What is when adding scientific notation what to do with exponents?

When adding numbers in scientific notation, you need to ensure they have the same exponent before you can add the coefficients. Here's a breakdown:

• Equal Exponents: If the numbers already have the same exponent, you can directly add the coefficients and keep the exponent the same. For example, (3.0 x 10^4) + (2.5 x 10^4) = (3.0 + 2.5) x 10^4 = 5.5 x 10^4

• Unequal Exponents: If the numbers have different exponents, you must first adjust one (or both) of the numbers so that they have the same exponent. This involves moving the decimal point and changing the exponent accordingly. Remember:

  • Moving the decimal point to the left increases the exponent.
  • Moving the decimal point to the right decreases the exponent.

  For example, to add (3.0 x 10^5) + (2.0 x 10^3), you could convert the second number to 0.020 x 10^5. Then, the addition becomes (3.0 x 10^5) + (0.020 x 10^5) = 3.020 x 10^5. Alternatively, you could convert the first number to 300 x 10^3 and add to 2.0 x 10^3 which becomes 302 x 10^3.

• Significant Figures: After adding, you may need to adjust the result to ensure it has the correct number of <a href="https://www.wikiwhat.page/kavramlar/significant%20figures">significant figures</a>, as determined by the numbers being added.

• Normalization: Finally, make sure that the result is in proper <a href="https://www.wikiwhat.page/kavramlar/scientific%20notation">scientific notation</a> format, which means the coefficient should be a number between 1 and 10 (but not including 10). If needed, adjust the decimal point and exponent accordingly.