Grade 6 Decimal Worksheets | Free Printables | Math Worksheets - Free Printable

Problem: Ordering Decimals

The task is to arrange the given sets of decimals from smallest to greatest. Let's solve each set step by step.

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#### Set i.
Numbers: \( 0.17, 1.19, 1.07 \)

1. Compare the whole number parts:
- \( 0.17 \) has a whole number part of \( 0 \).
- \( 1.19 \) and \( 1.07 \) both have a whole number part of \( 1 \).

2. Since \( 0.17 \) has the smallest whole number part, it is the smallest.
3. Compare \( 1.19 \) and \( 1.07 \):
- Look at the tenths place: \( 1.19 \) has \( 1 \), and \( 1.07 \) has \( 0 \).
- Therefore, \( 1.07 < 1.19 \).

Ordered: \( 0.17, 1.07, 1.19 \)

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#### Set ii.
Numbers: \( 1.45, 1.54, 1.34 \)

1. All numbers have the same whole number part (\( 1 \)).
2. Compare the tenths place:
- \( 1.45 \): Tenths place is \( 4 \).
- \( 1.54 \): Tenths place is \( 5 \).
- \( 1.34 \): Tenths place is \( 3 \).

3. From this, \( 1.34 < 1.45 < 1.54 \).

Ordered: \( 1.34, 1.45, 1.54 \)

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#### Set iii.
Numbers: \( 2.45, 2.56, 2.45 \)

1. All numbers have the same whole number part (\( 2 \)).
2. Compare the tenths place:
- \( 2.45 \) and \( 2.45 \): Tenths place is \( 4 \).
- \( 2.56 \): Tenths place is \( 5 \).

3. Since \( 2.45 = 2.45 \) and both are smaller than \( 2.56 \):

Ordered: \( 2.45, 2.45, 2.56 \)

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#### Set iv.
Numbers: \( 3.56, 3.64, 3.46 \)

1. All numbers have the same whole number part (\( 3 \)).
2. Compare the tenths place:
- \( 3.56 \): Tenths place is \( 5 \).
- \( 3.64 \): Tenths place is \( 6 \).
- \( 3.46 \): Tenths place is \( 4 \).

3. From this, \( 3.46 < 3.56 < 3.64 \).

Ordered: \( 3.46, 3.56, 3.64 \)

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#### Set v.
Numbers: \( 4.2, 4.325, 4.15 \)

1. All numbers have the same whole number part (\( 4 \)).
2. Compare the tenths place:
- \( 4.2 \): Tenths place is \( 2 \).
- \( 4.325 \): Tenths place is \( 3 \).
- \( 4.15 \): Tenths place is \( 1 \).

3. From this, \( 4.15 < 4.2 < 4.325 \).

Ordered: \( 4.15, 4.2, 4.325 \)

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#### Set vi.
Numbers: \( 5.017, 5.162, 4.978 \)

1. Compare the whole number parts:
- \( 5.017 \) and \( 5.162 \) have a whole number part of \( 5 \).
- \( 4.978 \) has a whole number part of \( 4 \).

2. Since \( 4.978 \) has the smallest whole number part, it is the smallest.
3. Compare \( 5.017 \) and \( 5.162 \):
- Look at the tenths place: \( 5.017 \) has \( 0 \), and \( 5.162 \) has \( 1 \).
- Therefore, \( 5.017 < 5.162 \).

Ordered: \( 4.978, 5.017, 5.162 \)

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#### Set vii.
Numbers: \( 5.834, 5.999, 5.806 \)

1. All numbers have the same whole number part (\( 5 \)).
2. Compare the tenths place:
- \( 5.834 \) and \( 5.806 \): Tenths place is \( 8 \).
- \( 5.999 \): Tenths place is \( 9 \).

3. From this, \( 5.806 < 5.834 < 5.999 \).

Ordered: \( 5.806, 5.834, 5.999 \)

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#### Set viii.
Numbers: \( 6.651, 6.836, 6.634 \)

1. All numbers have the same whole number part (\( 6 \)).
2. Compare the tenths place:
- \( 6.651 \) and \( 6.634 \): Tenths place is \( 6 \).
- \( 6.836 \): Tenths place is \( 8 \).

3. From this, \( 6.634 < 6.651 < 6.836 \).

Ordered: \( 6.634, 6.651, 6.836 \)

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#### Set ix.
Numbers: \( 7.468, 7.673, 7.462 \)

1. All numbers have the same whole number part (\( 7 \)).
2. Compare the tenths place:
- \( 7.468 \) and \( 7.462 \): Tenths place is \( 4 \).
- \( 7.673 \): Tenths place is \( 6 \).

3. From this, \( 7.462 < 7.468 < 7.673 \).

Ordered: \( 7.462, 7.468, 7.673 \)

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#### Set x.
Numbers: \( 8.285, 8.51, 8.29 \)

1. All numbers have the same whole number part (\( 8 \)).
2. Compare the tenths place:
- \( 8.285 \) and \( 8.29 \): Tenths place is \( 2 \).
- \( 8.51 \): Tenths place is \( 5 \).

3. From this, \( 8.285 < 8.29 < 8.51 \).

Ordered: \( 8.285, 8.29, 8.51 \)

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Final Answer:

\[
\boxed{
\begin{array}{lll}
\text{i.} & 0.17, 1.07, 1.19 \\
\text{ii.} & 1.34, 1.45, 1.54 \\
\text{iii.} & 2.45, 2.45, 2.56 \\
\text{iv.} & 3.46, 3.56, 3.64 \\
\text{v.} & 4.15, 4.2, 4.325 \\
\text{vi.} & 4.978, 5.017, 5.162 \\
\text{vii.} & 5.806, 5.834, 5.999 \\
\text{viii.} & 6.634, 6.651, 6.836 \\
\text{ix.} & 7.462, 7.468, 7.673 \\
\text{x.} & 8.285, 8.29, 8.51 \\
\end{array}
}
\]