Can someone please explain to me what exactly scientific notations are and what I need to know to solve them properly?? Also, provide worked out examples and explain the steps you followed. PLEASE, no joke responses... I just want a better understanding.
https://www.mathsisfun.com/numbers/scientific-notation.html
Scientific notation is a way of representing very large or very small numbers using powers of 10. It is commonly used in scientific and mathematical calculations to simplify calculations involving numbers with numerous digits.
To properly solve a scientific notation problem, there are a few key concepts you need to understand. Let's break it down step by step:
Step 1: Understand the notation
Scientific notation is expressed as a number multiplied by 10 raised to a power. It follows the general format: A × 10^n, where A is a number between 1 and 10 (known as the coefficient), and n is an integer representing the power of 10.
Step 2: Converting ordinary numbers to scientific notation
If you are given a number in standard form and need to convert it to scientific notation, follow these steps:
- Identify the coefficient A by moving the decimal point to the left or right until it is between 1 and 10.
- Count the number of places you moved the decimal point and denote this as n.
- Write down the coefficient A followed by × 10^n.
For example, let's convert the number 245,000 to scientific notation:
- Moving the decimal point 5 places to the left, we get 2.45.
- The power of 10 corresponds to the number of places moved, which is -5.
- Thus, 245,000 can be written as 2.45 × 10^5 in scientific notation.
Step 3: Performing arithmetic operations with scientific notation
To add or subtract numbers in scientific notation, you must ensure that they have the same power of 10. If the powers are different, you need to adjust one or both of the coefficients so that the powers match. Then, you can simply add or subtract the coefficients as usual, keeping the power of 10 unchanged.
For multiplication or division, you can simply multiply or divide the coefficients and add or subtract the powers.
Here's an example to demonstrate:
Example: Solve the following problem: (3 × 10^4) × (2 × 10^2)
- Multiply the coefficients: 3 × 2 = 6.
- Add the powers of 10: 4 + 2 = 6.
- The answer is 6 × 10^6 in scientific notation.
I hope this explanation helps you understand scientific notation better. Let me know if you have any further questions!