1. In this problem, you will practice adding, subtracting, multiplying, and dividing
numbers written in scientific notation. For each part, use the following numbers.
In scientific notation, scientific notation is a way to represent numbers that are very large or very small.
To write a number in scientific notation, we express the number as a product of a decimal number between 1 and 10 and a power of 10.
The general form of a number in scientific notation is: a x 10^n
where 'a' is the decimal number and 'n' is the power of 10.
Now, let's look at the numbers given for each part.
1. 1.2 x 10^3
2. 3.5 x 10^2
3. 6.8 x 10^4
4. 2.9 x 10^5
5. 5.7 x 10^7
For each part, we will perform the requested operation and express the result in scientific notation if necessary.
To solve problems involving scientific notation, follow these steps:
1. Write down the given numbers in scientific notation format. Scientific notation format is typically written as a number between 1 and 10, multiplied by a power of 10. For example, 2.5 x 10^4.
2. Perform the desired operation (addition, subtraction, multiplication, or division) on the numbers without considering the powers of 10.
3. After performing the operation, adjust the result to represent the answer in scientific notation.
Let's go through the examples you provided:
Example 1: Addition
Given numbers: 4 x 10^3 and 2 x 10^2
Step 1: Write the numbers in scientific notation format.
4 x 10^3 = 4.0 x 10^3
2 x 10^2 = 2.0 x 10^2
Step 2: Perform the addition operation.
4.0 x 10^3 + 2.0 x 10^2 = 4.0 x 10^3 + 0.2 x 10^3
Step 3: Adjust the result to scientific notation format.
4.0 x 10^3 + 0.2 x 10^3 = 4.2 x 10^3
Therefore, the sum of 4.0 x 10^3 and 2.0 x 10^2 is 4.2 x 10^3.
Example 2: Subtraction
Given numbers: 3 x 10^5 and 1 x 10^4
Step 1: Write the numbers in scientific notation format.
3 x 10^5 = 3.0 x 10^5
1 x 10^4 = 1.0 x 10^4
Step 2: Perform the subtraction operation.
3.0 x 10^5 - 1.0 x 10^4 = 3.0 x 10^5 - 0.1 x 10^5
Step 3: Adjust the result to scientific notation format.
3.0 x 10^5 - 0.1 x 10^5 = 2.9 x 10^5
Therefore, the difference between 3.0 x 10^5 and 1.0 x 10^4 is 2.9 x 10^5.
Example 3: Multiplication
Given numbers: 5 x 10^2 and 2 x 10^3
Step 1: Write the numbers in scientific notation format.
5 x 10^2 = 5.0 x 10^2
2 x 10^3 = 2.0 x 10^3
Step 2: Perform the multiplication operation.
5.0 x 10^2 * 2.0 x 10^3 = 5.0 * 2.0 x 10^2 * 10^3
Step 3: Adjust the result to scientific notation format.
5.0 * 2.0 x 10^2 * 10^3 = 10.0 x 10^5 = 1.0 x 10^6
Therefore, the product of 5.0 x 10^2 and 2.0 x 10^3 is 1.0 x 10^6.
Example 4: Division
Given numbers: 6 x 10^4 and 3 x 10^2
Step 1: Write the numbers in scientific notation format.
6 x 10^4 = 6.0 x 10^4
3 x 10^2 = 3.0 x 10^2
Step 2: Perform the division operation.
6.0 x 10^4 / 3.0 x 10^2 = 6.0 / 3.0 x 10^4 / 10^2
Step 3: Adjust the result to scientific notation format.
6.0 / 3.0 x 10^4 / 10^2 = 2.0 x 10^2
Therefore, the division of 6.0 x 10^4 by 3.0 x 10^2 is 2.0 x 10^2.
These are the steps to solve scientific notation problems involving addition, subtraction, multiplication, and division.
To solve problems involving addition, subtraction, multiplication, and division of numbers written in scientific notation, follow these steps:
1. Write down the given numbers and identify the operations to be performed.
2. Convert the numbers to standard scientific notation if they are not already in that form.
- Standard scientific notation has the form: a × 10^b, where a is a number between 1 and 10 (excluding 10) and b is an integer.
- For example, the number 500 can be written as 5 × 10^2 in scientific notation.
3. Perform the operation indicated for each part of the problem.
- Addition and subtraction:
- Make sure the numbers have the same power of 10.
- Add or subtract the significands (a) and keep the common power of 10.
- If necessary, adjust the decimal point in the result to make it a number between 1 and 10.
- Multiplication:
- Multiply the significands (a).
- Add the powers of 10 (b).
- Division:
- Divide the significands (a).
- Subtract the denominator's power of 10 from the numerator's power of 10 (b).
4. Write the final answer in scientific notation, if required.
Now let's solve the given problem using these steps. Please provide the specific numbers and operations from the problem.