Your rising sign describes how you appear to others. It's your outward presence, whereas your main sign (your sun sign) is more of who you are on the inside. What's more, rising signs make a trip through each zodiac sign every single day, meaning the astral rising sign shifts every two hours. So if you're off by two hours on your birth time, your sign will be wrong (via Gold Ring Astrology).
If your rising sign is wrong, you'll not only lose out on the ability to see how you outwardly present, but a lot of your chart will inherently be incorrect (via Lawyerment). Your rising sign determines the houses that your zodiac placements fall into. The wrong birth time would then give you the wrong rising sign, which would then give you the wrong houses for your other signs, including your moon sign.
Don't know the exact time you were born? If your parents don't remember or didn't write it down in your baby book, you can request your long-form birth certificate from the state in which you were born, which will have your exact time of birth (Allure).
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