Problem 37 - Fundamentals of Mathematics

Question

Round 506,207 to the nearest thousand.

Step-by-Step Solution

Answer

506,000

Step 1: Identify the Thousand's Place

In the number 506,207, the thousand's place is the digit 6. This is the digit we will round based on the digit to its immediate right.

Step 2: Check the Hundreds Place

The digit in the hundreds place is 2 (from 206). According to rounding rules, if this digit is 4 or less, we round down, and if it's 5 or more, we round up.

Step 3: Apply Rounding Rule

Since the digit in the hundreds place is 2, which is less than 5, we round down. This means the thousand's place stays the same, and all digits to the right become zero.

Step 4: Write the Rounded Number

The entire number, when rounded to the nearest thousand becomes 506,000.

Key Concepts

Thousand's Place

When you're asked to round a number to the nearest thousand, the first step involves identifying the digit in the thousand's place. The thousand's place refers to the fourth digit from the right in a number. By locating this digit, you can determine which specific number needs adjusting based on rounding rules.
For example, in the number 506,207, the thousand’s place is occupied by 6. This makes 6 the focal point for this rounding exercise. Knowing this helps establish the starting point for deciding whether the number needs to be rounded up or remains unchanged.

Rounding Rules

Rounding numbers follows general rules to help simplify estimates and maintain accuracy when full detail isn't necessary. The basic principle of rounding is as follows:

• If the digit to the immediate right of your rounding digit is 5 or greater, round up the digit in question.
• If that digit is less than 5, leave the rounding digit as it is, effectively rounding down.

In this exercise, the digit in the hundreds place helps determine if the number in the thousand's place remains the same or increases. Applying the rules correctly ensures the number is adjusted in accordance with standard mathematical practice.
These rules simplify larger numbers, making complex calculations easier to work with in an everyday context.

Hundreds Place

The hundreds place plays a crucial role when rounding to the nearest thousand. It is the third position from the right side of a multi-digit number. This digit holds the power to sway whether the number rounds up or stays the same.
In examining 506,207, we find the digit 2 in the hundreds place. Given that this digit is less than 5, it instructs us to "round down," which essentially means keeping the number in the thousand's place unchanged.
After rounding, all digits to the right of the thousand's place, including the hundreds, tens, and units, are converted to zeros. This conversion ensures the number accurately reflects the required number of thousands, providing a cleaner, more rounded figure.