How to convince my parents to let me get a hamster?

Start by telling them you want a snake and work your way down

Well first, I'd like to note that a common goldfish can grow to 2 feet, and needs a 150 gallon tank to live in. They can live for more than 30 years, and are a very large commitment. Maybe when someone's not home you should learn to clean his tank, and be very careful to use water conditioner and everything in the water. You can show your parents that you're responsible of taking care of him, first. Then you should work on chores. Find little jobs to do. Maybe babysit or petsit for people in your neighborhood. Help around the house, and be respectful and polite. Earn your own money to pay for some or all of this. Around $90 would be expected. Show that you know how to care for a hamster. Pick a nice roomy cage (crittertrail 2, crittertrail dazzle... ones around the size of those). Show that you know about proper diet and cage setup. Show that you know how to handle one. And you can always keep the hamster in your room away from your grandma. And always keep in mind that it's your parents decision. You cannot convince them to do something. They have to trust you, and see that you're a mature and responsible young adult. That's ready to care for another living being. Animals are not toys.

You need to show them that you are responsible. You do this by helping out around the house without being asked, come home on time and keep your grades up. Don't complain if you are told to do something like chores. Keep your room clean. Surprise your parents by making supper sometimes. Then bring up the subject. If they still say no remind them of how you've matured and have taken on responsibilities and that you have good grades in school.