Round To The Nearest Hundredth.1) Raise Each Side Of The Equation As The Power Of The Base Of The Log. In This Case, Choose The Base To Be E E E , Since It Is A Natural Logarithm:Example:$[ \begin{align*} \ln (2x) &= 9 \ e^{\ln (2x)} &=

Introduction

In various mathematical operations, rounding numbers to the nearest hundredth is a crucial step to simplify calculations and obtain accurate results. This article will delve into the concept of rounding to the nearest hundredth, providing a step-by-step guide on how to perform this operation. We will also explore a real-world example involving logarithmic equations, where rounding to the nearest hundredth is essential.

What is Rounding to the Nearest Hundredth?

Rounding to the nearest hundredth is a mathematical operation that involves approximating a number to the nearest hundredth place. This means that if a number has a decimal part that is less than 0.005, it is rounded down to the nearest hundredth, while a decimal part greater than or equal to 0.005 is rounded up.

Why is Rounding to the Nearest Hundredth Important?

Rounding to the nearest hundredth is essential in various mathematical operations, including logarithmic equations, exponential functions, and statistical analysis. In these contexts, rounding to the nearest hundredth helps to simplify calculations, reduce errors, and obtain more accurate results.

Step-by-Step Guide to Rounding to the Nearest Hundredth

To round a number to the nearest hundredth, follow these steps:

1. Identify the decimal part: Determine the decimal part of the number, which is the part after the hundredth place.
2. Check the thousandth place: Look at the thousandth place, which is the third decimal place.
3. Round up or down: If the thousandth place is less than 5, round the hundredth place down. If the thousandth place is 5 or greater, round the hundredth place up.

Example: Rounding to the Nearest Hundredth in Logarithmic Equations

Consider the logarithmic equation:

$${ \begin{align*} \ln (2x) &= 9 \\ e^{\ln (2x)} &= e^9 \end{align*} }$$

To solve for $x$, we need to isolate $x$ on one side of the equation. We can do this by raising both sides of the equation to the power of the base of the log, which is $e$ in this case.

$${ \begin{align*} e^{\ln (2x)} &= e^9 \\ 2x &= e^9 \end{align*} }$$

Now, we need to solve for $x$ by dividing both sides of the equation by 2.

$${ \begin{align*} 2x &= e^9 \\ x &= \frac{e^9}{2} \end{align*} }$$

To round the result to the nearest hundredth, we need to evaluate the expression $\frac{e^9}{2}$ and then round the result to the nearest hundredth.

Evaluating the Expression

Using a calculator, we can evaluate the expression $\frac{e^9}{2}$ as follows:

$${ \begin{align*} \frac{e^9}{2} &\approx \frac{8103.08}{2} \\ &\approx 4051.54 \end{align*} }$$

Rounding to the Nearest Hundredth

To round the result to the nearest hundredth, we need to check the thousandth place, which is 4 in this case. Since the thousandth place is less than 5, we round the hundredth place down.

$${ \begin{align*} 4051.54 &\approx 4051.54 \end{align*} }$$

Therefore, the result rounded to the nearest hundredth is 4051.54.

Conclusion

Rounding to the nearest hundredth is a crucial step in various mathematical operations, including logarithmic equations. By following the step-by-step guide outlined in this article, you can easily round numbers to the nearest hundredth and obtain accurate results. Remember to always check the thousandth place to determine whether to round up or down.

Frequently Asked Questions

Q: What is rounding to the nearest hundredth?

A: Rounding to the nearest hundredth is a mathematical operation that involves approximating a number to the nearest hundredth place.

Q: Why is rounding to the nearest hundredth important?

A: Rounding to the nearest hundredth is essential in various mathematical operations, including logarithmic equations, exponential functions, and statistical analysis.

Q: How do I round a number to the nearest hundredth?

A: To round a number to the nearest hundredth, follow these steps: identify the decimal part, check the thousandth place, and round up or down accordingly.

Q: Can I use a calculator to round numbers to the nearest hundredth?

A: Yes, you can use a calculator to evaluate expressions and round numbers to the nearest hundredth.

Additional Resources

For more information on rounding to the nearest hundredth, check out the following resources:

• Wikipedia: Rounding
• Math Is Fun: Rounding Numbers
• [Khan Academy: Rounding Numbers](https://www.khanacademy.org/math/algebra/x2f9f7d7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7
  Frequently Asked Questions: Rounding to the Nearest Hundredth ================================================================

Q: What is rounding to the nearest hundredth?

A: Rounding to the nearest hundredth is a mathematical operation that involves approximating a number to the nearest hundredth place. This means that if a number has a decimal part that is less than 0.005, it is rounded down to the nearest hundredth, while a decimal part greater than or equal to 0.005 is rounded up.

Q: Why is rounding to the nearest hundredth important?

A: Rounding to the nearest hundredth is essential in various mathematical operations, including logarithmic equations, exponential functions, and statistical analysis. It helps to simplify calculations, reduce errors, and obtain more accurate results.

Q: How do I round a number to the nearest hundredth?

A: To round a number to the nearest hundredth, follow these steps:

1. Identify the decimal part: Determine the decimal part of the number, which is the part after the hundredth place.
2. Check the thousandth place: Look at the thousandth place, which is the third decimal place.
3. Round up or down: If the thousandth place is less than 5, round the hundredth place down. If the thousandth place is 5 or greater, round the hundredth place up.

Q: Can I use a calculator to round numbers to the nearest hundredth?

A: Yes, you can use a calculator to evaluate expressions and round numbers to the nearest hundredth. However, it's essential to understand the concept of rounding to the nearest hundredth and how to apply it manually.

Q: What is the difference between rounding to the nearest hundredth and rounding to the nearest tenth?

A: Rounding to the nearest hundredth involves approximating a number to the nearest hundredth place, while rounding to the nearest tenth involves approximating a number to the nearest tenth place. The main difference is that rounding to the nearest hundredth is more precise than rounding to the nearest tenth.

Q: Can I round a negative number to the nearest hundredth?

A: Yes, you can round a negative number to the nearest hundredth. The process is the same as rounding a positive number, but you need to consider the sign of the number when rounding.

Q: How do I round a decimal number with multiple decimal places to the nearest hundredth?

A: To round a decimal number with multiple decimal places to the nearest hundredth, follow these steps:

1. Identify the decimal part: Determine the decimal part of the number, which is the part after the hundredth place.
2. Check the thousandth place: Look at the thousandth place, which is the third decimal place.
3. Round up or down: If the thousandth place is less than 5, round the hundredth place down. If the thousandth place is 5 or greater, round the hundredth place up.

Q: Can I use a calculator to round decimal numbers with multiple decimal places to the nearest hundredth?

A: Yes, you can use a calculator to evaluate expressions and round decimal numbers with multiple decimal places to the nearest hundredth. However, it's essential to understand the concept of rounding to the nearest hundredth and how to apply it manually.

Q: What are some real-world applications of rounding to the nearest hundredth?

A: Rounding to the nearest hundredth has various real-world applications, including:

• Finance: Rounding to the nearest hundredth is essential in financial calculations, such as calculating interest rates and investment returns.
• Science: Rounding to the nearest hundredth is used in scientific calculations, such as calculating the volume of a container and the mass of an object.
• Engineering: Rounding to the nearest hundredth is used in engineering calculations, such as calculating the stress on a material and the strain on a structure.

Conclusion

Rounding to the nearest hundredth is a fundamental concept in mathematics that has various real-world applications. By understanding the concept of rounding to the nearest hundredth and how to apply it manually, you can simplify calculations, reduce errors, and obtain more accurate results.