Problem 29 - Fundamentals of Mathematics

Question

In 1950 , there were 5,796 cases of diphtheria reported in the United States. Round to the nearest hundred.

Step-by-Step Solution

Answer

The rounded number is 5,800.

Step 1: Identify the number to round

We are given the number 5,796. Our task is to round this number to the nearest hundred.

Step 2: Find the hundreds place

Look at the number 5,796. The hundreds place is the third digit from the right, which is 7 in this case.

Step 3: Determine the rounding digit

To round to the nearest hundred, look at the digit right after the hundreds place. In 5,796, this is the tens digit, which is 9.

Step 4: Follow rounding rules

Since the tens digit is 9, which is greater than or equal to 5, we round up the hundreds digit. This means we add 1 to the 7 in the hundreds place.

Step 5: Rewrite the number

Since the hundreds place (7) is rounded up to 8, 5,796 becomes 5,800.

Key Concepts

Rounding to Nearest Hundred

Rounding numbers such as 5,796 to the nearest hundred is a common task that can simplify complex figures and make them easier to understand. When we round to the nearest hundred, we want to find the closest "century" mark. This helps us communicate numbers more clearly, especially when exact figures aren't necessary. In our example of 5,796, the nearest hundred could be either 5,700 or 5,800. To decide which, we analyze the digits based on place value and rounding rules. Each digit plays a vital role in rounding, bringing us neatly to the next concept.

Place Value

Place value is fundamental to understanding how to round numbers effectively. Each digit in a number has a value determined by its position. In the number 5,796, the "hundreds" place is the third digit from the right. This means that 7 represents 700 (or seven hundred). Knowing the place value guides us in deciding which digit to consider when rounding. This is why determining that 5,796's hundreds place is 7 is the first step toward identifying which digit may change when rounding. By locating the correct place value, we set the groundwork for applying the rounding rules.

Rounding Rules

Once we identify the significant place value, we turn to rounding rules. These rules dictate how we adjust our number. Looking at 5,796, we focus on the digit immediately following the hundreds place, which is 9 in this case. Here are the basic rounding rules:

• If the digit is 5 or greater, we increase the target place value by one.
• If the digit is less than 5, we leave the target place value unchanged.

In our number, since the following digit (9) is greater than 5, we apply the first rule, increasing the hundreds place by one. The 7 in 5,796's hundreds place becomes 8, changing the number to 5,800. This adjustment reflects our number rounded to the nearest hundred, ensuring our math is both precise and clear.