Free math worksheets

- Find an equivalent fraction with denominator \(10\). - Recall how tenths are written as decimals.

1. Make an equivalent fraction with denominator \(10\): \(\frac{3 \times 2}{5 \times 2} = \frac{6}{10}\). 2. Write six tenths as a decimal: \(\frac{6}{10} = 0.6\).

\(0.6\)

- Count the decimal places to choose the denominator. - One decimal place means tenths; two decimal places mean hundredths. - Use all the digits as the numerator after removing the decimal point.

1. One decimal place represents tenths, and two decimal places represent hundredths. 2. For a), \(0.4 = \frac{4}{10}\). 3. For b), \(0.12 = \frac{12}{100}\). 4. For c), \(0.05 = \frac{5}{100}\). 5. For d), \(3.7 = \frac{37}{10}\). 6. For e), \(0.08 = \frac{8}{100}\).

a) \(\frac{4}{10}\) b) \(\frac{12}{100}\) c) \(\frac{5}{100}\) d) \(\frac{37}{10}\) e) \(\frac{8}{100}\)

- Count the total number of equal sectors. - Count the shaded sectors. - The first digit after the decimal point represents tenths.

1. The circle has \(10\) equal sectors, and \(1\) sector is shaded. 2. The shaded fraction is \(\frac{1}{10}\). 3. One tenth is written as \(0.1\).

Fraction: \(\frac{1}{10}\) Decimal: \(0.1\)

- Count all the equal sections. - Count the shaded sections. - Write tenths as a decimal.

1. Seven of the \(10\) sections are shaded. 2. The shaded fraction is \(\frac{7}{10}\). 3. Seven tenths is written as \(0.7\).

Fraction: \(\frac{7}{10}\) Decimal: \(0.7\)

- Identify the whole-number part. - Place the \(7\) in the tenths place.

1. The whole-number part is \(4\). 2. Seven tenths is written as \(0.7\). 3. The decimal is \(4.7\).

\(4.7\)

- Compare the place of the digit \(9\) on each card. - The tenths place is immediately to the right of the decimal point.

1. Nine tenths means \(9\) is in the tenths place. 2. The card showing \(0.9\) has \(9\) in the tenths place.

\(0.9\)

- Identify the whole-number part. - Place the \(3\) in the hundredths place and use a zero in the tenths place.

1. The whole-number part is \(12\). 2. Three hundredths is written as \(0.03\). 3. The decimal is \(12.03\).

\(12.03\)

- Identify the place of the digit to the right of the decimal point. - Use “and” to separate the whole-number part from the fractional part.

1. The whole-number part is \(5\). 2. The digit \(2\) is in the tenths place. 3. The decimal is read as “five and two tenths.”

“five and two tenths”

- Write twenty-four hundredths as two decimal digits. - Identify the tenths digit.

1. Twenty-four hundredths is written as \(0.24\). 2. The tenths digit is \(2\). 3. The completed decimal is \(6.24\).

The missing digit is \(2\); the decimal is \(6.24\).

- The digits after the decimal point show cents. - Read \(0.05\) as five hundredths of a dollar.

1. The whole-dollar amount is \(3\). 2. The decimal part \(0.05\) equals \(5\) cents. 3. The amount is read as “three dollars and five cents.”

“three dollars and five cents”

- Write seventy-five hundredths using two decimal places. - Include the unit in your answer.

1. Seventy-five hundredths is \(\frac{75}{100}\). 2. As a decimal, \(\frac{75}{100} = 0.75\). 3. The mass is \(0.75\,\text{lb}\).

\(0.75\,\text{lb}\)

- Identify the place of the digit to the right of the decimal point. - Include the temperature unit in the reading.

1. The whole-number part is \(65\). 2. The digit \(4\) is in the tenths place. 3. The temperature is read as “sixty-five and four tenths degrees Fahrenheit.”

“sixty-five and four tenths degrees Fahrenheit”

- Write the dollar amount before the decimal point. - Write cents using exactly two digits after the decimal point.

1. The whole-dollar amount is \(24\). 2. Ninety cents is \(\$0.90\). 3. The price is \(\$24.90\).

\(\$24.90\)

- Use the number of decimal places to choose a denominator of \(10\) or \(100\). - Simplify by dividing the numerator and denominator by a common factor. - Check whether the numerator and denominator still share a factor.

