Problem 66 - Fundamentals of Mathematics

Question

(Section 1.4) Round 2,614,000 to the nearest thousand.

Step-by-Step Solution

Answer

2,614,000 remains the same when rounded to the nearest thousand.

Step 1: Identify the Digit to Round To

To round 2,614,000 to the nearest thousand, we first need to identify the digit at the thousand's place. In the number 2,614,000, the thousand's place is the fourth digit from the right, which is 4.

Step 2: Look at the Next Digit

The rule for rounding is to look at the digit immediately to the right of the thousand's place: the hundreds place. In 2,614,000, this digit is 0.

Step 3: Apply Rounding Rules

If the digit in the hundreds place (which is 0 in this case) is less than 5, you keep the thousand's digit as it is and round all following digits down to 0. Since 0 is less than 5, we do not need to change the thousand's digit 4.

Step 4: Write the Rounded Number

All digits to the right of the thousand's place become zeros. Thus, 2,614,000 rounded to the nearest thousand is 2,614,000.

Key Concepts

Understanding Place Value

Place value is a fundamental concept in mathematics that refers to the position of a digit in a number and its corresponding value. Each position in a number has a different value, determined by this system.
For example, in the number 2,614,000, each digit has its place value:

• 2 is in the millions place
• 6 is in the hundred thousands place
• 1 is in the ten thousands place
• 4 is in the thousands place
• 0s fill in the hundreds, tens, and ones places

Knowing where each digit sits helps us understand its value. This is essential when you need to perform tasks like rounding, as you'll be interested in which digit determines how the rest of the number changes.

The Rules of Rounding

Rounding numbers is a useful skill that simplifies numbers, making them easier to work with. To round a number, you'll follow specific rules that depend on the digit next to the place value you are rounding to.
Here’s how it works:

• Find the digit in the place you're rounding to.
• Look at the digit to the immediate right.
• If this digit is 5 or more, increase the rounding place digit by 1.
• If it is less than 5, leave the rounding place digit unchanged.
• Everything to the right of the rounding place digit becomes zero.

With practice, applying these rounding rules becomes intuitive, allowing for quick adjustments in various mathematical scenarios.

Rounding to the Thousands Place

Rounding to the thousands place involves focusing on the fourth digit from the right in a whole number. This digit holds the thousands place value, which is crucial when adjusting the number for simplicity.
For example, in rounding the number 2,614,000 to the nearest thousand, the digit in the thousands place is 4. To determine if it stays the same or changes, you check the digit to the right, which is in the hundreds place.
In our example, the hundreds place digit is 0. According to rounding rules, since 0 is less than 5, the thousands digit of 4 remains unchanged.
Therefore, 2,614,000 stays as it is when rounded to the nearest thousand, illustrating how understanding the thousands place helps in simplifying numbers accurately.