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Chapter 1: Problem 3

Round each whole number to the given place value. 635 to the nearest ten

Short Answer

Expert verified
635 rounded to the nearest ten is 640.

Step by step solution

01

Identify the Target Place Value

The exercise asks us to round the number 635 to the nearest ten. The tens digit in the number 635 is 3, which we need to focus on.
02

Identify the Neighboring Digit

To decide whether to round up or down, look at the digit to the immediate right of the tens place. In 635, this digit is 5.
03

Apply the Rounding Rule

According to rounding rules, if the neighboring digit is 5 or greater, we round up. Since 5 is equal to 5, we'll round 635 up to the next ten.
04

Adjust the Tens Digit

Increase the tens digit from 3 to 4, and change all following digits to zero. Therefore, 635 becomes 640.

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Key Concepts

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

Place Value
When rounding numbers, understanding place value is the key starting point. Each digit in a number has a specific place and value, based on its position.
For example, in the number 635, we have:
  • 6 is in the hundreds place, representing 600.
  • 3 is in the tens place, representing 30.
  • 5 is in the ones place, representing 5.
Knowing which place value you're rounding to helps you determine the digit you'll be working with. In 635, if we're rounding to the nearest ten, we focus on the tens place, which is the digit 3. Understanding place value ensures clarity in what each digit represents.
Rounding Rules
Rounding involves certain rules to decide whether to increase or leave the focused digit as is. Here are the standard rounding rules:
  • If the digit to the right of your rounding position is 5 or more, round up the digit you are focusing on.
  • If the digit is less than 5, leave the rounding focus digit the same.
For the number 635, we're examining the tens place, which contains the digit 3. We must look at the digit immediately to its right, the 5, to apply these rules. Since 5 is equal to 5, we round up, turning the 3 into a 4.
Nearest Ten
When rounding to the nearest ten, you adjust the number to the closest ten based on the rounding rules. This involves either moving up to the next multiple of ten or staying at the current one.
Consider the number 635:
  • Identify the tens place, which is 3.
  • Look at the following digit, 5, which tells us we need to round up.
  • As a result, we increase the tens digit to 4 and replace all digits that follow it with zero.
Therefore, rounding 635 to the nearest ten results in 640.
Digits
Digits are the individual numbers that make up larger numbers. In rounding, each digit has its role: either being the digit you round or a potential influencer in the rounding decision.
Using 635 as an example:
  • The digit 3 is our focus, based on the place value we are rounding to.
  • The digit 5 is the influencer, determining whether 3 will become 4.
  • Understanding each digit鈥檚 influence helps you accurately apply rounding rules.
By understanding the power of individual digits, making the right rounding decision becomes straightforward.

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