# +26 Lesson 6 Skills Practice Scientific Notation

## Lesson 6 Skills Practice Scientific Notation

### Introduction

Scientific notation is a powerful tool used in the field of science and mathematics to express very large or very small numbers in a more concise and manageable form. It involves writing numbers in the form of a coefficient multiplied by a power of 10. In this lesson, we will explore the concept of scientific notation and practice various skills related to it.

### Understanding Scientific Notation

Scientific notation is a way of expressing numbers that are either too large or too small to be conveniently written in standard decimal notation. It consists of two parts: the coefficient and the exponent. The coefficient is a number between 1 and 10, and the exponent represents the power of 10 by which the coefficient is multiplied.

### Converting Numbers to Scientific Notation

To convert a number to scientific notation, follow these steps:

- Identify the coefficient by moving the decimal point in the original number to a position between 1 and 10.
- Count the number of places the decimal point was moved. This will be the exponent.
- Write the coefficient followed by the letter "x" and the power of 10 represented by the exponent.

### Example: Converting a Large Number to Scientific Notation

Let's convert the number 1,250,000 to scientific notation:

- Move the decimal point to a position between 1 and 10. In this case, we can move it after the first digit, resulting in 1.25.
- The decimal point was moved 6 places, so the exponent is 6.
- The number in scientific notation is 1.25x10^6.

### Example: Converting a Small Number to Scientific Notation

Now, let's convert the number 0.000042 to scientific notation:

- Move the decimal point to a position between 1 and 10. In this case, we can move it after the first non-zero digit, resulting in 4.2.
- The decimal point was moved 5 places to the right, so the exponent is -5.
- The number in scientific notation is 4.2x10^-5.

### Performing Operations with Scientific Notation

When performing operations with numbers in scientific notation, it's important to understand the rules for addition, subtraction, multiplication, and division.

### Addition and Subtraction

To add or subtract numbers in scientific notation, the exponents must be the same. If they are not, you must adjust one or both of the numbers to make the exponents equal before performing the operation.

### Multiplication

To multiply numbers in scientific notation, multiply the coefficients and add the exponents.

### Example: Multiplying Numbers in Scientific Notation

Let's multiply 2.5x10^2 by 3.0x10^3:

- Multiply the coefficients: 2.5 x 3.0 = 7.5
- Add the exponents: 2 + 3 = 5
- The product in scientific notation is 7.5x10^5.

### Division

To divide numbers in scientific notation, divide the coefficients and subtract the exponents.

### Example: Dividing Numbers in Scientific Notation

Let's divide 6.0x10^4 by 2.5x10^2:

- Divide the coefficients: 6.0 / 2.5 = 2.4
- Subtract the exponents: 4 - 2 = 2
- The quotient in scientific notation is 2.4x10^2.

### Practice Problems

Now that we have covered the basics of scientific notation and the operations involved, it's time to put our skills to the test with some practice problems. Try solving the following exercises:

### Problem 1

Express the number 0.0000072 in scientific notation.

### Problem 2

Multiply 4.5x10^3 by 2.0x10^4.

### Problem 3

Divide 9.6x10^5 by 3.0x10^2.

### Solution

Problem 1:

- Move the decimal point to a position between 1 and 10: 7.2
- The decimal point was moved 6 places to the right, so the exponent is -6.
- The number in scientific notation is 7.2x10^-6.

Problem 2:

- Multiply the coefficients: 4.5 x 2.0 = 9.0
- Add the exponents: 3 + 4 = 7
- The product in scientific notation is 9.0x10^7.

Problem 3:

- Divide the coefficients: 9.6 / 3.0 = 3.2
- Subtract the exponents: 5 - 2 = 3
- The quotient in scientific notation is 3.2x10^3.

### Conclusion

Scientific notation is an essential skill for anyone working in the fields of science and mathematics. It allows us to express very large or very small numbers in a more manageable form, making calculations and comparisons easier. By understanding the basics of scientific notation and practicing the associated skills, you will be well-equipped to tackle complex problems and communicate numerical information effectively.