Problem 74 - Fundamentals of Mathematics

Question

Round 26,584 to the nearest ten.

Step-by-Step Solution

Answer

26,580

Step 1: Identify the Tens and Units Digits

Look at the number 26,584. Identify the tens digit, which is the second-to-last digit of the number, and the units digit, which is the last digit. For 26,584, the tens digit is 8 and the units digit is 4.

Step 2: Analyze the Units Digit

Determine if the units digit (4) is less than 5 or greater than or equal to 5. If it's less than 5, the tens digit remains unchanged. If it's 5 or more, increase the tens digit by 1. Here, 4 is less than 5.

Step 3: Determine the Rounded Number

Since the units digit (4) is less than 5, keep the tens digit (8) unchanged. Therefore, the rounded number is 26,580. Replace the units digit with a zero for proper rounding.

Key Concepts

Understanding the Tens Digit

In the process of rounding numbers, the tens digit plays a crucial role. This is the second-to-last digit of a whole number, and it determines the scale to which the number will be approximated when rounding to the nearest ten.

For example, in the number 26,584, the tens digit is 8.
This digit helps us make decisions about whether to increase or maintain the nearby digits, thereby simplifying numbers for ease of use.

Understanding the function of the tens digit is essential to mastering rounding.

• It gives us insight into the current size category of the number.
• When rounding, we only need to change the tens digit if the units digit dictates it.

By focusing on the tens digit, we can make effective and accurate rounding decisions.

Grasping the Units Digit

The units digit is another key determinant in the rounding process. It is the last digit in a number and decides whether the rounding affects the tens digit.

Taking the example of 26,584, the units digit is 4.
This number directly influences what happens to the tens digit when rounding occurs.

• If this digit is less than 5, as it is here, we keep the tens digit unchanged.
• If it were 5 or more, the tens digit would need to be increased by 1.

Understanding the role of the units digit makes the rounding process intuitive and straightforward, ensuring that every decimal place is accounted for correctly.

Step by Step Rounding Process

Rounding numbers can initially seem complex, but breaking it down into simple steps can make it clear and manageable. Let's go through each phase to understand how it works in practice.

1. **Identify the Key Digits**: First, pick out the tens digit and the units digit from the number.
In 26,584, the tens digit is 8, and the units digit is 4.
2. **Evaluate the Units Digit**: Here, we determine if the units digit will impact the tens digit. Since 4 is less than 5, it means no increase is needed for the tens digit.
3. **Apply the Rounding Rule**: When the units digit is less than 5, as it is here, retain the tens digit as is and replace the units digit with zero.
Hence, rounding 26,584 to the nearest ten results in 26,580.

This systematic approach ensures accuracy and helps maintain clarity when dealing with large or numerous numbers.