Question

Arrange the following decimals from smallest to largest: 5.15,5.05,5.55 ______

Short answer

The correct order is 5.05, 5.15, 5.55.

Step-by-step solution

List the Numbers

First, write down all the decimals that need to be arranged: 5.15, 5.05, and 5.55.

Compare Whole Numbers

Look at the whole number part of each decimal. All of them have the whole number part of 5.

Compare Decimal Parts

Since the whole numbers are the same, compare the decimal parts (the numbers after the decimal point): 0.15, 0.05, and 0.55.

Identify the Smallest Decimal Part

The smallest decimal part is 0.05, thus 5.05 is the smallest decimal.

Identify the Middle Decimal Part

The next smallest decimal part is 0.15, so 5.15 is the middle number.

Identify the Largest Decimal Part

Lastly, the largest decimal part is 0.55, making 5.55 the largest number.

Write the Final Order

Arrange the numbers from the smallest to the largest based on your findings: 5.05, 5.15, 5.55.

Key concepts

Decimal Comparison

When comparing decimals, it's essential to focus on both the whole number and the fractional part of the number (the portion after the decimal point). This approach ensures accuracy when you're deciding which numbers are larger or smaller than others.

• Start by examining the whole number: The whole number gives you a quick initial comparison. If two decimals have different whole numbers, you know the answer straight away. The one with the smaller whole number is the smaller decimal.
• Focus on the decimal part: When the whole numbers are the same, which was the case in our exercise — 5.15, 5.05, and 5.55 — you need to compare the decimals' parts. This part tells you the precise order of the numbers.

Comparing decimal parts is much like comparing whole numbers. Just remember to line them up by their decimal points and compare digit by digit.

Numerical Order

Understanding how to order numbers numerically is vital for everyday situations, whether you're working with decimals or whole numbers.
Sorting decimals involves placing them in a sequence from least to greatest (or vice-versa), based on either their value. In our example, after examining the decimal parts, we found that
\[0.05 < 0.15 < 0.55\]
This ordering helps us list the full numbers as
\[5.05, 5.15, 5.55\]

• Start with the smallest digit: Look at the smallest decimal value and know it's your starting point.
• Find the median value: Identify the middle number once the smallest is established.
• End with the largest number: Complement your list with the largest decimal.

Mastering this process helps create an efficiently ordered list and ensures clarity in representing numbers in many areas of mathematics.

Mathematical Reasoning

Mathematical reasoning forms the basis of understanding and solving problems, such as ordering decimals. It's the thought process that allows you to make sense of numbers logically and systematically.

• Assess and plan: Initiate by clearly stating what needs to be followed. As in our example, succinctly denote all numbers requiring ordering.
• Use logical steps: Follow a proven, structured sequence. We started by listing numbers, then compared them as needed.
• Verify results: Ensure each step in your reasoning is accurate. Verify by double-checking your list after comparisons.

With effective reasoning, mathematics becomes more than just numbers and equations. It evolves into a structured way of thinking to solve a range of problems, making tasks like decimal ordering second nature.