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Chapter 1: Problem 13

Round each number to the given place value. \(725 ;\) tens

Short Answer

Expert verified
730

Step by step solution

01

Identify the digit in the tens place

Look at the number 725. The digit in the tens place is 2.
02

Check the digit to the right

To determine if rounding is needed, look at the digit immediately to the right of the tens place. In 725, this digit is 5.
03

Apply rounding rules

Since the digit to the right (5) is 5 or greater, increase the tens place digit by 1. Change the tens digit from 2 to 3.
04

Change all digits to the right to zero

After adjusting the tens place digit, change all digits to the right of it to zero. Therefore, 725 becomes 730 when rounded to the nearest tens.

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Key Concepts

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

Place Value
The concept of place value is essential when rounding numbers. Each digit in a number has a different value based on its position. For example, in the number 725, each digit has a place value:
  • The digit 7 is in the hundreds place, so it represents 700.
  • The digit 2 is in the tens place, so it represents 20.
  • The digit 5 is in the ones place, so it represents 5.
Understanding place value helps us know which digits to focus on when rounding. In this example, to round to the nearest tens, we look at the digit in the tens place, which is 2. Rounded values depend on which digit we are rounding to and the value of the digits to the right.
Rounding Rules
Rounding involves adjusting numbers to make them simpler but still close to the original value. Here are the basic rules for rounding numbers:
  • If the digit to the right of the place value you're rounding to is less than 5, keep the rounding digit the same. Change all digits to its right to 0.
  • If the digit to the right is 5 or more, increase the rounding digit by 1. Change all digits to its right to 0.
In our example of rounding 725 to the nearest tens, the digit in the ones place is 5. According to the rules, we increase the tens digit (2) by 1, making it 3, and change the ones place to 0. Therefore, 725 rounded to the nearest tens becomes 730. These rounding rules help simplify numbers for estimation and easier calculations.
Nearest Tens
Rounding to the nearest tens means finding the closest number that is a multiple of 10. To summarize the process:
  • Identify the digit in the tens place.
  • Examine the digit in the ones place.
  • Apply the rounding rules.
  • Change all digits to the right of the rounding place to zero.
For the number 725:
  • The tens place digit is 2.
  • The ones place digit is 5, which is equal to or greater than 5.
Following the rounding rules, increase the tens digit by 1, resulting in 3. Then, replace the ones digit with 0, converting 725 into 730 when rounded to the nearest tens. This method ensures we get the simplest form of the number while remaining close to the original value.

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Most popular questions from this chapter

Check the following division problems. If it does not check, find the correct answer. $$\frac{1021}{9}=113 \mathrm{R} 4$$

Convert the numbers to standard form. 5 hundreds \(+2\) tens \(+4\) ones

Convert the numbers to expanded form. $$382$$

Rewrite the expression, using the indicated property. \((4 \cdot 15) \cdot 5 ;\) associative property of multiplication

Write the number in words. $$241$$
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