C) 0,05 105 +0,7 107= D) 1,2 101 +5,7 102-32.10¯3 =​

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Introduction

Mathematical equations can be complex and challenging to solve, especially when they involve multiple operations and variables. In this article, we will focus on solving a specific type of equation that involves adding and subtracting numbers with different exponents. We will break down the equation step by step and provide a clear explanation of each step.

The Equation

The equation we will be solving is:

0.05 × 10^5 + 0.7 × 10^7 = 1.2 × 10^1 + 5.7 × 10^2 - 3.2 × 10^-3

Step 1: Evaluate the Exponents

To solve this equation, we need to evaluate the exponents first. The exponents are the numbers that are raised to a power, in this case, 10.

  • 10^5 = 100,000
  • 10^7 = 10,000,000
  • 10^1 = 10
  • 10^2 = 100
  • 10^-3 = 0.001

Step 2: Multiply the Numbers

Now that we have evaluated the exponents, we can multiply the numbers.

  • 0.05 × 100,000 = 5,000
  • 0.7 × 10,000,000 = 7,000,000
  • 1.2 × 10 = 12
  • 5.7 × 100 = 570
  • 3.2 × 0.001 = 0.0032

Step 3: Add and Subtract the Numbers

Now that we have multiplied the numbers, we can add and subtract them.

  • 5,000 + 7,000,000 = 7,005,000
  • 12 + 570 = 582
  • 582 - 0.0032 = 581.9968

Step 4: Write the Final Answer

Now that we have added and subtracted the numbers, we can write the final answer.

7,005,000 + 581.9968 = 7,005,581.9968

Conclusion

Solving complex mathematical equations requires patience, attention to detail, and a clear understanding of the operations involved. By breaking down the equation step by step and evaluating the exponents, multiplying the numbers, and adding and subtracting them, we can arrive at the final answer. In this article, we solved a specific type of equation that involved adding and subtracting numbers with different exponents.

Tips and Tricks

  • When solving complex mathematical equations, it's essential to evaluate the exponents first.
  • Make sure to multiply the numbers correctly, paying attention to the signs and exponents.
  • When adding and subtracting numbers, make sure to line up the decimal points correctly.
  • Use a calculator or a computer program to check your work and ensure accuracy.

Common Mistakes

  • Failing to evaluate the exponents correctly.
  • Multiplying the numbers incorrectly.
  • Adding and subtracting the numbers incorrectly.
  • Not lining up the decimal points correctly.

Real-World Applications

Solving complex mathematical equations has many real-world applications, including:

  • Physics and engineering: Solving equations is essential in physics and engineering to model and analyze complex systems.
  • Economics: Solving equations is essential in economics to model and analyze economic systems.
  • Computer science: Solving equations is essential in computer science to model and analyze complex algorithms.

Conclusion

Introduction

In our previous article, we solved a complex mathematical equation step by step. However, we understand that some readers may still have questions or need further clarification on certain concepts. In this article, we will address some of the most frequently asked questions related to solving complex mathematical equations.

Q&A

Q: What is the order of operations when solving complex mathematical equations?

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

  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 evaluate exponential expressions?

A: To evaluate exponential expressions, you need to raise the base number to the power of the exponent. For example, 2^3 = 2 × 2 × 2 = 8.

Q: What is the difference between a coefficient and a variable?

A: A coefficient is a number that is multiplied by a variable. For example, in the equation 2x, 2 is the coefficient and x is the variable.

Q: How do I add and subtract fractions with different denominators?

A: To add and subtract fractions with different denominators, you need to find a common denominator. The common denominator is the least common multiple (LCM) of the two denominators.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable is 1. For example, 2x + 3 = 5 is a linear equation. A quadratic equation is an equation in which the highest power of the variable is 2. For example, x^2 + 4x + 4 = 0 is a quadratic equation.

Q: How do I solve a system of linear equations?

A: To solve a system of linear equations, you need to find the values of the variables that satisfy both equations. There are several methods to solve a system of linear equations, including substitution, elimination, and graphing.

Q: What is the difference between a function and a relation?

A: A function is a relation in which each input corresponds to exactly one output. For example, f(x) = 2x is a function. A relation is a set of ordered pairs that satisfy a certain condition. For example, {(1, 2), (2, 3), (3, 4)} is a relation.

Q: How do I graph a function?

A: To graph a function, you need to plot the points on a coordinate plane and draw a smooth curve through the points.

Conclusion

Solving complex mathematical equations requires a strong understanding of mathematical concepts and operations. By following the order of operations, evaluating exponential expressions, and adding and subtracting fractions with different denominators, you can solve complex mathematical equations with ease. In this article, we addressed some of the most frequently asked questions related to solving complex mathematical equations.

Tips and Tricks

  • Make sure to evaluate exponential expressions correctly.
  • Use a calculator or a computer program to check your work and ensure accuracy.
  • Practice solving complex mathematical equations regularly to improve your skills.

Common Mistakes

  • Failing to evaluate exponential expressions correctly.
  • Multiplying the numbers incorrectly.
  • Adding and subtracting the numbers incorrectly.
  • Not lining up the decimal points correctly.

Real-World Applications

Solving complex mathematical equations has many real-world applications, including:

  • Physics and engineering: Solving equations is essential in physics and engineering to model and analyze complex systems.
  • Economics: Solving equations is essential in economics to model and analyze economic systems.
  • Computer science: Solving equations is essential in computer science to model and analyze complex algorithms.

Conclusion

Solving complex mathematical equations requires a strong understanding of mathematical concepts and operations. By following the order of operations, evaluating exponential expressions, and adding and subtracting fractions with different denominators, you can solve complex mathematical equations with ease. In this article, we addressed some of the most frequently asked questions related to solving complex mathematical equations.