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Chapter 6: Problem 3

Round each decimal to the specified position. 82.1 to the nearest one.

Short Answer

Expert verified
82 stays the same when rounded to the nearest one.

Step by step solution

01

Identify the Digit to Round

The number given is 82.1. To round it to the nearest one, we need to focus on the digit right after the decimal point, which is in the tenths position. This digit will tell us if we round the number up or keep it the same.
02

Analyze the Tenths Position

The digit in the tenths position of 82.1 is 1. According to the rounding rules, if this digit is 5 or greater, we round the number in the ones position up by one. If it is less than 5, we leave the ones digit as it is.
03

Apply the Rounding Rule

Since the tenths digit in 82.1 is 1, which is less than 5, we will not round up. This means that the ones digit, 82, stays the same.

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Key Concepts

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

Understanding Decimal Places
Decimal places are the digits that appear after the decimal point in a number. They help us represent values more precisely. For example, in the number 82.1, the digit 1 is in the first decimal place. Understanding the concept of decimal places is crucial in various mathematical and real-life applications such as measurements, financial calculations, and scientific data.
  • The first digit after the decimal point is in the tenths place.
  • The second digit, if any, is in the hundredths place.
  • The third digit, if available, is in the thousandths place, and so on.
Recognizing decimal places enables us to perform essential arithmetic operations accurately and make informed decisions when it comes to rounding numbers.
Exploring the Tenths Position
The tenths position is the first place to the right of the decimal point in any number. In the number 82.1, the digit 1 is in the tenths position. This digit plays a crucial role when rounding numbers. For instance, when asked to round to the nearest whole number (or one), we look at the tenths position to determine what to do with the digit in the ones place. Knowing where the tenths position lies allows us to understand its influence on the rounding process.
  • If the digit is 5 or more, it influences the number to its left to increase by one.
  • If the digit is less than 5, it doesn't change the number to its left.
Having a clear understanding of the tenths position helps in performing calculations that involve precise values and making accurate estimations.
Mastering Rounding Rules
Rounding is a mathematical procedure used to simplify numbers while keeping them close to their original value. The rounding process is guided by specific rules which depend on the value of the digit in a particular decimal place. The main rules are quite simple and easy to follow.
  • Identify the digit at the specified rounding place (e.g., tenths for rounding to the nearest whole number).
  • If this digit is 5 or greater, you increase the number to the left by one.
  • If this digit is less than 5, you keep the number to the left unchanged.
Applying these rounding rules helps ensure that numbers are easier to work with while maintaining their meaningfulness. When you master these rules, you can tackle common mathematical problems and make approximations confidently. For example, rounding 82.1 to the nearest whole number results in 82, because the tenths digit is less than 5.

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Most popular questions from this chapter

Round each decimal to the specified position. 4.087 to the nearest hundredth.

Perform the following operations. \(5.198-0.26 \cdot\left(\frac{14}{250}+0.119\right)\)

Perform the following operations. \(0.588+\frac{1}{40} \cdot 0.24\)

Read each decimal by writing it in words. 0.005

Perform each operation and simplify. \(1.2 \cdot 8.6\)
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