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Chapter 3: Problem 51

Round each number to the given place value. 586 to the nearest ten

Short Answer

Expert verified
586 rounds to 590.

Step by step solution

01

Identify the place value to round to

We are asked to round the number 586 to the nearest ten. Therefore, we need to focus on the tens place in the number, which is the digit 8.
02

Look at the digit in the next smallest place

To determine whether to round up or stay the same, look at the digit in the ones place, which is 6. According to rounding rules, if this digit is 5 or greater, we round up.
03

Round the number

Since the digit in the ones place is 6 (which is greater than 5), we round up the tens place. Thus, the 8 in the tens place becomes 9, and the number becomes 590.

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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 crucial concept in understanding our number system. It refers to the value of a digit depending on its position in a number. Each position represents a different power of ten.
  • The rightmost digit represents units or ones place.
  • Moving left, the next digit represents tens place, which is valued at ten times the units place.
  • Continuing, the hundreds place follows, at one hundred times the units place.
For example, in the number 586, the 6 is in the ones place, the 8 is in the tens place, and the 5 is in the hundreds place. This gives us 5 hundred, 8 tens, and 6 ones. Understanding place value allows us to properly manipulate numbers when performing operations such as rounding.
Focusing on the Tens Place
The tens place in a number is significant for rounding to the nearest ten. It determines the base value for our rounding decision.
To find the digit in the tens place:
  • Identify the second digit from the right. For example, in 586, the tens digit is 8.
The importance of the tens place lies in its role in holding tens. In our rounding example, we focus on this digit to know what value our rounded number will start from. Replacing or adjusting the tens digit changes the most immediately significant part of the number when rounding.
Rounding Rules Simplified
Rounding rules help us decide whether to increase a number's value or keep it the same based on the digits. Let's break down the simple rules:
  • Look at the digit to the right of the place value you're rounding to. For rounding tens, check the ones place.
  • If this digit is 5 or greater, round up the tens place digit by one.
  • If it's less than 5, keep the tens place digit the same.
In the exercise, the number 586 is rounded to the nearest ten. The ones place digit, 6, determines our action鈥攕ince 6 is greater than 5, we increase 8 in the tens place by one, resulting in 590. Always remember to change digits to the right of your rounding place to zero.

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