Problem 30 - Fundamentals of Mathematics

Question

In 1979,19,309,000 people in the United States received federal food stamps. Round to the nearest ten thousand.

Step-by-Step Solution

Answer

19,310,000

Step 1: Identify the Number

The given number of people is 19,309,000. This is the number we are going to round.

Step 2: Understand the Rounding Process

To round to the nearest ten thousand, we need to look at the digits in the thousands and ten thousands places. The ten thousand digit is in the seventh position from the right.

Step 3: Examine the Digits

In the number 19,309,000, the digit in the ten thousand place is 0, and the digit in the thousand place is 9.

Step 4: Apply the Rounding Rule

Since the digit in the thousand's place is 9, which is greater than 5, we increase the ten thousand's place by 1. Thus, we increase the 0 in the ten-thousands place by 1, resulting in 10.

Step 5: Round the Number

The number after rounding 19,309,000 to the nearest ten thousand becomes 19,310,000.

Key Concepts

Nearest Ten Thousand

Rounding a number to the nearest ten thousand can be a practical skill in mathematics, especially when dealing with large numbers. For instance, understanding data in reports or simplifying figures for easy communication can often involve rounding.
To round to the nearest ten thousand, you'll focus your attention on both the ten thousand's and the thousand's place of the number.

• The ten thousand's place is the fourth digit from the right in a number.
• The thousand's place is the third digit from the right.

Once these place values are identified, you decide whether to round up or stay the same based on the digit in the thousand's place. Always remember this process as it will guide you in accurately rounding numbers to not just ten thousand, but other place values as well.

Rounding Rules

Rounding rules are essential when you want to simplify a number while still keeping it consistent and meaningful. The general rule for rounding is as follows: When you look at the digit to the right of the place you are rounding to:

• If it is 5 or greater, round the chosen digit up by one.
• If it is less than 5, keep the chosen digit the same and eliminate all other digits to the right.

In our given example of 19,309,000, when rounding to the nearest ten thousand, you look at the digit in the thousand's place, which is 9. Since 9 is greater than 5, you round the ten thousand's place from 0 up to 1. This process helps in reducing complexities without losing significance in numbers.

Mathematics Education

Rounding numbers is a fundamental concept in mathematics education. It is typically introduced in primary school and is used throughout all levels of learning, including higher education. The ability to round numbers efficiently is crucial for solving complex mathematical problems and performing everyday estimations.
In teaching and learning, rounding helps students understand the concept of place value, which is the basis of our number system. This knowledge assists in various applications:

• Helps in estimating values quickly when exact numbers aren’t necessary.
• Simplifies complex calculations without a need for exact answers.
• Facilitates understanding of orders of magnitude.

Developing an intuition for rounding numbers is an integral part of mathematics, allowing students to handle large figures efficiently. It also sets the foundation for more advanced topics like statistics and data analysis.