Gravity is the attractive force that any object with mass exerts on every other object with mass. You and I exert a gravitational force on each other because we each have mass. That force is extremely small because our masses are small. The Earth, on the other hand, has a large mass and has a large gravitational force pulling objects to it. The farther you get from Earth (or any object with mass) the weaker that force becomes. That force, however, extends to an infinite distance, so it never reaches zero. There are always gravitational forces acting on you and the gravity of Earth acting on you is never zero.
On the surface of Earth, the acceleration of gravity is approximately 9.81 m/s^2. The International Space Station (ISS) is in space about 400 km above the surface of the Earth. However, the acceleration of gravity is not zero. Running through the calculations, the acceleration of gravity acting on the astronauts is about 8.6 m/s^2. It's smaller but not significantly smaller. That's more than enough gravity to prevent someone from floating.
A person floats in space because they are orbiting the Earth. As a curved object, the person falls toward the Earth at the same rate that the Earth curves away from them. Think of throwing a baseball. Imagine throwing the baseball harder and harder. It travels farther and farther before striking the ground. Imagine throwing the baseball harder and harder such that the rate at which is falls to the ground is the same as the rate at which the Earth curves downward. Ignoring friction, the baseball is now in orbit around the Earth! The same thing takes place in the space station. The gravity is not zero. In fact, it's far from it. Earth curves out from under the astronauts as it pulls them downward. Thus it appears there is no gravity in space.
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