1. For a), \(0.15 = \frac{15}{100} = \frac{3}{20}\). 2. For b), \(0.08 = \frac{8}{100} = \frac{2}{25}\). 3. For c), \(0.75 = \frac{75}{100} = \frac{3}{4}\). 4. For d), \(2.4 = \frac{24}{10} = \frac{12}{5}\).

a) \(\frac{3}{20}\) b) \(\frac{2}{25}\) c) \(\frac{3}{4}\) d) \(\frac{12}{5}\)

- What number multiplies \(20\) to make \(100\)? - Multiply the numerator by the same number. - You can check by dividing the numerator by the denominator.

1. Multiply the numerator and denominator by \(5\): \(\frac{11}{20} = \frac{55}{100}\). 2. Write the fraction with denominator \(100\) as a decimal: \(\frac{55}{100} = 0.55\). 3. The result can also be checked by division: \(11 \div 20 = 0.55\).

\(0.55\)

- First write the decimal as a fraction with denominator \(100\). - Find a common factor of the numerator and denominator. - Divide both by the same factor until the fraction is in simplest form.

1. Write the decimal as a fraction with denominator \(100\): \(0.48 = \frac{48}{100}\). 2. The greatest common factor of \(48\) and \(100\) is \(4\). 3. Divide the numerator and denominator by \(4\): \(\frac{48 \div 4}{100 \div 4} = \frac{12}{25}\).

\(\frac{12}{25}\)

- Use the place value of the last decimal digit. - A whole number can also be written as a fraction. - Think about how many hundredths equal one whole.

1. For a), \(0.75\) is \(75\) hundredths, so \(\square = 100\). 2. For b), \(0.03\) is \(3\) hundredths, so \(\square = 3\). 3. For c), \(2.1\) is \(21\) tenths, so \(\square = 21\). 4. For d), \(0.06\) is \(6\) hundredths, so \(\square = 100\). 5. For e), \(9 = 9 \times \frac{100}{100} = \frac{900}{100}\), so \(\square = 900\).

a) \(100\) b) \(3\) c) \(21\) d) \(100\) e) \(900\)

- How many cents make one dollar? - Use two digits for the cents. - Add a zero placeholder when the cents amount has one digit.

1. Write dollars to the left of the decimal point and cents in the two places to the right. 2. Use a zero as a placeholder when the number of cents has only one digit. 3. The amounts are \(\$9.40\), \(\$3.08\), \(\$0.06\), and \(\$15.55\).

a) \(\$9.40\) b) \(\$3.08\) c) \(\$0.06\) d) \(\$15.55\)

- The two digits after the decimal point show the cents; use a zero placeholder when needed. - An amount less than one dollar has \(0\) to the left of the decimal point.

1. Write \(4\) dollars \(7\) cents as \(\$4.07\). 2. Write \(\$0.12\) as \(12\) cents. 3. Write \(20\) dollars \(80\) cents as \(\$20.80\). 4. Write \(\$1.01\) as \(1\) dollar \(1\) cent.

a) \(\$4.07\) b) \(12\) cents c) \(\$20.80\) d) \(1\) dollar \(1\) cent

- Rewrite all amounts in the same form. - Pay attention to whether the \(4\) is in the tenths or hundredths place.

1. Express the amounts in matching forms. 2. \(\$2.40\) equals \(2\) dollars \(40\) cents. 3. \(\$0.24\) equals \(24\) cents. 4. \(\$2.04\) equals \(2\) dollars \(4\) cents.

\(\$2.40\) and \(2\) dollars \(40\) cents \(\$0.24\) and \(24\) cents \(\$2.04\) and \(2\) dollars \(4\) cents

- One dollar equals \(100\) cents. - Think about what each digit after the decimal point represents in money. - Pay special attention to placeholder zeros in amounts such as \(\$12.05\).

1. \(\$5.75=575\) cents. 2. \(\$12.05=1205\) cents. 3. \(\$110.10=11{,}010\) cents. 4. \(\$2.04=204\) cents.

a) \(575\) cents b) \(1205\) cents c) \(11{,}010\) cents d) \(204\) cents

- Think of one dollar as \(100\) equal cents. - The hundredths place in a dollar amount records cents. - For part b), make two different coin totals that both equal \(25\) cents.

