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Chapter 1: Problem 13

Round each of the numbers to the nearest ten. $$56,782$$

Short Answer

Expert verified
56,782 rounded to the nearest ten is 56,780.

Step by step solution

01

Identify the Tens and Units Digits

In the number 56,782, the tens digit is 8, and the units (or ones) digit is 2. When rounding to the nearest ten, we focus on these two digits.
02

Determine Whether to Round Up or Down

Look at the units digit (2). According to rounding rules, if this digit is 5 or higher, we round up. If it is 4 or lower, we round down. Since 2 is less than 5, we will round down.
03

Perform the Rounding

Since we are rounding down, we leave the tens digit as it is and change the units digit to 0. Therefore, 56,782 rounded to the nearest ten is 56,780.

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Key Concepts

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

Place Value
Place value is a fundamental concept in mathematics that helps us understand the value of each digit in a number. Each position in a number has a different value based on powers of ten. From right to left, the positions are typically named as ones, tens, hundreds, thousands, and so on. Each position increases in value by a factor of ten.
For example, in the number 56,782:
  • The digit in the ones place is 2.
  • The digit in the tens place is 8.
  • The digit in the hundreds place is 7.
  • The digit in the thousands place is 6.
  • The digit in the ten-thousands place is 5.
Understanding place value is crucial when rounding numbers, since it allows us to identify which digits are meaningful and which digits we may adjust.
Rounding Rules
Rounding is a mathematical technique used to simplify numbers, making them easier to work with. To round a number, we generally follow a set of rounding rules. The basic rounding rules state:
  • Identify the place value you are rounding to, such as tens, hundreds, etc.
  • Look at the digit to the immediate right of the place value you're considering. This is your guide digit.
  • If the guide digit is 5 or more, you round up by adding 1 to the digit in the rounding place.
  • If the guide digit is less than 5, you round down by keeping the digit in the rounding place the same and changing all the digits to its right to zero.
These rules are designed to approximate a number in a way that retains its significant value and is closer to its original form.
Nearest Ten
Rounding to the nearest ten can simplify calculations by focusing on multiples of ten. To round a number to the nearest ten, focus on the tens and ones digits.
Here鈥檚 how you can do it:
  • Begin by identifying the tens digit and the ones digit in the original number.
  • Use the ones digit as the guide digit according to rounding rules.
  • If the ones digit is 5 or higher, increase the tens digit by 1 and drop the ones digit to 0.
  • If the ones digit is 4 or lower, retain the tens digit and replace the ones digit with 0.
In our example of 56,782, since the ones digit is 2 (which is less than 5), we round down, making the tens digit 8 remain the same, and changing the ones digit to 0, resulting in 56,780.

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Most popular questions from this chapter

Find a solution for each equation. $$17=n+9$$

Mentally give a one-digit estimate for each of the following quotients. That is, for each quotient, mentally estimate the answer using one of the digits \(1,2,3,4,5,6,7,8,\) or 9 $$921 \div 243$$

Divide. You shouldn't have any wrong answers because you can always check your results with multiplication. $$\frac{4,606}{49}$$

Find a solution for each equation. $$n+6=15$$

Mentally give a one-digit estimate for each of the following quotients. That is, for each quotient, mentally estimate the answer using one of the digits \(1,2,3,4,5,6,7,8,\) or 9 $$728 \div 177$$
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