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Chapter 1: Problem 14

Round each of the numbers to the nearest ten. $$32,807$$

Short Answer

Expert verified
Round 32,807 to 32,810.

Step by step solution

01

Identify Place Value

Examine the number 32,807 and determine which digit is in the tens place. The number is written as 32,807 and the digit in the tens place is 0.
02

Examine the Ones Digit

Look at the digit right after the tens place, which is the ones place, to decide whether to round up or keep the tens digit the same. In this case, the ones place has the digit 7.
03

Determine Rounding Action

Since the ones digit is 7, which is 5 or greater, we need to round up. This means we increase the tens digit (0) by 1.
04

Apply Rounding

Increase the tens digit from 0 to 1, and change all the digits to the right to zero. Therefore, the number 32,807 is rounded to 32,810.

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Key Concepts

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

Understanding Place Value
Place value is a fundamental concept in mathematics, which helps us understand the position of each digit in a number. It assigns a value to each digit, based on its position within the number sequence. For example, in the number 32,807:
  • The 3 is in the ten-thousands place.
  • The 2 is in the thousands place.
  • The 8 is in the hundreds place.
  • The 0 is in the tens place.
  • The 7 is in the ones place.
This understanding allows us to determine which digits are important when performing operations like rounding numbers. Each place represents a power of ten, making it easier to perform mathematical operations. Knowing the place value helps us in identifying which digit needs attention when rounding numbers.
The Tens Place in Rounding
The tens place is a critical factor when rounding numbers because it helps determine the digit we need to alter. In our example with the number 32,807, the tens place is occupied by the digit 0. The role of the tens place in rounding is twofold:
  • To act as the immediate focus of the rounding operation.
  • To potentially change if the number in the ones place suggests it.
When we need to round to the nearest ten, we look at the tens place to decide whether the entire number should be rounded up or remain the same. If the ones digit is 5 or greater, we increase the tens digit by 1 and convert all rightward digits to zero.
The Role of the Ones Place
The ones place, located to the immediate right of the tens place, plays a decisive role when rounding numbers. It is this digit that dictates whether the digit in the tens place should stay the same or increase. Here's how it works:
  • If the ones digit is less than 5, the tens digit stays the same.
  • If the ones digit is 5 or greater, the tens digit increases by one.
In our example of 32,807, the ones place has the digit 7, which tells us to round up. This means increasing the 0 in the tens place to 1. Understanding the role of the ones place in rounding helps ensure accuracy and ensures students clearly see how place values interact to adjust numbers.

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Most popular questions from this chapter

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