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Chapter 3: Problem 5

Identify the decimal with the largest value in the following sets. 0.725,0.357,0.125 ______

Short Answer

Expert verified
0.725 is the largest decimal.

Step by step solution

01

Understand the Problem

We need to identify the decimal number with the largest value among the given set of numbers: 0.725, 0.357, and 0.125.
02

Compare the Tenths Place

Start by comparing the digit in the tenths place of each decimal. The numbers are 7 in 0.725, 3 in 0.357, and 1 in 0.125. The highest tenths place value is 7.
03

Determine the Largest Decimal

Since the digit in the tenths place for 0.725 is greater than the tenths place digits for the other two numbers (3 and 1), 0.725 is the largest decimal number in the set.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Tenths Place
When working with decimal numbers, the tenths place is one of the key value holders. It is the first position to the right of the decimal point. Here's how it works:
  • It represents the first power of ten in the decimal places, and hence has a positional value of \( \frac{1}{10} \) or 0.1.
  • Each digit in the tenths place contributes directly to the number's overall value, making its identification crucial when comparing decimals.
In the decimal numbers 0.725, 0.357, and 0.125, the digits in the tenths place are 7, 3, and 1 respectively. To compare these numbers, you focus first on this primary position since a higher digit here indicates a larger overall value in the entire number. Thus, identifying and understanding the tenths place gives you a quick shortcut to determining which decimal might be largest at a glance.
Digit Analysis
Digit analysis is a critical part of understanding and comparing decimal numbers. By examining each digit from left to right, starting from the highest place value, we can determine the relative size of different numbers.
  • Begin with the tenths place as it holds the most significant contribution among the digits of a decimal less than one.
  • If all tenths place digits are equal, proceed to the hundredths place, and so on.
In our given example, the digit analysis starts with the tenths place. Since the tenths digits are different, we already know that the number in the set with the highest tenths digit will be the largest. This process might seem straightforward, but it requires careful attention to ensure each digit is accurately compared against others in the same place value.
Largest Value Identification
Understanding how to identify the decimal with the largest value involves more than just finding the bigger number. It's about methodically comparing place values.
  • The largest value identification begins with examining the tenths place of each number, as we've discussed.
  • Once the tenths place digits are compared, if no decision is reached due to a tie, move to the next place value (hundredths, thousandths, etc.).
In the scenario provided, 0.725 emerged as the largest value because its tenths digit of 7 surpasses those of the others in the set (3 in 0.357 and 1 in 0.125). This procedure highlights the simplicity and precision of place value comparison in deciding the magnitude of decimal numbers.

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