Round $\sqrt{119}$ To Two Decimal Places.Provide Your Answer Below:
Introduction
Rounding numbers is an essential skill in mathematics, particularly in calculations involving decimals and fractions. It is a technique used to approximate a value to a specific number of decimal places or significant figures. In this article, we will explore the concept of rounding numbers, focusing on the specific problem of rounding the square root of 119 to two decimal places.
What is Rounding?
Rounding is the process of approximating a number to a specific number of decimal places or significant figures. It involves reducing the precision of a number to make it easier to work with or to simplify calculations. Rounding can be done in two ways: up or down.
- Rounding up: When rounding up, we increase the number to the next highest decimal place or significant figure.
- Rounding down: When rounding down, we decrease the number to the next lowest decimal place or significant figure.
How to Round Numbers
To round a number, follow these steps:
- Identify the decimal place: Determine the decimal place you want to round to.
- Look at the digit to the right: Examine the digit to the right of the decimal place you want to round to.
- Round up or down: If the digit to the right is 5 or greater, round up. If it is less than 5, round down.
Rounding the Square Root of 119
Now, let's apply the rounding technique to the square root of 119.
Step 1: Calculate the Square Root
The square root of 119 is approximately 10.950.
Step 2: Round to Two Decimal Places
To round 10.950 to two decimal places, we need to look at the digit to the right of the second decimal place, which is 5.
Since 5 is greater than or equal to 5, we round up the second decimal place.
Rounded Value
The rounded value of the square root of 119 to two decimal places is 10.95.
Conclusion
Rounding numbers is an essential skill in mathematics, and it is used to approximate values to a specific number of decimal places or significant figures. By following the steps outlined in this article, you can round numbers with ease. Remember to identify the decimal place, look at the digit to the right, and round up or down accordingly.
Practice Problems
Try rounding the following numbers to two decimal places:
- 12.456
- 7.982
- 3.141
Answer Key
- 12.46
- 7.98
- 3.14
Additional Resources
For more practice problems and examples, check out the following resources:
- Khan Academy: Rounding Numbers
- Mathway: Rounding Numbers
- IXL: Rounding Numbers
Introduction
In our previous article, we explored the concept of rounding numbers in mathematics, focusing on the specific problem of rounding the square root of 119 to two decimal places. In this article, we will provide a Q&A guide to help you better understand the concept of rounding numbers and how to apply it in various mathematical situations.
Q&A Guide
Q1: What is rounding in mathematics?
A1: Rounding is the process of approximating a number to a specific number of decimal places or significant figures. It involves reducing the precision of a number to make it easier to work with or to simplify calculations.
Q2: Why is rounding important in mathematics?
A2: Rounding is important in mathematics because it helps to simplify calculations, reduce errors, and make it easier to work with large numbers. It is also used in real-world applications, such as finance, science, and engineering.
Q3: How do I round a number to two decimal places?
A3: To round a number to two decimal places, look at the digit to the right of the second decimal place. If it is 5 or greater, round up. If it is less than 5, round down.
Q4: What is the difference between rounding up and rounding down?
A4: Rounding up involves increasing the number to the next highest decimal place or significant figure, while rounding down involves decreasing the number to the next lowest decimal place or significant figure.
Q5: Can I round a number to any decimal place?
A5: Yes, you can round a number to any decimal place. However, the more decimal places you round to, the more precise the result will be.
Q6: How do I round a negative number?
A6: To round a negative number, follow the same steps as rounding a positive number. The sign of the number will not affect the rounding process.
Q7: Can I use a calculator to round numbers?
A7: Yes, most calculators have a rounding function that allows you to round numbers to a specific decimal place.
Q8: What is the rule for rounding numbers that end in 5?
A8: When rounding numbers that end in 5, you can round up or down, depending on the context of the problem. However, in general, it is common to round up when the number is positive and round down when the number is negative.
Q9: Can I round a fraction to a decimal place?
A9: Yes, you can round a fraction to a decimal place by converting the fraction to a decimal and then rounding it.
Q10: How do I round a number that has a repeating decimal?
A10: To round a number that has a repeating decimal, look at the repeating pattern and round the number accordingly. For example, if the repeating pattern is 0.333..., you can round it to 0.33.
Conclusion
Rounding numbers is an essential skill in mathematics, and it is used to approximate values to a specific number of decimal places or significant figures. By following the steps outlined in this Q&A guide, you can better understand the concept of rounding numbers and how to apply it in various mathematical situations.
Practice Problems
Try answering the following questions:
- What is the rounded value of 12.456 to two decimal places?
- What is the rounded value of -7.982 to two decimal places?
- What is the rule for rounding numbers that end in 5?
Answer Key
- 12.46
- -7.98
- Round up when the number is positive and round down when the number is negative.
Additional Resources
For more practice problems and examples, check out the following resources:
- Khan Academy: Rounding Numbers
- Mathway: Rounding Numbers
- IXL: Rounding Numbers
By mastering the art of rounding numbers, you will become more confident in your mathematical calculations and be able to solve problems with ease.