50% decrease then 100% increase: same as the original; the number is halved then that new number is doubled, which brings it back to the original, x * 2 * ¹/₂ = x (¹/₂ and 2 cancel out)
50% increase then 33¹/₃% decrease: same as the original; x * ³/₂ * ²/₃ = x (³/₂ and ²/₃ cancel out)
20% increase then 25% decrease: less than the original ; x * ⁶/₅ * ³/₄ = ⁹/₁₀x
$10 increase then $10 decrease: same as the original; x + 10 - 10 = x
25% increase then 20% decrease: same as the original; x * ⁵/₄ * ⁴/₅ = x
50% decrease then 100% increase: same as the original; the number is halved then that new number is doubled, which brings it back to the original, x * 2 * ¹/₂ = x (¹/₂ and 2 cancel out)
50% increase then 33¹/₃% decrease: same as the original; x * ³/₂ * ²/₃ = x (³/₂ and ²/₃ cancel out)
20% increase then 25% decrease: less than the original ; x * ⁶/₅ * ³/₄ = ⁹/₁₀x
$10 increase then $10 decrease: same as the original; x + 10 - 10 = x
25% increase then 20% decrease: same as the original; x * ⁵/₄ * ⁴/₅ = x
You're less likely to make mistakes reading or writing very big and very small numbers if you use scientific notation. It also makes it much easier to tell at a glance which numbers are bigger or smaller without counting long strings of zeros.
