Comparing and Ordering Decimals

Key Concepts

Comparing and ordering decimals involves understanding the value of each digit after the decimal point and arranging numbers in ascending or descending order.

Comparing Decimals

To compare decimals, follow these steps:

1. Align the decimal points.
2. Compare the digits from left to right.
3. If the digits are the same, move to the next digit.
4. If one number runs out of digits, add zeros to the end of that number to make the comparison easier.

Example

Compare 0.45 and 0.438:

• Align the decimal points: 0.45 and 0.438.
• Compare the digits: 0.450 and 0.438 (add a zero to 0.45 to make it 0.450).
• Start comparing from the left: 4 = 4, move to the next digit.
• Next digit: 5 > 3.

So, 0.45 > 0.438.

Ordering Decimals

To order decimals, follow these steps:

1. Compare each pair of decimals using the method above.
2. Arrange the decimals from smallest to largest (ascending order) or largest to smallest (descending order).

Example

Order the decimals 0.2, 0.15, 0.3, and 0.25 in ascending order:

• Compare 0.2 and 0.15: 0.2 > 0.15.
• Compare 0.2 and 0.3: 0.2 < 0.3.
• Compare 0.2 and 0.25: 0.2 < 0.25.
• Compare 0.15 and 0.3: 0.15 < 0.3.
• Compare 0.15 and 0.25: 0.15 < 0.25.
• Compare 0.3 and 0.25: 0.3 > 0.25.

So, the ascending order is 0.15, 0.2, 0.25, 0.3.

Analogies

Think of comparing decimals as comparing the lengths of two pieces of string. If you line them up at the start, the longer string represents the larger decimal number.

Ordering decimals can be likened to arranging toys by their size. The smallest toy represents the smallest decimal, and the largest toy represents the largest decimal.

Practical Application

Understanding how to compare and order decimals is useful in everyday life. For example, when comparing prices of items at a store, you can quickly determine which item is cheaper by comparing the decimal prices.