Representing the Decimal Number

Oct 13, 2025 by recoveryshake.com 6 views

Introduction

In this article, we will explore a mathematical problem that involves the relationship between the tenths and hundredths digits of a decimal number. The problem states that the hundredths digit of a decimal is three more than the tenths digit, and we need to find the decimal number if the sum of the digits is 11.

Understanding the Problem

Let's break down the problem and understand what it's asking for. We have a decimal number that can be represented as a two-digit number in the tenths place and a two-digit number in the hundredths place. The problem states that the hundredths digit is three more than the tenths digit. This means that if the tenths digit is x, then the hundredths digit is x + 3.

Representing the Decimal Number

We can represent the decimal number as 0.xx, where x is the tenths digit and xx is the hundredths digit. Since the hundredths digit is three more than the tenths digit, we can write the decimal number as 0.x(x+3).

Finding the Decimal Number

We are given that the sum of the digits is 11. This means that the sum of the tenths digit, the hundredths digit, and the decimal point is 11. We can write this as an equation:

x + (x+3) + 0.x(x+3) = 11

Simplifying the Equation

We can simplify the equation by combining like terms:

2x + 3 + 0.x(x+3) = 11

Subtracting 3 from Both Sides

Subtracting 3 from both sides of the equation gives us:

2x + 0.x(x+3) = 8

Understanding the Equation

The equation 2x + 0.x(x+3) = 8 is a bit tricky to understand. The term 0.x(x+3) represents the decimal part of the number, which is a two-digit number. We can rewrite this term as 10x + 3, since the decimal part is a two-digit number.

Rewriting the Equation

Rewriting the equation with the new term gives us:

2x + 10x + 3 = 8

Combining Like Terms

Combining like terms gives us:

12x + 3 = 8

Subtracting 3 from Both Sides

Subtracting 3 from both sides of the equation gives us:

12x = 5

Dividing Both Sides by 12

Dividing both sides of the equation by 12 gives us:

x = 5/12

Converting the Fraction to a Decimal

Converting the fraction 5/12 to a decimal gives us:

x = 0.4167

Finding the Hundredths Digit

Since the hundredths digit is three more than the tenths digit, we can find the hundredths digit by adding 3 to the tenths digit:

hundredths digit = 0.4167 + 3 = 0.4167 + 0.03 = 0.4467

Finding the Decimal Number

Now that we have the tenths and hundredths digits, we can find the decimal number by combining them:

decimal number = 0.4 + 0.4467 = 0.8467

Conclusion

In this article, we explored a mathematical problem that involved the relationship between the tenths and hundredths digits of a decimal number. We represented the decimal number as 0.xx, where x is the tenths digit and xx is the hundredths digit. We found the decimal number by solving the equation 2x + 0.x(x+3) = 8, which gave us the value of x as 0.4167. We then found the hundredths digit by adding 3 to the tenths digit, and finally, we found the decimal number by combining the tenths and hundredths digits.

Final Answer

The final answer is 0.8467.

Introduction

In our previous article, we explored a mathematical problem that involved the relationship between the tenths and hundredths digits of a decimal number. We represented the decimal number as 0.xx, where x is the tenths digit and xx is the hundredths digit. We found the decimal number by solving the equation 2x + 0.x(x+3) = 8, which gave us the value of x as 0.4167. We then found the hundredths digit by adding 3 to the tenths digit, and finally, we found the decimal number by combining the tenths and hundredths digits.

Q&A

Q: What is the relationship between the tenths and hundredths digits of a decimal number?

A: The hundredths digit of a decimal number is three more than the tenths digit.

Q: How do we represent the decimal number?

A: We can represent the decimal number as 0.xx, where x is the tenths digit and xx is the hundredths digit.

Q: What is the equation that we need to solve to find the decimal number?

A: The equation is 2x + 0.x(x+3) = 8.

Q: How do we simplify the equation?

A: We can simplify the equation by combining like terms and rewriting the term 0.x(x+3) as 10x + 3.

Q: What is the value of x that we find by solving the equation?

A: The value of x is 0.4167.

Q: How do we find the hundredths digit?

A: We find the hundredths digit by adding 3 to the tenths digit.

Q: What is the decimal number that we find by combining the tenths and hundredths digits?

A: The decimal number is 0.8467.

Q: What is the final answer to the problem?

A: The final answer is 0.8467.

Additional Questions and Answers

Q: Can we use this method to find the decimal number for any given sum of digits?

A: No, this method is specific to the problem where the sum of the digits is 11.

Q: How do we know that the hundredths digit is three more than the tenths digit?

A: This is given in the problem statement.

Q: Can we use this method to find the decimal number for a decimal with more than two digits?

A: No, this method is only applicable to decimals with two digits.

Q: How do we know that the decimal number is unique?

A: We can verify that the decimal number is unique by checking that it satisfies the equation 2x + 0.x(x+3) = 8.

Conclusion

In this Q&A article, we have answered some common questions related to the problem of finding the decimal number where the hundredths digit is three more than the tenths digit. We have also provided additional questions and answers to clarify any doubts that readers may have.

Final Answer

The final answer is 0.8467.