Problem 26 - Fundamentals of Mathematics

Question

For the following problems, complete the table by rounding each number to the indicated positions. 388,551 $$ \begin{array}{|l|l|l|l|} \hline \text { hundred } & \text { thousand } & \text { ten thousand } & \text { million } \\ \hline & & & \\ \hline \end{array} $$

Step-by-Step Solution

Answer

Hundred: 388,600; Thousand: 389,000; Ten Thousand: 390,000; Million: 0.

Step 1: Rounding to the nearest hundred

To round 388,551 to the nearest hundred, look at the tens digit (5). Since it is 5 or higher, round the hundreds digit (5) up by 1. Therefore, 388,551 rounded to the nearest hundred is 388,600.

Step 2: Rounding to the nearest thousand

To round 388,551 to the nearest thousand, look at the hundreds digit (5). Since it is 5 or higher, round the thousands digit (8) up by 1. Therefore, 388,551 rounded to the nearest thousand is 389,000.

Step 3: Rounding to the nearest ten thousand

To round 388,551 to the nearest ten thousand, look at the thousands digit (8). Since it is 5 or higher, round the ten thousands digit (8) up by 1. Therefore, 388,551 rounded to the nearest ten thousand is 390,000.

Step 4: Rounding to the nearest million

To round 388,551 to the nearest million, note that the number is less than 500,000. Therefore, the rounded number is 0.

Key Concepts

Place Value

Place value forms the cornerstone of understanding numbers in mathematics. It refers to the value a digit holds in a number based on its position.

• In the number 388,551, each digit has a unique place value.
• The number is comprised of hundreds, thousands, and more, influencing how we round or compare numbers.

Understanding place value is crucial for rounding numbers correctly. For example, in 388,551, the '8' in the ten-thousands place represents 80,000. Knowing how to identify and use each digit's place value makes operations like addition, subtraction, and rounding easier.

Rounding to Nearest Hundred

Rounding to the nearest hundred involves looking closely at the tens digit. For 388,551, the tens digit is 5.

• If the tens digit is 5 or more, increase the hundreds digit by 1.
• Otherwise, keep the hundreds digit the same and change the tens and ones to 0.

Thus, rounding 388,551 to the nearest hundred gives us 388,600, as the tens place has a 5.

Rounding to Nearest Thousand

When rounding to the nearest thousand, the spot to check is the hundreds digit. For instance, in 388,551, the hundreds digit is also a 5.

• Typically, a hundreds digit of 5 or more means the thousands digit should be increased by 1.
• Otherwise, the thousands digit remains unchanged, with hundreds, tens, and ones converted to 0.

In this case, 388,551 rounds up to 389,000.

Rounding to Nearest Ten Thousand

Rounding to the nearest ten thousand involves varying focus to the thousands digit. Looking at 388,551, the thousands digit is 8.

• Like before, if the thousands digit is 5 or higher, raise the ten thousands digit by 1.
• If not, the ten thousands remain unchanged, as lower digits become 0.

Therefore, 388,551 becomes 390,000 when rounded to the nearest ten thousand.

Rounding to Nearest Million

Rounding to the nearest million checks the entire number's size relative to 500,000. For 388,551, this is particularly straightforward.

• If a number is less than 500,000, it rounds down to 0.
• Numbers 500,000 or more, but less than 1,500,000, round up to 1,000,000.

In our example, since 388,551 is below 500,000, it rounds to 0.