1. One cent is one hundredth of a dollar, so it is \(\$0.01\). 2. Five cents is five hundredths of a dollar, so it is \(\$0.05\). 3. Forty cents is forty hundredths of a dollar, so it is \(\$0.40\). 4. \(\$0.25\) is \(25\) cents. One possible coin combination is one quarter. 5. Another possible combination is two dimes and one nickel.

a) \(\$0.01\), \(\$0.05\), \(\$0.40\) b) For example, one quarter; or two dimes and one nickel.

- One dollar equals \(100\) cents. - Dollar amounts use two decimal places for cents. - A placeholder zero is needed when the cents amount has only one digit.

1. \(\$15.24\) is \(\$15\) and \(24\) cents, or \(1524\) cents. 2. \(\$6\) and \(2\) cents is \(\$6.02\), or \(602\) cents. 3. \(90\) cents is \(\$0.90\), or \(\$0\) and \(90\) cents. 4. \(\$0.05\) is \(\$0\) and \(5\) cents, or \(5\) cents.

<table> <thead><tr><th>Decimal dollars</th><th>Dollars and cents</th><th>Cents only</th></tr></thead> <tbody> <tr><td>\(\$15.24\)</td><td>\(\$15\) and \(24\) cents</td><td>\(1524\) cents</td></tr> <tr><td>\(\$6.02\)</td><td>\(\$6\) and \(2\) cents</td><td>\(602\) cents</td></tr> <tr><td>\(\$0.90\)</td><td>\(\$0\) and \(90\) cents</td><td>\(90\) cents</td></tr> <tr><td>\(\$0.05\)</td><td>\(\$0\) and \(5\) cents</td><td>\(5\) cents</td></tr> </tbody> </table>

- Cents occupy two decimal places in a dollar amount. - Think about how many cents make one whole dollar. - Use a placeholder zero when a cents amount has only one digit.

1. \(\$24.08\) is \(\$24\) and \(8\) cents, or \(2408\) cents. 2. \(\$3\) and \(70\) cents is \(\$3.70\), or \(370\) cents. 3. \(1005\) cents is \(\$10\) and \(5\) cents, or \(\$10.05\). 4. \(\$0.40\) is \(\$0\) and \(40\) cents, or \(40\) cents.

a) \(\$24.08=\$24\) and \(8\) cents \(=2408\) cents b) \(\$3.70=\$3\) and \(70\) cents \(=370\) cents c) \(\$10.05=\$10\) and \(5\) cents \(=1005\) cents d) \(\$0.40=\$0\) and \(40\) cents \(=40\) cents

- Count the total number of equal squares and the shaded squares. - Simplify the shaded fraction before converting it. - To write the fraction as a decimal, look for an equivalent fraction with denominator \(100\).

1. The grid has \(5\) rows and \(4\) columns, so it contains \(5\times4=20\) equal squares. 2. There are \(15\) shaded squares, so the fraction is \(\frac{15}{20}\). 3. Simplify: \(\frac{15}{20}=\frac{3}{4}\). 4. Rename fourths as hundredths: \(\frac{3}{4}=\frac{75}{100}=0.75\).

a) \(\frac{3}{4}\) b) \(0.75\)

- How many small squares are in the whole grid? - Count the shaded squares. - A fraction with denominator \(100\) can be written directly as a decimal.

1. One full row of \(10\) squares and \(2\) more squares are shaded, for a total of \(10 + 2 = 12\) shaded squares. 2. Since \(12\) of \(100\) squares are shaded, the fraction is \(\frac{12}{100}\). 3. Twelve hundredths is written as \(0.12\).

Fraction: \(\frac{12}{100}\) Decimal: \(0.12\)

- Count the shaded squares out of \(100\). - Write the portion as a decimal in hundredths. - Simplify the fraction by dividing the numerator and denominator by a common factor.

1. Eight full rows of \(10\) squares are shaded, so \(8 \times 10 = 80\) squares are shaded. 2. The shaded portion is \(\frac{80}{100} = 0.80 = 0.8\). 3. Divide the numerator and denominator by \(20\): \(\frac{80}{100} = \frac{4}{5}\).

