Multiply 4.82 x 10^12 + 3.2 x 10^4. show your work.
To multiply numbers in scientific notation, you need to multiply the coefficients (the numbers in front of the powers of 10) and add the exponents. Here's how you can calculate it step by step:
1. Multiply the coefficients: 4.82 x 10^12 * 3.2 x 10^4.
4.82 * 3.2 = 15.424
2. Add the exponents: 10^12 + 10^4.
When adding exponents, if the base is the same, you can simply add the exponents.
10^12 + 10^4 = 10^(12+4) = 10^16
3. Combine the coefficient and the exponent: 15.424 x 10^16
So, the multiplication of 4.82 x 10^12 and 3.2 x 10^4 is equal to 15.424 x 10^16.
To calculate the sum (4.82 x 10^12) + (3.2 x 10^4), we need to make the exponents of the numbers equal by adjusting the larger number.
Since 10^4 is smaller than 10^12, we can multiply (3.2 x 10^4) by 10^8 to match the exponents.
(4.82 x 10^12) + (3.2 x 10^4) = (4.82 x 10^12) + (3.2 x 10^4) x (10^8 / 10^8)
Now let's calculate the values separately:
4.82 x 10^12 = 4.82e12
3.2 x 10^4 x (10^8 / 10^8) = 3.2 x 10^4 x 10^8
Now, multiply the two values:
4.82e12 + 3.2 x 10^4 x 10^8 = 4.82e12 + 3.2e4 x 10^8
Now we have the same exponent, so we can add the two numbers:
4.82e12 + 3.2e4 x 10^8 = 4.82e12 + 3.2e12
Now, add the two values:
4.82e12 + 3.2e12 = 8.02e12
Therefore, (4.82 x 10^12) + (3.2 x 10^4) = 8.02 x 10^12.
To multiply numbers written in scientific notation, we need to follow a few steps:
Step 1: Multiply the decimal numbers.
4.82 x 3.2 = 15.424
Step 2: Multiply the powers of 10.
10^12 x 10^4 = 10^(12+4) = 10^16
Step 3: Combine the results from Steps 1 and 2.
15.424 x 10^16
So, the expression 4.82 x 10^12 + 3.2 x 10^4 is equal to 15.424 x 10^16.