Problem 476 - Prealgebra

Question

Round to the nearest hundred. $$75,992$$

Step-by-Step Solution

Answer

76,000

Step 1: Identify the hundreds and tens digits

In the number 75,992, the hundreds digit is 9 and the tens digit is also 9.

Step 2: Examine the tens digit

The tens digit is 9. If a digit in the tens place is 5 or more, the hundreds digit is increased by 1.

Step 3: Adjust the hundreds digit

Since the tens digit is 9, add 1 to the hundreds digit. Therefore, the hundreds digit (9) becomes 10. As a result, change the thousands digit (5) to 6.

Step 4: Set other digits to zero

The digits in the tens and units places are converted to zero. Thus, the number after rounding is 76,000.

Key Concepts

Place Value

Understanding place value is essential for number rounding. Place value refers to the value of each digit in a number based on its position.
Each position represents a power of 10. For instance, in the number 75,992:

• The '2' is in the units place.
• The '9' is in the tens place.
• The other '9' is in the hundreds place.
• The '5' is in the thousands place.
• The '7' is in the ten-thousands place.

Understanding this structure allows you to realize how altering one digit affects the entire number. It's crucial to become comfortable with identifying these positions quickly, as they are fundamental to rounding numbers correctly.

Nearest Hundred

When rounding to the nearest hundred, you focus on the hundreds place and the digit right next to it, which is the tens place.
For example, to round 75,992 to the nearest hundred, follow these steps:

• Identify the hundreds digit, which is 9.
• Look at the tens digit, which is also 9.

The rule is straightforward: if the tens digit is 5 or more, you round up by increasing the hundreds digit. If it's less than 5, you keep the hundreds digit the same.
In this case, since the tens digit is 9, you increase the hundreds digit from 9 to 10. This has an interesting effect: changing the thousands digit (5) to 6 because 10 is another higher place value.

Number Rounding

Number rounding simplifies a number while keeping its value close to the original. Here's a detailed look at how to round a number:

• Identify the digit to round to (in our case, the hundreds place).
• Look at the next smallest place value (tens place).
• If the digit in the tens place is 5 or more, increase the hundreds digit by 1.
• If it's less than 5, keep the hundreds digit the same.

Once the decision to round up or down is made, all digits to the right of the target place become zero. So for 75,992 rounded to the nearest hundred, we get 76,000. Here’s how:
Since the tens place digit (9) is greater than 5, add 1 to the 9 in the hundreds place to make it 10, causing the thousands digit to increase. Finally, replace all digits to the right of the hundreds place with zero.