Comparing and Ordering Decimals Worksheets - Math Monks - Free Printable

To solve the problem of ordering fractions and decimals in ascending and descending order, we need to convert all the given numbers into a common format (either all decimals or all fractions) and then compare them. Let's go through each part step by step.

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Part 1: Ordering in Ascending Order

#### Problem ①
Numbers: \(0.6\), \(\frac{1}{6}\), \(\frac{1}{2}\), \(0.06\), \(0.66\), \(66.6\)

1. Convert all numbers to decimals:
- \(0.6\) is already a decimal.
- \(\frac{1}{6} = 0.1666\ldots \approx 0.167\)
- \(\frac{1}{2} = 0.5\)
- \(0.06\) is already a decimal.
- \(0.66\) is already a decimal.
- \(66.6\) is already a decimal.

2. List the decimals:
- \(0.6\), \(0.167\), \(0.5\), \(0.06\), \(0.66\), \(66.6\)

3. Arrange in ascending order:
- \(0.06\), \(0.167\), \(0.5\), \(0.6\), \(0.66\), \(66.6\)

4. Replace the decimals with their original forms:
- \(0.06\), \(\frac{1}{6}\), \(\frac{1}{2}\), \(0.6\), \(0.66\), \(66.6\)

Answer for ①:
\[
\boxed{0.06, \frac{1}{6}, \frac{1}{2}, 0.6, 0.66, 66.6}
\]

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#### Problem ②
Numbers: \(9.9\), \(\frac{1}{4}\), \(\frac{3}{4}\), \(19.5\), \(9.09\), \(\frac{1}{9}\)

1. Convert all numbers to decimals:
- \(9.9\) is already a decimal.
- \(\frac{1}{4} = 0.25\)
- \(\frac{3}{4} = 0.75\)
- \(19.5\) is already a decimal.
- \(9.09\) is already a decimal.
- \(\frac{1}{9} = 0.111\ldots \approx 0.111\)

2. List the decimals:
- \(9.9\), \(0.25\), \(0.75\), \(19.5\), \(9.09\), \(0.111\)

3. Arrange in ascending order:
- \(0.111\), \(0.25\), \(0.75\), \(9.09\), \(9.9\), \(19.5\)

4. Replace the decimals with their original forms:
- \(\frac{1}{9}\), \(\frac{1}{4}\), \(\frac{3}{4}\), \(9.09\), \(9.9\), \(19.5\)

Answer for ②:
\[
\boxed{\frac{1}{9}, \frac{1}{4}, \frac{3}{4}, 9.09, 9.9, 19.5}
\]

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#### Problem ③
Numbers: \(101.5\), \(10.15\), \(1.015\), \(\frac{1}{5}\), \(\frac{2}{5}\), \(\frac{3}{5}\)

1. Convert all numbers to decimals:
- \(101.5\) is already a decimal.
- \(10.15\) is already a decimal.
- \(1.015\) is already a decimal.
- \(\frac{1}{5} = 0.2\)
- \(\frac{2}{5} = 0.4\)
- \(\frac{3}{5} = 0.6\)

2. List the decimals:
- \(101.5\), \(10.15\), \(1.015\), \(0.2\), \(0.4\), \(0.6\)

3. Arrange in ascending order:
- \(0.2\), \(0.4\), \(0.6\), \(1.015\), \(10.15\), \(101.5\)

4. Replace the decimals with their original forms:
- \(\frac{1}{5}\), \(\frac{2}{5}\), \(\frac{3}{5}\), \(1.015\), \(10.15\), \(101.5\)

Answer for ③:
\[
\boxed{\frac{1}{5}, \frac{2}{5}, \frac{3}{5}, 1.015, 10.15, 101.5}
\]

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Part 2: Ordering in Descending Order

#### Problem ①
Numbers: \(23.3\), \(\frac{2}{3}\), \(0.23\), \(\frac{2}{5}\), \(2.2\), \(2.15\)

1. Convert all numbers to decimals:
- \(23.3\) is already a decimal.
- \(\frac{2}{3} = 0.666\ldots \approx 0.667\)
- \(0.23\) is already a decimal.
- \(\frac{2}{5} = 0.4\)
- \(2.2\) is already a decimal.
- \(2.15\) is already a decimal.

