Problem 23 - Fundamentals of Mathematics

Question

For the following problems, complete the table by rounding each number to the indicated positions. 94,312 $$ \begin{array}{|l|l|l|l|} \hline \text { hundred } & \text { thousand } & \text { ten thousand } & \text { million } \\ \hline & & & \\ \hline \end{array} $$

Step-by-Step Solution

Answer

94,300 (hundred), 94,000 (thousand), 90,000 (ten thousand), 0 (million)

Step 1: Understanding Rounding

Rounding a number means adjusting it up or down to the nearest place value as specified. We will round the number 94,312 to different place values: hundred, thousand, ten thousand, and million. Remember, if the digit to the right of the place you're rounding to is 5 or more, round up. Otherwise, round down.

Step 2: Round to the Hundred

The hundred place in 94,312 is 3 (in the hundreds position). The digit to the right is 1 (in the tens position). Since 1 is less than 5, we round down. Thus, 94,312 rounded to the nearest hundred is 94,300.

Step 3: Round to the Thousand

The thousand place in 94,312 is 4. The digit to the right is 3 (in the hundreds position). Since 3 is less than 5, we round down. Thus, 94,312 rounded to the nearest thousand is 94,000.

Step 4: Round to the Ten Thousand

The ten thousand place in 94,312 is 9. The digit to the right is 4 (in the thousand position). Since 4 is less than 5, we round down. Thus, 94,312 rounded to the nearest ten thousand is 90,000.

Step 5: Round to the Million

For the million place, which does not exist in the number 94,312, assume it is 0. Since all the digits 9, 4, 3, 1, and 2 are less than 5, we round down and consider it as 0. Thus, 94,312 rounded to the nearest million is 0.

Key Concepts

Understanding Place Value

Place value is the value of where a digit is in a number. For example, in the number 94,312, each digit has a different place value:

• The '9' is in the ten thousand place.
• The '4' is in the thousand place.
• The '3' is in the hundred place.
• The '1' is in the ten place.
• The '2' is in the one place.

Knowing the place value helps us determine the size of the number and is crucial for operations like rounding.

Number Rounding Basics

Rounding numbers is a method used to simplify numbers to make them easier to work with. It involves adjusting the digits up or down based on specific rules.

• If the digit immediately right of the place you are rounding is 5 or higher, you round up.
• If it's less than 5, you round down.

This helps in making approximations while maintaining a value close to the original number.

Rounding to the Nearest Hundred

When rounding to the nearest hundred, you focus on the hundreds digit and the digit to its immediate right. For example, in 94,312:

• The hundreds digit is 3.
• The digit to the right, in the tens position, is 1.

Since 1 is less than 5, you keep the hundreds digit the same and turn all digits to the right into zeros. Therefore, 94,312 becomes 94,300 when rounded to the nearest hundred.

Rounding to the Nearest Thousand

To round to the nearest thousand, you look at the thousands digit and the digit following it. Take the number 94,312:

• The thousands digit is 4.
• The hundreds digit, which follows, is 3.

Since 3 is less than 5, you do not increase the 4. Replace the hundreds and below with zeros, resulting in 94,000.

Rounding to the Nearest Ten Thousand

Rounding to the nearest ten thousand looks at the ten thousands digit and the digit next to it. For instance, in 94,312:

• The ten thousand digit is 9.
• The thousands digit is 4.

Since 4 is less than 5, the 9 remains the same and all digits to the right become zeros. Thus, 94,312 rounded to the nearest ten thousand is 90,000.

Rounding to the Nearest Million

When rounding to the nearest million, consider the digit in the millions place even if it is 0. For 94,312:

• No digit exists in the millions place, so consider it as 0.
• All digits 9, 4, 3, 1, and 2 are less than 5.

Hence, rounding results in all zeros, making 94,312 rounded to the nearest million, 0. This shows how smaller numbers can drastically simplify to zero at very high place values.