Problem 61 - Fundamentals of Mathematics

Question

For the following problems, perform the additions and round to the nearest hundred. $$ \begin{array}{r} 11,172 \\ 22,749 \\ 12,248 \\ \hline \end{array} $$

Step-by-Step Solution

Answer

46,200

Step 1: Add the Numbers

First, we need to add the three numbers together. Start by adding them up:\[11,172 + 22,749 + 12,248 = 46,169\]

Step 2: Determine the Rounding Digit

Identify the hundreds place in the total sum of 46,169. The hundreds digit here is 1.

Step 3: Apply Rounding Rules

Look at the digit to the right of the hundreds place, which is 6. Since this digit is 5 or higher, we round the hundreds place up from 1 to 2. The rest of the digits to the right of the hundreds place become zeros.

Step 4: Find the Rounded Result

After rounding, the number 46,169 becomes 46,200. Thus, the sum of the numbers, rounded to the nearest hundred, is 46,200.

Key Concepts

Addition

Addition is a fundamental mathematical operation that involves finding the total of two or more numbers. In the context of the exercise provided, the task is to add three numbers together. Here's how addition works:

• Start from the rightmost column, which is the units place, and move left, column by column.
• For each column, add the numbers, carrying over any value greater than 9 to the next column to the left.

In this exercise, we added:\[11,172 + 22,749 + 12,248 = 46,169\]The sum of these numbers gives us the initial result required to begin the rounding process later on. Addition sets the stage for the next step, which involves understanding the place value of the digits.

Place Value

Place value is crucial for understanding how each digit in a number contributes to its overall value. Each position in a number represents a different power of ten. From right to left, these are units (or ones), tens, hundreds, thousands, etc. In the sum obtained from the addition, 46,169:

• 9 is in the units place.
• 6 is in the tens place.
• 1 is in the hundreds place.
• 6 is in the thousands place.
• 4 is in the ten-thousands place.

Identifying the hundreds place is key when rounding to the nearest hundred. Here, the hundreds digit is 1. The place value dictates the magnitude of each digit and is essential when applying rounding rules.

Rounding Rules

Rounding rules help simplify numbers, making them easier to work with, especially when exact precision is not required. When rounding to the nearest hundred, follow these steps:

• Identify the digit in the hundreds place. For the number 46,169, this is 1.
• Look at the digit right next to it, in the tens place, which is 6.
• If this digit is 5 or more, round up the hundreds digit by one. Otherwise, keep it the same.

Since the digit in the tens place is 6, which is more than 5, we round up 1 to 2 in the hundreds place. After applying rounding rules:

• The hundreds digit changes to 2.
• All digits to the right of the hundreds place become zeros.

Thus, 46,169 rounds to 46,200. Rounding ensures simpler and more manageable results in calculations.