Problem 8 - Fundamentals of Mathematics

Question

Round 427 to the nearest hundred.

Step-by-Step Solution

Answer

427 rounded to the nearest hundred is 400.

Step 1: Identify the Hundreds and Tens Digits

The number 427 is composed of hundreds, tens, and unit digits. The hundreds digit is 4, and the tens digit is 2. We'll focus on these digits to decide on rounding.

Step 2: Evaluate the Tens Digit

Look at the tens digit, which is 2. According to rounding rules, if the tens digit is less than 5, then we keep the hundreds digit as it is and change the tens and units digit to 0.

Step 3: Perform the Rounding

Since the tens digit is 2, which is less than 5, we round 427 down to the nearest hundred. The rounded number is 400.

Key Concepts

Rounding Rules

Rounding is a mathematical process used to simplify numbers, making them easier to work with or understand. The basic idea is to approximate a number to the nearest specified place value (like the nearest ten, hundred, or thousand). Here's a simple and clear guide for rounding:

• First, identify the digit at the place you need to round to. This is your target digit.
• Look at the digit immediately to the right of your target digit. This is the focus digit that decides whether to round up or leave the target digit the same.
• If the focus digit is 5 or greater, increase the target digit by one and change all digits to its right to zero.
• If the focus digit is less than 5, keep the target digit the same and change all digits to its right to zero.

Understanding these rounding rules is crucial for making accurate and efficient calculations. By applying these steps, rounding becomes a straightforward task, simplifying numbers without significantly changing their value.

Hundreds Digit

When you round to the nearest hundred, the hundreds digit becomes the target digit. This digit represents the number of hundreds in a given number.
For instance, in the number 427, the hundreds digit is 4. This number tells us that there are four complete sets of one hundred within 427.

When rounding, the hundreds digit is the primary focus, as changes to it will determine how much we adjust the original number. If changes need to be made based on the rounding rules, the hundreds digit may increase by one, or stay the same, while remaining digits become zero. This adjustment simplifies the number, making large numerical calculations more manageable.

Tens Digit

The tens digit plays a crucial role in determining how a number will be rounded when rounding to the nearest hundred. It serves as the focus digit in rounding, similar to a tie-breaker.
In our example, 427 has a tens digit of 2. When rounding, examine this tens digit to decide the fate of the hundreds digit.

• If this tens digit is 5 or more, it pushes the hundreds digit up by one, rounding the total number higher.
• If it is less than 5, it keeps the hundreds digit unchanged, rounding down the complete number.

This key function of the tens digit ensures that rounded values are not only simplified but also as accurate as possible to their original form. It acts as the final determining factor in the rounding process.