem 1

Add: \(8+0.002+3.1+0.04\)

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Preston cc
Preston
Molly M. cc
Molly M.
Edwin cc spanish language icon
Edwin
Problem 2

Subtract: \(39.812-14.236\)

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Preston cc
Preston
Stephanie cc
Stephanie
Edwin cc
Edwin
Edwin cc spanish language icon
Edwin
Problem 3

Subtract: \(5.9-3.0814\)

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Molly M. cc
Molly M.
Edwin cc
Edwin
Julieta cc spanish language icon
Julieta
Problem 4

Subtract \(3.09\) from the sum of \(9\) and \(5.472\).

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Molly M. cc
Molly M.
Edwin cc
Edwin
Edwin cc spanish language icon
Edwin
Problem 5

Add: \(-4.75+(-2.25)\)

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Julieta cc
Julieta
Matt cc
Matt
David spanish language icon
David
Problem 6

Add: \(3.42+(-6.89)\)

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Matt cc
Matt
David spanish language icon
David

3
Multiplication with Decimals

Problem 1

Change to a fraction and multiply: \(0.5\times 0.3\)

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Lauren cc
Lauren
Preston cc
Preston
Edwin cc spanish language icon
Edwin
Problem 2

Change to a fraction and multiply: \(0.05\times 0.003\)

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Lauren cc
Lauren
Gordon cc
Gordon
Edwin cc spanish language icon
Edwin
Problem 3

Multiply: \(2.1 \times 0.07\)

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Lauren cc
Lauren
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 4

How many digits will be to the right of the decimal point in: \(2.897\times 24.82\)

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Betsy cc
Betsy
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 5

Multiply: \(3.05 \times 4.36\)

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Molly M. cc
Molly M.
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 6

Simplify each expression:

  1. \((-5)(3.4)\)

  2. \((-0.4)(-0.8)\)

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Dr. Cavanah cc
Dr. Cavanah
Julieta cc
Julieta
Julieta cc spanish language icon
Julieta
Problem 7

Estimate each of the following products:

  1. \(29.4\times 8.2\)

  2. \(68.5\times 175\)

  3. \((6.32)^2\)

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Lauren cc
Lauren
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 8

Perform the indicated operations: \(0.05(4.2+0.03)\)

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Lauren cc
Lauren
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 9

Simplify: \(4.8+12(3.2)^2\)

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Molly M. cc
Molly M.
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 10

Sally earns \(\$6.32\) for each of the first \(36\) hours she works in one week and \(\$9.48\) in overtime pay for each additional hour she works in the same week. How much money will she make if she works \(42\) hours in one week?

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Mrs. Mooney cc
Mrs. Mooney
Stephanie cc
Stephanie
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin

4
Division with Decimals

Problem 1

Divide: \(5,974\div 20\)

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Lauren cc
Lauren
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 2

Divide: \(\, 34.8\div 4\)

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Lauren cc
Lauren
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 3

Divide: \(49.896\div 27\)

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Rachel cc
Rachel
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 4

Divide: \(1,138.9\div 35\)

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Lauren cc
Lauren
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 5

Divide: \(31.35\div 3.8\)

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Molly S. cc
Molly S.
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 6

Divide and round to the nearest tenth: \[2.184\div 28\]

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Julieta cc
Julieta
Julieta cc spanish language icon
Julieta
Problem 7

Divide, round to the nearest hundredth: \(0.3778\div 0.25\)

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Lauren cc
Lauren
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 8

Divide and round to the nearest tenth: \(17\div 0.03\)

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Molly S. cc
Molly S.
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 9

If a man earning \(\$5.26\) an hour receives a paycheck for \(\$170.95\), how many hours did he work?

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Mrs. Mooney cc
Mrs. Mooney
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 10

A telephone company charges \(\$0.43\) fir the first minute and \(\$0.35\) for each additional minute for a call. If a call costs \(\$3.07\), how many minutes was the call?

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Lauren cc
Lauren
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 11

Calculate the student’s grade point average using information in the section.

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Betsy cc
Betsy
Aaron cc
Aaron
Julieta cc spanish language icon
Julieta

5
Fractions and Decimals

Problem 1

Write \(\displaystyle\frac{3}{4}\) as a decimal.

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Stephanie cc
Stephanie
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 2

Write \(\displaystyle\frac{7}{12}\) as a decimal to the correct thousandths.

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Molly S. cc
Molly S.
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 3

Write \(\dfrac{3}{11}\) as a decimal.

