Subtract 3.2 x 104 - 2.56 x 10-2
To subtract these two numbers in scientific notation, you need to have the same exponent.
3.2 x 10^4 - 2.56 x 10^-2
Since 10^4 is the same as 10,000 and 10^-2 is the same as 0.01, the expression becomes:
3.2 x 10,000 - 2.56 x 0.01
Which simplifies to:
32,000 - 0.0256
Subtracting these two numbers gives:
31,999.9744
Therefore, 3.2 x 10^4 - 2.56 x 10^-2 = 31,999.9744.
To subtract these numbers, we need to make sure the exponents are the same.
Given:
3.2 x 10^4
2.56 x 10^-2
To make the exponents the same, we can rewrite 2.56 x 10^-2 as 0.0256 x 10^4.
Now,
3.2 x 10^4 - 0.0256 x 10^4
Combining the numbers with the same exponent:
(3.2 - 0.0256) x 10^4
The subtraction results in:
3.1744 x 10^4
To subtract the two numbers written in scientific notation, you need to ensure that both numbers have the same exponent. Here are the steps to subtract 3.2 x 10^4 from 2.56 x 10^-2 using scientific notation:
Step 1: Convert both numbers to the same exponent.
- The first number, 3.2 x 10^4, is already in scientific notation with a positive exponent (4).
- The second number, 2.56 x 10^-2, has a negative exponent (-2). To convert to the same exponent as the first number, move the decimal point two places to the right, resulting in 0.0256 x 10^0.
Step 2: Subtract the decimal parts.
- Subtract the decimal parts of the numbers: 3.2 - 0.0256 = 3.1744.
Step 3: Keep the exponent of the number with the larger exponent.
- Since 3.2 x 10^4 has a larger exponent than 0.0256 x 10^0, keep the exponent of the first number (10^4).
Step 4: Check if the result needs to be normalized.
- In this case, since 3.1744 falls between 1 and 10, we don't need to normalize.
Step 5: Write the final answer in scientific notation.
- The final answer is 3.1744 x 10^4.
Therefore, the subtraction of 3.2 x 10^4 - 2.56 x 10^-2 is 3.1744 x 10^4.