Arranging Decimals in Ascending/Descending Order - Math Worksheets ... - Free Printable
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Step-by-step solution for: Arranging Decimals in Ascending/Descending Order - Math Worksheets ...
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Show Answer Key & Explanations
Step-by-step solution for: Arranging Decimals in Ascending/Descending Order - Math Worksheets ...
To solve the problem of ordering the given sets of decimal numbers in ascending or descending order, we need to carefully compare the numbers digit by digit. Here's a step-by-step explanation for each part:
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Numbers: 56.9, 56.98, 56.278, 5.699
- Step 1: Compare the whole number parts first.
- The smallest whole number is 5 (from 5.699).
- Next, compare the remaining numbers: 56.9, 56.98, and 56.278. All have the same whole number part (56), so we move to the decimal parts.
- Step 2: Compare the decimal parts.
- For 56.278, the tenths place is 2.
- For 56.9 and 56.98, the tenths place is 9.
- Between 56.9 and 56.98, the hundredths place determines the order: 56.9 has 0 in the hundredths place, while 56.98 has 8.
- Final Order:
5.699, 56.278, 56.9, 56.98
Answer:
5.699, 56.278, 56.9, 56.98
---
Numbers: 137.687, 136.2, 137.788, 136.567
- Step 1: Compare the whole number parts first.
- The largest whole number is 137 (from 137.687 and 137.788).
- Next, compare the remaining numbers: 136.2 and 136.567. Both have the same whole number part (136), so we move to the decimal parts.
- Step 2: Compare the decimal parts.
- For 137.687 and 137.788, the tenths place determines the order: 137.687 has 6, while 137.788 has 7.
- For 136.2 and 136.567, the tenths place determines the order: 136.2 has 2, while 136.567 has 5.
- Final Order:
137.788, 137.687, 136.567, 136.2
Answer:
137.788, 137.687, 136.567, 136.2
---
Numbers: 6.900, 6.909, 6.009, 6.09
- Step 1: Compare the whole number parts first.
- All numbers have the same whole number part (6), so we move to the decimal parts.
- Step 2: Compare the decimal parts.
- For 6.900 and 6.909, the tenths place is 9 for both, so we compare the thousandths place: 6.900 has 0, while 6.909 has 9.
- For 6.009 and 6.09, the tenths place determines the order: 6.009 has 0, while 6.09 has 9.
- Final Order:
6.909, 6.900, 6.09, 6.009
Answer:
6.909, 6.900, 6.09, 6.009
---
Numbers: 400.60, 40.444, 40.045, 4.699
- Step 1: Compare the whole number parts first.
- The smallest whole number is 4 (from 4.699).
- Next, compare the remaining numbers: 40.444, 40.045, and 400.60. Both 40.444 and 40.045 have the same whole number part (40), while 400.60 has a larger whole number part (400).
- Step 2: Compare the decimal parts for 40.444 and 40.045.
- The tenths place determines the order: 40.444 has 4, while 40.045 has 0.
- Final Order:
4.699, 40.045, 40.444, 400.60
Answer:
4.699, 40.045, 40.444, 400.60
---
Numbers: 18.298, 18.453, 18.45, 18.682
- Step 1: Compare the whole number parts first.
- All numbers have the same whole number part (18), so we move to the decimal parts.
- Step 2: Compare the decimal parts.
- For 18.298, the tenths place is 2.
- For 18.453 and 18.45, the tenths place is 4. Between these, the hundredths place determines the order: both have 5, so we compare the thousandths place: 18.453 has 3, while 18.45 has 0.
- For 18.682, the tenths place is 6.
- Final Order:
18.298, 18.45, 18.453, 18.682
Answer:
18.298, 18.45, 18.453, 18.682
---
Numbers: 10.788, 100.007, 100.072, 100.1
- Step 1: Compare the whole number parts first.
- The largest whole number is 100 (from 100.007, 100.072, and 100.1).
