Problem 4 - Fundamentals of Mathematics

Question

Use the method of rounding whole numbers to solve each problem. Round 39 to the nearest hundred.

Step-by-Step Solution

Answer

39 rounds to 0 when rounded to the nearest hundred.

Step 1: Identify the place value to round to

To round 39 to the nearest hundred, first identify the hundreds place. In this case, the hundreds place is represented by the digit '0' before 39 since 39 is less than 100.

Step 2: Look at the digit in the tens place

Next, look at the digit right after the hundreds place, which is the tens place. For the number 39, the digit in the tens place is 3.

Step 3: Decide whether to round up or down

If the digit in the tens place is 5 or more, you'll round up the hundreds digit. If it is less than 5, you'll round down and keep the hundreds digit the same. In this case, 3 is less than 5, so you will round down.

Step 4: Apply rounding to the number

Since you are rounding down and the hundreds place is represented by zero, 39 rounds to 0 when rounding to the nearest hundred.

Key Concepts

Understanding Place Value

Place value is a cornerstone concept in mathematics and helps us understand the value of each digit in a number based on its position. It is important when rounding numbers, as it determines which digits affect the rounding process.

To explain, each place in a number has a different value:

• The unit place holds the smallest value and represents ones.
• The tens place is next, representing ten times the value of the unit place.
• The hundreds place follows, representing ten times the value of the tens place, or a hundred times the unit place.

For example, in the number 275, the 7 is in the tens place, giving it a value of 70, while the 2 in the hundreds place represents 200. Understanding place value is crucial for rounding because it lets us know which digit governs the size of the number.

Exploring the Tens Place

The tens place is often key when it comes to rounding numbers because it determines whether you round up or down. This place is the second position from the right in a whole number.

Let’s see how the tens place works using the number 39.

• The digit in the tens place is 3, meaning it represents 30 (as it is 3 tens).
• When rounding numbers, especially considering larger place values, the tens place tells you if you should increase the digit in the next significant place (like the hundreds place) or keep it as it is.

If the digit in the tens place is 5 or higher, we round up, which means increasing the digit in the place we are rounding to. If it's 4 or lower, we round down, or keep the digit in the target place the same. In our example, 39 has a tens digit of 3, so it informs us to round down, hence toward zero when aiming to the nearest hundred.

Rounding to the Nearest Hundred

Rounding to the nearest hundred means adjusting a number to the closest hundred mark. This operation smooths out numbers for easier calculation or approximation.

To round any number to the nearest hundred:

• First, locate the hundreds place. If the number is less than 100, consider the hundreds place as 0.
• Second, you must examine the digit in the tens place, as it directs the rounding decision.
• Lastly, apply the rounding rule based on the tens digit. For tens digit 5 or more, round up. For fewer than 5, round down.

Applying this to the number 39: - The hundreds digit is 0 because 39 is less than 100. - The tens digit is 3, which is below 5. Consequently, you round down 39 to 0 when rounding to the nearest hundred. Understanding this rule allows you to round numbers quickly and accurately to simplify complex math problems or data.