2. List the decimals:
- \(23.3\), \(0.667\), \(0.23\), \(0.4\), \(2.2\), \(2.15\)

3. Arrange in descending order:
- \(23.3\), \(2.2\), \(2.15\), \(0.667\), \(0.4\), \(0.23\)

4. Replace the decimals with their original forms:
- \(23.3\), \(2.2\), \(2.15\), \(\frac{2}{3}\), \(\frac{2}{5}\), \(0.23\)

Answer for ①:
\[
\boxed{23.3, 2.2, 2.15, \frac{2}{3}, \frac{2}{5}, 0.23}
\]

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#### Problem ②
Numbers: \(0.94\), \(9.45\), \(9.44\), \(\frac{4}{5}\), \(\frac{5}{4}\), \(0.95\)

1. Convert all numbers to decimals:
- \(0.94\) is already a decimal.
- \(9.45\) is already a decimal.
- \(9.44\) is already a decimal.
- \(\frac{4}{5} = 0.8\)
- \(\frac{5}{4} = 1.25\)
- \(0.95\) is already a decimal.

2. List the decimals:
- \(0.94\), \(9.45\), \(9.44\), \(0.8\), \(1.25\), \(0.95\)

3. Arrange in descending order:
- \(9.45\), \(9.44\), \(1.25\), \(0.95\), \(0.94\), \(0.8\)

4. Replace the decimals with their original forms:
- \(9.45\), \(9.44\), \(\frac{5}{4}\), \(0.95\), \(0.94\), \(\frac{4}{5}\)

Answer for ②:
\[
\boxed{9.45, 9.44, \frac{5}{4}, 0.95, 0.94, \frac{4}{5}}
\]

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#### Problem ③
Numbers: \(111.9\), \(\frac{1}{9}\), \(\frac{11}{9}\), \(1.19\), \(11.9\), \(0.19\)

1. Convert all numbers to decimals:
- \(111.9\) is already a decimal.
- \(\frac{1}{9} = 0.111\ldots \approx 0.111\)
- \(\frac{11}{9} = 1.222\ldots \approx 1.222\)
- \(1.19\) is already a decimal.
- \(11.9\) is already a decimal.
- \(0.19\) is already a decimal.

2. List the decimals:
- \(111.9\), \(0.111\), \(1.222\), \(1.19\), \(11.9\), \(0.19\)

3. Arrange in descending order:
- \(111.9\), \(11.9\), \(1.222\), \(1.19\), \(0.19\), \(0.111\)

4. Replace the decimals with their original forms:
- \(111.9\), \(11.9\), \(\frac{11}{9}\), \(1.19\), \(0.19\), \(\frac{1}{9}\)

Answer for ③:
\[
\boxed{111.9, 11.9, \frac{11}{9}, 1.19, 0.19, \frac{1}{9}}
\]

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Final Answers:

- Ascending Order:
1. \(\boxed{0.06, \frac{1}{6}, \frac{1}{2}, 0.6, 0.66, 66.6}\)
2. \(\boxed{\frac{1}{9}, \frac{1}{4}, \frac{3}{4}, 9.09, 9.9, 19.5}\)
3. \(\boxed{\frac{1}{5}, \frac{2}{5}, \frac{3}{5}, 1.015, 10.15, 101.5}\)

- Descending Order:
1. \(\boxed{23.3, 2.2, 2.15, \frac{2}{3}, \frac{2}{5}, 0.23}\)
2. \(\boxed{9.45, 9.44, \frac{5}{4}, 0.95, 0.94, \frac{4}{5}}\)
3. \(\boxed{111.9, 11.9, \frac{11}{9}, 1.19, 0.19, \frac{1}{9}}\)