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Lauren cc
Lauren
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 4

Write \(0.38\) as a fraction in lowest terms.

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Lauren cc
Lauren
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 5

Convert \(0.075\) to a fraction.

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Julieta cc
Julieta
Molly S. cc
Molly S.
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 6

Write \(15.6\) as a mixed number.

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Lauren cc
Lauren
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 7

Simplify: \(\displaystyle\frac{19}{50}(1.32+0.48)\)

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Lauren cc
Lauren
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 8

Simplify: \(\displaystyle\frac{1}{2}+(0.75)\cdot\left(\displaystyle\frac{2}{5}\right)\)

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Molly S. cc
Molly S.
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 9

Simplify: \(\left(\displaystyle\frac{1}{2}\right)^3\cdot(2.4)+\left(\displaystyle\frac{1}{4}\right)^2\cdot(3.2)\)

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Molly S. cc
Molly S.
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 10

If a shirt sells for \(\$27.99\) is on sale for \(\dfrac{1}{3}\) off, what is the sale price of the shirt?

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Stephanie cc
Stephanie
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 11

Mini Lecture

  1. Convert \(\dfrac{7}{8}\) to a decimal.

  2. Convert \(\dfrac{3}{11}\) to a decimal.

  3. Convert \(0.375\) to a decimal.

Simplify.

  1. \(\dfrac{1}{2}(2.3+2.5)\)

  2. \(\dfrac{2}{3}(0.3)+\dfrac{3}{5}(0.3)\)

  3. \((0.25)^2+\left(\dfrac{1}{4}\right)^2(3)\)

  4. Find the volume of a sphere with a radius of \(2\) miles.

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Mr. McKeague cc
Mr. McKeague

6
Equations With Decimals

Problem 1

Solve the equation: \(x-3.5=8.7\)

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Rachel cc
Rachel
Logan cc
Logan
Octabio cc spanish language icon
Octabio
Problem 2

Solve: \(4y=-3.32\)

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Rachel cc
Rachel
Octabio cc
Octabio
Octabio cc spanish language icon
Octabio
Problem 3

Solve: \(\dfrac{1}{2}x-2.59=3.81\)

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Rachel cc
Rachel
Logan cc
Logan
Octabio cc spanish language icon
Octabio
Problem 4

Solve: \(7a+0.61=-5a-0.89\)

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Rachel cc
Rachel
Octabio cc
Octabio
Octabio cc spanish language icon
Octabio
Problem 5

Solve: \(1.18x+0.24=0.84x-0.78\)

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Katherine cc
Katherine
Logan cc
Logan
Octabio cc spanish language icon
Octabio
Problem 6

A car rental company charges \(\$11\) per day and \(16\) cents per mile for their cars. If a car was rented for \(1\) day and the charge was \(\$25.40\), how many miles was it driven?

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Elisabeth cc
Elisabeth
Logan cc
Logan
Octabio cc spanish language icon
Octabio
Problem 7

Diane has a \(\$1.60\) in dimes and nickels. If she has \(7\) more dimes than nickels, how many of each coin does she have?

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Julieta cc
Julieta
Logan cc
Logan
Octabio cc spanish language icon
Octabio
Problem 8

A cellphone company charges \(\$49.99\) per month for unlimited texting and \(450\) voice minutes. If a customer is charged \(\$0.45\) each overtime minute and receives a bill for \(\$104.89\), by how many minutes did he exceed his monthly allowance?

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Logan cc
Logan
Katherine cc
Katherine
Octabio cc spanish language icon
Octabio
Problem 9

Mini Lecture
Solve.

  1. \(x-0.45=-0.32\)

  2. \(0.5n=-0.4\)

  3. \(4x-4.7=3.5\)

  4. \(0.1x+0.5(x+8=7)\)

  5. A car rental company charges \(\$10\) a day and \(16\) cents per mile for their cars. If a car was rented for \(1\) day for a total charge of \(\$23.93\), how many miles was it driven?

  6. Mary has \(\$2.20\) in dimes and nickels. If she has \(10\) more dimes than nickels, how many of each coin does she have?

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Mr. McKeague cc
Mr. McKeague

7
Square Roots and The Pythagorean Theorem

Problem 1

Simplify: \(7\sqrt{64}\)

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Stephanie cc
Stephanie
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 2

Simplify: \(\, \sqrt{9} +\sqrt{16}\)

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Mrs. Mooney cc
Mrs. Mooney
Stephanie cc
Stephanie
Logan cc
Logan
Edwin cc spanish language icon
Edwin
Problem 3

Simplify: \(\, \sqrt{\dfrac{25}{81}}\)

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Richard cc
Richard
Stephanie cc
Stephanie
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 4

Approximate \(5\sqrt{12}\) to the nearest ten-thousandth.

