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Chapter 6: Problem 25

Round each decimal to the specified position. 0.9811602 to the nearest one.

Short Answer

Expert verified
0.9811602 rounded to the nearest one is 1.

Step by step solution

01

Identifying the Digit to Round

The number 0.9811602 has digits representing different place values. The digit in the 'ones' place that we focus on rounding to is '0' since we are rounding to the nearest whole number.
02

Checking the Digit to the Right

To round a number to the nearest whole number, we look at the digit immediately to the right of the ones place. In 0.9811602, the digit immediately to the right is '9'.
03

Applying Rounding Rules

According to rounding rules, if the digit to the right is 5 or greater, add 1 to the digit in the target place value. Since the digit '9' is greater than 5, we add 1 to the '0' in the ones place.
04

Calculating the Rounded Number

Adding 1 to 0 gives us a rounded value of 1. Hence, 0.9811602 rounded to the nearest one is 1.

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Key Concepts

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

Place Value
Understanding place value is crucial when rounding decimals. Each digit in a number holds a specific place value, which determines its worth. For example, in the number 0.9811602:
  • The digit '9' is in the tenths place.
  • The digit '8' is in the hundredths place.
  • The digit '1' is in the thousandths place.
But when rounding to the nearest whole number, our focus is on the 'ones' place, represented by '0' in this case. Place value helps us decide which digit to keep and which to adjust when rounding a number. With a solid understanding of place value, you can easily determine where to make your calculations and what impact they will have on the final rounded number.
Rounding Rules
Rounding decimals adheres to specific rules which help simplify numbers while retaining their significant value. The main rule to remember is:
  • If the digit to the right of your target place is 5 or greater, round up by adding 1 to your target digit.
  • If it's less than 5, round down by keeping the target digit unchanged.
In the context of the exercise, to round 0.9811602 to the nearest whole number, we examine the tenths place, which is '9'. Since '9' is greater than 5, it signals an increase to the ones place digit, transforming '0' to '1'. Rounding rules, therefore, provide a clear guideline to effectively minimize decimals, making numbers easier to work with and interpret.
Whole Numbers
Whole numbers are non-decimal, positive integers without fractions or decimal components. When rounding a decimal to the nearest whole number, the outcome removes any fractional or decimal part of the original number. Consider the decimal 0.9811602. By rounding it to the nearest whole number (which means focusing on the digit in the 'ones' place), we arrive at a clean and simple whole number: 1. Converting decimals to whole numbers simplifies calculations and is often necessary in real-world scenarios where precision isn't critical. Understanding how to round to whole numbers properly ensures clarity and precision in various mathematical and practical applications.

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Most popular questions from this chapter

Read each decimal by writing it in words. 16.52

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Convert each fraction to a decimal. $$ \frac{43}{100} $$

Convert 8.016 to a fraction.

Perform the following operations. Exercise 6.10 .26\((0.6)^{2} \cdot\left(\frac{1}{20}-\frac{1}{25}\right)\)
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