Problem 8 - Fundamentals of Mathematics

Question

For the following problems, complete the table by rounding each number to the indicated positions. 91,803 $$ \begin{array}{|l|l|l|l|} \hline \text { hundred } & \text { thousand } & \text { ten thousand } & \text { million } \\ \hline & & & \\ \hline \end{array} $$

Step-by-Step Solution

Answer

91,800; 92,000; 90,000; 0

Step 1: Rounding to the nearest hundred

To round 91,803 to the nearest hundred, we look at the tens digit, which is 0. Since it is less than 5, we round down, leaving the hundreds digit unchanged. The rounded number is 91,800.

Step 2: Rounding to the nearest thousand

To round 91,803 to the nearest thousand, we look at the hundreds digit, which is 8. Since it is 5 or more, we round up, increasing the thousands digit by 1. The rounded number is 92,000.

Step 3: Rounding to the nearest ten thousand

To round 91,803 to the nearest ten thousand, we look at the thousands digit, which is 1. Since it is less than 5, we round down, leaving the ten thousand digit unchanged. The rounded number is 90,000.

Step 4: Rounding to the nearest million

To round 91,803 to the nearest million, we would consider its size compared to a million. Since 91,803 is much smaller than a million, it rounds to 0.

Key Concepts

Rounding to the Nearest Hundred

Rounding numbers can simplify them, making them easier to work with. To understand rounding to the nearest hundred, let's explore this concept. When you round a number to the nearest hundred, you focus on the tens digit—the digit immediately to the right of the hundreds place.
If the tens digit is 5 or greater, you increase the hundreds digit by 1. If it's less than 5, you keep the hundreds digit the same.
Let's illustrate this with an example: if our number is 91,803, our tens digit is 0, which is less than 5. Therefore, we leave the hundreds digit, 8, unchanged. The closest hundred is thus 91,800.

• Find the hundreds digit and the tens digit.
• If the tens digit is 5 or more, round up.
• If the tens digit is less than 5, round down.
• The rounded number: 91,800.

Rounding to the Nearest Thousand

The process of rounding to the nearest thousand focuses on simplifying numbers by evaluating the hundreds place. You check the hundreds digit to decide where the number rounds to.
In our example, 91,803, the hundreds digit is 8. Since this digit is 5 or greater, we round up, increasing the thousands digit by 1.
This gives us 92,000—an easier number to work with compared to the original.

• Identify the thousands and hundreds digit.
• Round up if the hundreds digit is 5 or more.
• Round down if the hundreds digit is less than 5.
• The rounded number: 92,000.

Rounding to the Nearest Ten Thousand

Understanding rounding to the nearest ten thousand involves examining the thousands digit of a number. This digit is key to deciding if you round the number up or keep it the same.
For our number, 91,803, the thousands digit is 1. Since this is less than 5, we round down. This means the ten thousand digit stays unchanged.
Therefore, rounding 91,803 to the nearest ten thousand results in 90,000.

• Locate the ten thousand and thousands digit.
• If the thousands digit is 5 or more, round up.
• If the thousands digit is less than 5, round down.
• The rounded number: 90,000.

Rounding to the Nearest Million

Rounding to the nearest million can feel different since you're working with such large numbers. In this process, assess whether the number is closer to zero or one million.
For a number like 91,803, since its size is vastly smaller than a million, it rounds to 0.
This technique is useful when dealing with large scale figures, where the exact smaller numbers are not significant in comparison.

• Consider if the number is closer to zero or one million.
• If closer to zero, round down to 0.
• If number was closer to a million, round up to 1,000,000.
• The rounded number: 0.