Calculate The Following Expressions:1. $1.8 \div 72$2. $2.3 \cdot \sqrt{9}$

Introduction

Mathematical expressions are a fundamental part of mathematics, and understanding how to calculate them is crucial for solving problems in various fields. In this article, we will focus on calculating two mathematical expressions: $1.8 \div 72$ and $2.3 \cdot \sqrt{9}$. We will break down each expression step by step, explaining the concepts and techniques used to arrive at the final answer.

Expression 1: $1.8 \div 72$

Understanding Division

Division is a mathematical operation that involves splitting a number into equal parts or groups. In the expression $1.8 \div 72$, we are dividing the number 1.8 by 72.

Step-by-Step Calculation

To calculate this expression, we can follow these steps:

1. Understand the concept of division: Division involves finding the quotient of two numbers. In this case, we need to find the number of times 72 fits into 1.8.
2. Perform the division: We can perform the division by using a calculator or by manually dividing 1.8 by 72.
3. Round the answer: Since we are dealing with a decimal number, we may need to round the answer to a certain number of decimal places.

Calculation

Using a calculator, we can perform the division as follows:

$1.8 \div 72 = 0.025$

Alternatively, we can manually divide 1.8 by 72:

$1.8 \div 72 = 0.025$

Conclusion

The final answer to the expression $1.8 \div 72$ is 0.025.

Expression 2: $2.3 \cdot \sqrt{9}$

Understanding Multiplication and Square Roots

Multiplication is a mathematical operation that involves repeated addition, while square roots are a way of finding the number that, when multiplied by itself, gives a specified value. In the expression $2.3 \cdot \sqrt{9}$, we are multiplying the number 2.3 by the square root of 9.

Step-by-Step Calculation

To calculate this expression, we can follow these steps:

1. Understand the concept of multiplication: Multiplication involves repeated addition. In this case, we need to find the product of 2.3 and the square root of 9.
2. Calculate the square root: We need to find the square root of 9, which is a number that, when multiplied by itself, gives 9.
3. Perform the multiplication: We can perform the multiplication by using a calculator or by manually multiplying 2.3 by the square root of 9.
4. Round the answer: Since we are dealing with a decimal number, we may need to round the answer to a certain number of decimal places.

Calculation

Using a calculator, we can calculate the square root of 9 as follows:

$\sqrt{9} = 3$

Now, we can multiply 2.3 by the square root of 9:

$2.3 \cdot \sqrt{9} = 2.3 \cdot 3 = 6.9$

Alternatively, we can manually multiply 2.3 by the square root of 9:

$2.3 \cdot \sqrt{9} = 2.3 \cdot 3 = 6.9$

Conclusion

The final answer to the expression $2.3 \cdot \sqrt{9}$ is 6.9.

Conclusion

In this article, we have calculated two mathematical expressions: $1.8 \div 72$ and $2.3 \cdot \sqrt{9}$. We have broken down each expression step by step, explaining the concepts and techniques used to arrive at the final answer. By following these steps, you can calculate mathematical expressions with confidence and accuracy.

Key Takeaways

• Division involves finding the quotient of two numbers.
• Multiplication involves repeated addition.
• Square roots are a way of finding the number that, when multiplied by itself, gives a specified value.
• Calculators can be used to perform calculations quickly and accurately.
• Manual calculations can be used to understand the concepts and techniques used in calculations.

Further Reading

If you want to learn more about mathematical expressions and calculations, here are some recommended resources:

• Khan Academy: Mathematics
• Mathway: Math Problem Solver
• Wolfram Alpha: Math Calculator

Introduction

Mathematical expressions are a fundamental part of mathematics, and understanding how to calculate them is crucial for solving problems in various fields. In this article, we will answer some frequently asked questions about mathematical expressions, covering topics such as division, multiplication, and square roots.

Q: What is the difference between division and multiplication?

A: Division and multiplication are two fundamental mathematical operations. Division involves finding the quotient of two numbers, while multiplication involves repeated addition. For example, in the expression $1.8 \div 72$, we are dividing 1.8 by 72, while in the expression $2.3 \cdot \sqrt{9}$, we are multiplying 2.3 by the square root of 9.

Q: How do I calculate the square root of a number?

A: To calculate the square root of a number, you can use a calculator or manually find the number that, when multiplied by itself, gives the specified value. For example, to calculate the square root of 9, you can use a calculator or manually find the number that, when multiplied by itself, gives 9.

Q: What is the order of operations in mathematical expressions?

A: The order of operations in mathematical expressions is a set of rules that dictate the order in which operations should be performed. The order of operations is as follows:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I round a decimal number to a certain number of decimal places?

A: To round a decimal number to a certain number of decimal places, you can use a calculator or manually round the number. For example, to round 3.14159 to 2 decimal places, you can use a calculator or manually round the number to 3.14.

Q: What is the difference between a calculator and a manual calculation?

A: A calculator is a device that can perform calculations quickly and accurately, while a manual calculation involves performing calculations by hand. While calculators can be convenient, manual calculations can help you understand the concepts and techniques used in calculations.

Q: How do I use a calculator to perform calculations?

A: To use a calculator to perform calculations, you can follow these steps:

1. Enter the numbers and operations into the calculator.
2. Press the equals button to perform the calculation.
3. Read the result on the calculator screen.

Q: What are some common mathematical expressions that I should know?

A: Some common mathematical expressions that you should know include:

• $a \div b$: Division of a by b
• $a \cdot b$: Multiplication of a by b
• $\sqrt{a}$: Square root of a
• $a^b$: Exponential expression of a to the power of b

Conclusion

In this article, we have answered some frequently asked questions about mathematical expressions, covering topics such as division, multiplication, and square roots. By understanding these concepts and techniques, you can become proficient in calculating mathematical expressions and solving problems in various fields.

Key Takeaways

• Division involves finding the quotient of two numbers.
• Multiplication involves repeated addition.
• Square roots are a way of finding the number that, when multiplied by itself, gives a specified value.
• Calculators can be used to perform calculations quickly and accurately.
• Manual calculations can help you understand the concepts and techniques used in calculations.

Further Reading

If you want to learn more about mathematical expressions and calculations, here are some recommended resources:

• Khan Academy: Mathematics
• Mathway: Math Problem Solver
• Wolfram Alpha: Math Calculator

By following these resources and practicing calculations, you can become proficient in calculating mathematical expressions and solving problems in various fields.