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Chapter 3: Problem 64

Round to the nearest ten: \(45,765 .\) [1.6a]

Short Answer

Expert verified
45,770

Step by step solution

01

Identify the Tens Place

Look at the number 45,765. Identify the digit in the tens place, which is the second-to-last digit. In this case, the digit in the tens place is 6.
02

Look at the Ones Digit

Now, look at the digit to the right of the tens place, which is the ones place. The digit in the ones place is 5.
03

Determine Rounding Direction

If the digit in the ones place (5 in this case) is 5 or greater, round the tens place digit up by 1. Otherwise, leave the tens place digit unchanged.
04

Apply Rounding and Zero Out the Ones Place

Since the ones place digit (5) is 5 or greater, add 1 to the tens place digit (6) to get 7, and convert the ones place digit to 0. Therefore, 45,765 rounded to the nearest ten is 45,770.

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Key Concepts

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

place value
In mathematics, each digit in a number has a specific position or place called the place value. These values determine the value of the digit in the number. For example, in the number 45,765, each digit has a different place value.
The place values starting from the right are:
  • Ones place (5)
  • Tens place (6)
  • Hundreds place (7)
  • Thousands place (5)
  • Ten-thousands place (4)
Understanding place value helps us perform various operations, such as rounding numbers. Identifying the digit in the tens place (which is 6 in this case) is the first step in rounding to the nearest ten.
rounding rules
Rounding is a mathematical process used to simplify numbers, making them easier to work with. The key is to follow specific rounding rules. When rounding to the nearest ten, focus on the digit in the ones place.
The rules for rounding are:
  • If the digit in the ones place is 0-4, keep the tens place digit the same, and change the ones place digit to 0.
  • If the digit in the ones place is 5-9, increase the tens place digit by 1, and change the ones place digit to 0.
For example, in 45,765, since the ones place digit is 5 (which is 5 or greater), we round the tens place digit up from 6 to 7. The rounded number becomes 45,770.
tens place
The tens place is the second-to-last digit in a number. It represents how many sets of ten are in the number. Understanding the tens place is crucial for rounding to the nearest ten.
Returning to our example, 45,765, the digit in the tens place is 6. By knowing this, we can determine whether to round up or down based on the digit in the ones place. Since the ones place digit is 5, we round the tens place digit (6) up to 7. Thus, the resulting number after rounding is 45,770.
Learning how to identify and work with the tens place ensures accurate rounding, making numerical operations simpler and more manageable.

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