Decimal: \(0.8\) Fraction in simplest form: \(\frac{4}{5}\)

- Count the rows and columns in the shaded block. - Compare the shaded count with the total of \(100\) squares. - Use the hundredths place when writing the decimal.

1. The shaded block is \(3 \times 3\), so it contains \(3 \times 3 = 9\) squares. 2. Since the grid has \(100\) squares, the shaded fraction is \(\frac{9}{100}\). 3. Nine hundredths is written as \(0.09\).

Fraction: \(\frac{9}{100}\) Decimal: \(0.09\)

- First write the value using tenths. - Add a trailing zero so the display shows two decimal places.

1. Two thousand and six tenths is \(2000.6\). 2. Adding a trailing zero does not change the value. 3. With exactly two digits after the decimal point, the entry is \(2000.60\).

\(2000.60\)

- Identify the place named by “hundredths.” - Decide what must appear in the tenths place when there are no tenths. - Check the value of the decimal after placing the digits.

1. Nine hundredths means the \(9\) belongs in the hundredths place. 2. A zero is needed in the tenths place. 3. The correct decimal is \(508.09\).

Amara's entry is incorrect. The correct decimal is \(508.09\).

- Locate the digit \(4\) on a place-value chart. - Name the place that is two positions to the right of the decimal point.

1. The \(4\) is two places to the right of the decimal point. 2. Therefore, the \(4\) is in the hundredths place, not the tenths place. 3. The correct reading is “four hundredths.”

He used “tenths” incorrectly. The correct reading is “four hundredths.”

- Identify the place named by “hundredths.” - Check whether the tenths place needs a zero placeholder.

1. The whole-number part is \(5\). 2. The digit \(2\) belongs in the hundredths place, so a zero is needed in the tenths place. 3. Choice B, \(5.02\), is correct.

B: \(5.02\)

- Write forty-eight hundredths as a fraction with denominator \(100\). - Use two digits after the decimal point.

1. The whole-number part is \(0\). 2. Forty-eight hundredths places \(4\) in the tenths place and \(8\) in the hundredths place. 3. The decimal is \(0.48\).

\(0.48\)

- Write thirty-five hundredths using two decimal places. - Combine the fractional part with the whole-number part.

1. Thirty-five hundredths places \(3\) in the tenths place and \(5\) in the hundredths place. 2. The whole-number part is \(2\). 3. The decimal is \(2.35\).

The digits are \(3\) and \(5\); the decimal is \(2.35\).

- Look at the first and second digits to the right of the decimal point. - Match those positions to tenths and hundredths.

1. The tenths digit is \(0\). 2. The hundredths digit is \(5\). 3. The completed statement is: The decimal has \(0\) tenths and \(5\) hundredths.

\(0\) tenths and \(5\) hundredths

- Identify the place named by “tenths.” - Check the position of the digit \(3\).

1. Three tenths means the digit \(3\) belongs in the tenths place. 2. In \(12.03\), the \(3\) is in the hundredths place. 3. The correct decimal is \(12.3\).

Lina placed the \(3\) in the hundredths place. The correct decimal is \(12.3\).

- Identify the place named by “hundredths.” - Use a zero as a placeholder in the tenths place.

1. Eight hundredths places \(8\) in the hundredths place. 2. A zero is needed in the tenths place. 3. The correct decimal is \(0.08\).

Zoe placed the \(8\) in the tenths place. The correct decimal is \(0.08\).

- Identify which digits form the whole-number part. - Keep the digits in their original order.

1. The whole-number part must be \(40\). 2. The fractional part must be \(75\) hundredths. 3. Place the decimal point after the second digit to get \(40.75\).

\(40.75\)

- Keep the digits \(3\) and \(8\) in the given order. - Use the zero as a placeholder in the tenths place.

1. The whole-number part is \(3\). 2. Eight hundredths requires \(0\) in the tenths place and \(8\) in the hundredths place. 3. The decimal is \(3.08\).

\(3.08\)

- Identify which digits form the whole-number part. - Keep the digits in their original order.

1. The whole-number part must be \(120\). 2. The digit \(5\) must be in the tenths place. 3. Place the decimal point before the \(5\) to get \(120.5\).