- The smallest whole number is 10 (from 10.788).
- Step 2: Compare the decimal parts for the numbers with the same whole number part (100).
- For 100.007, 100.072, and 100.1, the tenths place determines the order: 100.007 and 100.072 have 0, while 100.1 has 1.
- Between 100.007 and 100.072, the hundredths place determines the order: 100.007 has 0, while 100.072 has 7.
- Final Order:
100.1, 100.072, 100.007, 10.788
Answer:
100.1, 100.072, 100.007, 10.788
---
Numbers: 123.29, 1.2329, 1232.9, 12.329
- Step 1: Compare the whole number parts first.
- The largest whole number is 1232 (from 1232.9).
- The next largest is 123 (from 123.29).
- The next is 12 (from 12.329).
- The smallest is 1 (from 1.2329).
- Final Order:
1232.9, 123.29, 12.329, 1.2329
Answer:
1232.9, 123.29, 12.329, 1.2329
---
1. Ascending Order: 5.699, 56.278, 56.9, 56.98
2. Descending Order: 137.788, 137.687, 136.567, 136.2
3. Descending Order: 6.909, 6.900, 6.09, 6.009
4. Ascending Order: 4.699, 40.045, 40.444, 400.60
5. Ascending Order: 18.298, 18.45, 18.453, 18.682
6. Descending Order: 100.1, 100.072, 100.007, 10.788
7. Descending Order: 1232.9, 123.29, 12.329, 1.2329
Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
1. \text{Ascending Order: } 5.699, 56.278, 56.9, 56.98 \\
2. \text{Descending Order: } 137.788, 137.687, 136.567, 136.2 \\
3. \text{Descending Order: } 6.909, 6.900, 6.09, 6.009 \\
4. \text{Ascending Order: } 4.699, 40.045, 40.444, 400.60 \\
5. \text{Ascending Order: } 18.298, 18.45, 18.453, 18.682 \\
6. \text{Descending Order: } 100.1, 100.072, 100.007, 10.788 \\
7. \text{Descending Order: } 1232.9, 123.29, 12.329, 1.2329 \\
\end{array}
}
\]
---
1. Ascending Order:
Numbers: 56.9, 56.98, 56.278, 5.699
- Step 1: Compare the whole number parts first.
- The smallest whole number is 5 (from 5.699).
- Next, compare the remaining numbers: 56.9, 56.98, and 56.278. All have the same whole number part (56), so we move to the decimal parts.
- Step 2: Compare the decimal parts.
- For 56.278, the tenths place is 2.
- For 56.9 and 56.98, the tenths place is 9.
- Between 56.9 and 56.98, the hundredths place determines the order: 56.9 has 0 in the hundredths place, while 56.98 has 8.
- Final Order:
5.699, 56.278, 56.9, 56.98
Answer:
5.699, 56.278, 56.9, 56.98
---
2. Descending Order:
Numbers: 137.687, 136.2, 137.788, 136.567
- Step 1: Compare the whole number parts first.
- The largest whole number is 137 (from 137.687 and 137.788).
- Next, compare the remaining numbers: 136.2 and 136.567. Both have the same whole number part (136), so we move to the decimal parts.
- Step 2: Compare the decimal parts.
- For 137.687 and 137.788, the tenths place determines the order: 137.687 has 6, while 137.788 has 7.
- For 136.2 and 136.567, the tenths place determines the order: 136.2 has 2, while 136.567 has 5.
- Final Order:
137.788, 137.687, 136.567, 136.2
Answer:
137.788, 137.687, 136.567, 136.2
---
3. Descending Order:
Numbers: 6.900, 6.909, 6.009, 6.09
- Step 1: Compare the whole number parts first.
- All numbers have the same whole number part (6), so we move to the decimal parts.
- Step 2: Compare the decimal parts.
- For 6.900 and 6.909, the tenths place is 9 for both, so we compare the thousandths place: 6.900 has 0, while 6.909 has 9.
