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Chapter 1: Problem 26

In the following, round to the indicated place value. Round to the nearest ten. ? 792 ? 5,647

Short Answer

Expert verified
792 rounds to 790, and 5,647 rounds to 5,650.

Step by step solution

01

Identify the digit at the tens place

To round to the nearest ten, first identify the digit in the tens place. For the number 792, this is the digit 9. For the number 5,647, this is the digit 4.
02

Identify the digit to the right of the tens place

Next, look at the digit immediately to the right of the tens place. For 792, this is the digit 2. For 5,647, this is the digit 7.
03

Apply the rounding rule to each number

If the digit to the right of the tens place is 5 or greater, increase the tens digit by 1. If it is less than 5, leave the tens digit as it is. For 792, the digit to the right is 2 (less than 5), so the tens digit (9) stays the same. For 5,647, the digit to the right is 7 (greater than or equal to 5), so the tens digit (4) increases by 1 to become 5.
04

Replace digits to the right with zeroes

Replace all digits to the right of the tens place with zeroes to complete the rounding process. Therefore, 792 rounded to the nearest ten is 790, and 5,647 rounded to the nearest ten is 5,650.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Place Value
Place value is a fundamental concept in mathematics. It helps us understand the value of each digit based on its position in a number.

For example, the number 792 has three digits: 7, 9, and 2.
  • The digit '7' is in the hundreds place, so it represents 700.
  • The digit '9' is in the tens place, so it represents 90.
  • The digit '2' is in the ones place, so it represents 2.
Understanding place value allows us to break down numbers and make rounding simpler.

By focusing on the digit in the tens place, we can decide whether to round up or down based on the digit to its right. This grasp of place value sets the stage for effective rounding.
Rounding Rules
Rounding numbers follows simple rules that make it quick and easy. When rounding to the nearest ten, these rules are key:

  • Identify the digit in the place value you are rounding to (here it's the tens place).
  • Look at the digit immediately to the right of the tens place.
  • If that digit is 5 or greater, increase the tens digit by 1.
  • If that digit is less than 5, keep the tens digit the same.
For instance, in the number 792:

  • The tens place digit is 9.
  • The digit right next to it is 2, which is less than 5.
So, 792 rounds down to 790.
The process is the same for any number, such as 5,647, where the tens place digit is 4 and the digit right next to it is 7. Since 7 is greater than 5, we round up, making it 5,650.
Nearest Ten
Understanding how to round to the nearest ten ensures quick approximation. This method simplifies calculations and helps in estimating values.

First, identify the tens place digit and the digit right next to it. Applying our rounding rules, decide whether to round up or down.

For example:
  • 792 becomes 790 after rounding down.
  • 5,647 becomes 5,650 after rounding up.
These steps ensure that numbers are rounded correctly, making it easier to handle large numbers without compromising too much accuracy.

Practicing with different numbers will strengthen this technique and build confidence in mathematical handling of numbers.

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