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Mrs. Mooney cc
Mrs. Mooney
Stephanie cc
Stephanie
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 5

Approximate \(\sqrt{301}+\sqrt{137}\) to the nearest hundedth.

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Julieta cc
Julieta
Logan cc
Logan
Edwin cc spanish language icon
Edwin
Problem 6

Approximate \(\sqrt{\dfrac{7}{11}}\) to the nearest thousandth.

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Julieta cc
Julieta
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 7

Find the length of the hypotenuse in each right triangle.

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Lauren cc
Lauren
Logan cc
Logan
Cynthia cc spanish language icon
Cynthia
Problem 8

Find the length of the missing side in each right triangle. Use a calculator to round to the nearest hundredth.

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Mr. McKeague cc
Mr. McKeague
Julieta cc
Julieta
Julieta cc spanish language icon
Julieta
Problem 9

A ladder is leaning against the top of a \(6\)-foot wall. If the bottom of the ladder is \(8\) feet from the wall, how long is the ladder?

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Julieta cc
Julieta
Elisabeth cc
Elisabeth
Aaron cc
Aaron
Cynthia cc spanish language icon
Cynthia
Problem 10

Mini Lecture
Simplify.

  1. \(\sqrt{81}\)

  2. \(16\sqrt{9}\)

  3. \(\sqrt{49}+\sqrt{64}\)

  4. \(\sqrt{16}-\sqrt{9}\)

  5. \(3\sqrt{25}-9\sqrt{49}\)

  6. \(\sqrt{\frac{16}{49}}\)

  7. \(\sqrt{\frac{100}{121}}\)

Approximate to the nearest hundredth with a calculator.

  1. \(5\sqrt{5}\)

  2. \(\sqrt{18}+\sqrt{19}\)

  3. Find the hypotenuse of a right triangle if the lengths of the two other sides are \(5\) feet and \(12\) feet.

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Mr. McKeague cc
Mr. McKeague

8
Simplifying Square Roots

Problem 1

Simplify: \(\sqrt{45}\)

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Stephanie cc
Stephanie
Winston cc
Winston
Julieta cc spanish language icon
Julieta
Problem 2

Simplify: \(\sqrt{18x^2}\)

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Dr. Cavanah cc
Dr. Cavanah
Stephanie cc
Stephanie
Winston cc
Winston
Julieta cc spanish language icon
Julieta
Problem 3

Simplify: \(\sqrt{180}\)

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Dr. Cavanah cc
Dr. Cavanah
Stephanie cc
Stephanie
Winston cc
Winston
Julieta cc spanish language icon
Julieta
Problem 4

Simplify: \(\sqrt{48x^2}\)

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Mr. McKeague cc
Mr. McKeague
Julieta cc
Julieta
Julieta cc spanish language icon
Julieta

9
Adding and Subtracting Square Roots

Problem 1

Combine using the distributive property: \(5\sqrt{6}-2\sqrt{6}\)

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Stephanie cc
Stephanie
Winston cc
Winston
Julieta cc spanish language icon
Julieta
Problem 2

Combine using the distributive property: \(6\sqrt{x}+3\sqrt{x}\)

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Stephanie cc
Stephanie
Winston cc
Winston
Julieta cc spanish language icon
Julieta
Problem 3

Combine using the distributive property: \(4\sqrt{3}+3\sqrt{3}-2\sqrt{3}\)

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Stephanie cc
Stephanie
Winston cc
Winston
Julieta cc spanish language icon
Julieta
Problem 4

Combine, if possible: \[\sqrt{18}+\sqrt{50}-\sqrt{8}\]

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Stephanie cc
Stephanie
Winston cc
Winston
Julieta cc spanish language icon
Julieta
Problem 5

Combine, if possible: \[5\sqrt{54}-3\sqrt{24}\]

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Stephanie cc
Stephanie
Winston cc
Winston
Julieta cc spanish language icon
Julieta
Problem 6

Assume \(x\) is a positive number and combine, if possible: \[5\sqrt{12x^3}-3\sqrt{75x^3}\]

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Dr. Cavanah cc
Dr. Cavanah
Julieta cc
Julieta
Julieta cc
Julieta