- For 6.009 and 6.09, the tenths place determines the order: 6.009 has 0, while 6.09 has 9.
- Final Order:
6.909, 6.900, 6.09, 6.009
Answer:
6.909, 6.900, 6.09, 6.009
---
4. Ascending Order:
Numbers: 400.60, 40.444, 40.045, 4.699
- Step 1: Compare the whole number parts first.
- The smallest whole number is 4 (from 4.699).
- Next, compare the remaining numbers: 40.444, 40.045, and 400.60. Both 40.444 and 40.045 have the same whole number part (40), while 400.60 has a larger whole number part (400).
- Step 2: Compare the decimal parts for 40.444 and 40.045.
- The tenths place determines the order: 40.444 has 4, while 40.045 has 0.
- Final Order:
4.699, 40.045, 40.444, 400.60
Answer:
4.699, 40.045, 40.444, 400.60
---
5. Ascending Order:
Numbers: 18.298, 18.453, 18.45, 18.682
- Step 1: Compare the whole number parts first.
- All numbers have the same whole number part (18), so we move to the decimal parts.
- Step 2: Compare the decimal parts.
- For 18.298, the tenths place is 2.
- For 18.453 and 18.45, the tenths place is 4. Between these, the hundredths place determines the order: both have 5, so we compare the thousandths place: 18.453 has 3, while 18.45 has 0.
- For 18.682, the tenths place is 6.
- Final Order:
18.298, 18.45, 18.453, 18.682
Answer:
18.298, 18.45, 18.453, 18.682
---
6. Descending Order:
Numbers: 10.788, 100.007, 100.072, 100.1
- Step 1: Compare the whole number parts first.
- The largest whole number is 100 (from 100.007, 100.072, and 100.1).
- The smallest whole number is 10 (from 10.788).
- Step 2: Compare the decimal parts for the numbers with the same whole number part (100).
- For 100.007, 100.072, and 100.1, the tenths place determines the order: 100.007 and 100.072 have 0, while 100.1 has 1.
- Between 100.007 and 100.072, the hundredths place determines the order: 100.007 has 0, while 100.072 has 7.
- Final Order:
100.1, 100.072, 100.007, 10.788
Answer:
100.1, 100.072, 100.007, 10.788
---
7. Descending Order:
Numbers: 123.29, 1.2329, 1232.9, 12.329
- Step 1: Compare the whole number parts first.
- The largest whole number is 1232 (from 1232.9).
- The next largest is 123 (from 123.29).
- The next is 12 (from 12.329).
- The smallest is 1 (from 1.2329).
- Final Order:
1232.9, 123.29, 12.329, 1.2329
Answer:
1232.9, 123.29, 12.329, 1.2329
---
Final Answers:
1. Ascending Order: 5.699, 56.278, 56.9, 56.98
2. Descending Order: 137.788, 137.687, 136.567, 136.2
3. Descending Order: 6.909, 6.900, 6.09, 6.009
4. Ascending Order: 4.699, 40.045, 40.444, 400.60
5. Ascending Order: 18.298, 18.45, 18.453, 18.682
6. Descending Order: 100.1, 100.072, 100.007, 10.788
7. Descending Order: 1232.9, 123.29, 12.329, 1.2329
Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
1. \text{Ascending Order: } 5.699, 56.278, 56.9, 56.98 \\
2. \text{Descending Order: } 137.788, 137.687, 136.567, 136.2 \\
3. \text{Descending Order: } 6.909, 6.900, 6.09, 6.009 \\
4. \text{Ascending Order: } 4.699, 40.045, 40.444, 400.60 \\
5. \text{Ascending Order: } 18.298, 18.45, 18.453, 18.682 \\
6. \text{Descending Order: } 100.1, 100.072, 100.007, 10.788 \\
7. \text{Descending Order: } 1232.9, 123.29, 12.329, 1.2329 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of ordering decimal numbers worksheet year.
