1. Introduction to Ascending and Descending Order
Ascending order means arranging numbers from the smallest to the largest.
Descending order means arranging numbers from the largest to the smallest.
Key Terms:
- Smallest: The number with the lowest value.
- Largest: The number with the highest value.
2. Understanding Ascending Order
When arranging numbers in ascending order, you start with the smallest number and gradually move to the largest.
Example 1: Arrange 4, 12, 7, 19, and 2 in ascending order.
- Start with the smallest: 2.
- Then 4, 7, 12, and 19.
Answer: 2, 4, 7, 12, 19.
Example 2: Arrange 5,324, 9,875, 4,231, and 6,543 in ascending order.
- Compare each number by looking at the thousands, hundreds, tens, and ones.
- The smallest is 4,231, then 5,324, followed by 6,543, and finally 9,875.
Answer: 4,231, 5,324, 6,543, 9,875.
3. Understanding Descending Order
In descending order, numbers are arranged from the largest to the smallest.
Example 1: Arrange 45, 12, 89, 37, and 23 in descending order.
- Start with the largest: 89.
- Then 45, 37, 23, and finally 12.
Answer: 89, 45, 37, 23, 12.
Example 2: Arrange 15,789, 12,345, 23,456, and 18,901 in descending order.
- Start with the largest number: 23,456.
- Then 18,901, 15,789, and 12,345.
Answer: 23,456, 18,901, 15,789, 12,345.
4. Steps for Ordering Large Numbers
Step 1: Count the Number of Digits
- Numbers with more digits are generally larger.
Step 2: Compare Place Values
- If two numbers have the same number of digits, compare the place values starting from the leftmost digit (thousands, hundreds, etc.).
Step 3: Arrange the Numbers
- For ascending order, place the smallest number first and the largest number last.
- For descending order, place the largest number first and the smallest number last.
Example: Arrange 1,453, 3,248, 5,789, and 2,302 in descending order.
- 5,789 is the largest.
- Then 3,248, followed by 2,302, and finally 1,453.
Answer: 5,789, 3,248, 2,302, 1,453.
5. Ascending and Descending Order with Decimals
When dealing with decimals, start by comparing the whole number part. If the whole numbers are the same, move to the decimal part and compare digit by digit.
Example 1: Arrange 3.45, 3.78, 3.51, and 3.25 in ascending order.
- Start by comparing the whole number part (3), which is the same for all.
- Then compare the decimal part:
- 3.25 is the smallest.
- Then 3.45, followed by 3.51, and finally 3.78.
Answer: 3.25, 3.45, 3.51, 3.78.
Example 2: Arrange 7.895, 7.9, 7.75, and 7.805 in descending order.
- Compare the whole number part: all are 7.
- Compare the decimal part:
- 7.9 is the largest.
- Then 7.895, followed by 7.805, and finally 7.75.
Answer: 7.9, 7.895, 7.805, 7.75.
6. Advanced: Comparing and Ordering Numbers
6.1: Company Profits
Question:
Four companies made the following profits this year:
- Company A: $9,876,432
- Company B: $8,564,210
- Company C: $12,345,678
- Company D: $11,987,654
Arrange the companies’ profits in ascending order.
Solution:
- Compare the values:
- Company B: 8,564,210 (smallest)
- Company A: 9,876,432
- Company D: 11,987,654
- Company C: 12,345,678 (largest)
Answer:
Company B < Company A < Company D < Company C.
6.2: Population Growth
Question:
The population of four cities is as follows:
- City X: 1,345,678
- City Y: 2,987,654
- City Z: 1,234,567
- City W: 2,123,456
Arrange the populations in descending order.
Solution:
- City Y: 2,987,654 (largest)
- City W: 2,123,456
- City X: 1,345,678
- City Z: 1,234,567 (smallest)
Answer:
City Y > City W > City X > City Z.
6.3: Real Estate Prices
Question:
The prices of four houses in a neighborhood are:
- House A: $875,000
- House B: $675,000
- House C: $1,250,000
- House D: $980,000
Arrange the house prices in ascending order.
Solution:
- House B: $675,000 (smallest)
- House A: $875,000
- House D: $980,000
- House C: $1,250,000 (largest)
Answer:
House B < House A < House D < House C.
7. More Examples
7.1: Annual Budget Allocation
Question:
The government allocated the following amounts to four departments this year:
- Education: $8,900,000
- Health: $7,800,000
- Defense: $12,000,000
- Transport: $6,500,000
Arrange the department budgets in descending order.
Solution:
- Defense: $12,000,000 (largest)
- Education: $8,900,000
- Health: $7,800,000
- Transport: $6,500,000 (smallest)
Answer:
Defense > Education > Health > Transport.
7.2: Comparing Test Scores
Question:
The test scores of four students are as follows:
- Student A: 89.75
- Student B: 92.5
- Student C: 88.25
- Student D: 91.0
Arrange the test scores in ascending order.
Solution:
- Student C: 88.25 (smallest)
- Student A: 89.75
- Student D: 91.0
- Student B: 92.5 (largest)
Answer:
Student C < Student A < Student D < Student B.
7.3: Comparing Distances
Question:
The distances between Earth and four stars are as follows:
- Star X: 5.67 light-years
- Star Y: 4.32 light-years
- Star Z: 6.01 light-years
- Star W: 5.22 light-years
Arrange the distances in ascending order.
Solution:
- Star Y: 4.32 light-years (smallest)
- Star W: 5.22 light-years
- Star X: 5.67 light-years
- Star Z: 6.01 light-years (largest)
Answer:
Star Y < Star W < Star X < Star Z.
8. Practice Problems
- Arrange the following in ascending order: 5,789, 2,345, 6,432, 3,120.
- Arrange the following in descending order: 3.45, 2.89, 4.12, 3.99.
- Four people earned $12,340, $14,500, $9,876, and $10,200. Arrange the earnings in descending order.
- The populations of four countries are 45,786,230; 34,567,890; 23,456,700; and 56,789,432.
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