\(120.5\)

- Write the value first using tenths. - Add a trailing zero without changing the value.

1. Six and five tenths is \(6.5\). 2. Add a trailing zero to show exactly two decimal places: \(6.50\). 3. The displayed value can be read as “six and fifty hundredths.”

\(6.50\); “six and fifty hundredths”

- Separate the digits by their place values. - The first digit after the decimal point counts tenths. - The second digit after the decimal point counts hundredths.

1. The whole-number part is \(2\). 2. The digit \(4\) represents \(\frac{4}{10}\), and the digit \(8\) represents \(\frac{8}{100}\). 3. Therefore, \(2.48=2+\frac{4}{10}+\frac{8}{100}\).

\(2+\frac{4}{10}+\frac{8}{100}\)

- Convert each amount to one common form before grouping. - Compare the resulting values carefully. - Pay attention to the difference between \(2\) cents and \(20\) cents.

1. \(\$3.20=\$3\) and \(20\) cents \(=320\) cents. 2. \(\$3.02=\$3\) and \(2\) cents \(=302\) cents. 3. \(\$0.32=\$0\) and \(32\) cents \(=32\) cents.

Group 1: \(\$3.20\), \(\$3\) and \(20\) cents, \(320\) cents Group 2: \(\$3.02\), \(\$3\) and \(2\) cents, \(302\) cents Group 3: \(\$0.32\), \(\$0\) and \(32\) cents, \(32\) cents

- Count the equal intervals from \(0\) to \(1\) to find the tick spacing. - Use the tick spacing to read each point. - Write each decimal as tenths and simplify.

1. There are \(5\) equal intervals from \(0\) to \(1\), so each minor tick represents \(1 \div 5 = 0.2\). 2. The points are \(K = 0.4\), \(L = 1.2\), and \(M = 1.6\). 3. Convert \(K\): \(0.4 = \frac{4}{10} = \frac{2}{5}\). 4. Convert \(L\): \(1.2 = \frac{12}{10} = \frac{6}{5} = 1\frac{1}{5}\). 5. Convert \(M\): \(1.6 = \frac{16}{10} = \frac{8}{5} = 1\frac{3}{5}\).

\(K = 0.4 = \frac{2}{5}\) \(L = 1.2 = 1\frac{1}{5}\) \(M = 1.6 = 1\frac{3}{5}\)

- List digit pairs whose sum matches the clue. - Check which pair has the required difference and order. - Place the larger digit in the tenths position as stated.

1. The digit pair must have a sum of \(9\) and differ by \(3\). 2. The tenths digit is \(6\) and the hundredths digit is \(3\). 3. The decimal is \(3.63\), and its fractional part is \(\frac{6}{10}+\frac{3}{100}\).

\(3.63=3+\frac{6}{10}+\frac{3}{100}\)

- Name the place value of the digit \(7\) on each card. - A zero after the last nonzero decimal digit behaves differently from a zero before it. - Compare each card with seventy hundredths, not only with the digits shown.

1. \(\frac{70}{100}=\frac{7}{10}\), so \(0.7\) and \(0.70\) are equal to the fraction. 2. In \(0.70\), the final zero records zero additional hundredths and does not change the value. 3. In \(0.07\), the zero holds the tenths place, so the value is seven hundredths. In \(7.0\), the \(7\) is in the ones place.

Equal: \(0.7\), \(0.70\). The final zero in \(0.70\) adds no hundredths. Not equal: \(0.07\), \(7.0\). In \(0.07\), the zero holds the tenths place; in \(7.0\), the zero shows no tenths after seven ones.

- Write both decimals as mixed numbers with hundredths. - Pay attention to the position of the digit \(6\), not just its appearance. - Compare the fractional parts after giving them the same unit.

1. In \(4.06\), the zero is in the tenths place and the \(6\) is in the hundredths place, so the number is \(4\frac{6}{100}\). 2. The number \(4.6\) is \(4\frac{60}{100}\). 3. Therefore, \(4.6\) is greater by \(\frac{60}{100}-\frac{6}{100}=\frac{54}{100}\).

The zero in \(4.06\) is a necessary tenths placeholder. \(4.6\) is greater by \(54\) hundredths.