On average, the moon is 384,400 kilometers from the earth . how is this distance written in scientific notation?

In scientific notation, you need a number from 1 to less than 10 multiplied by a power of 10.

To turn 384,400 into a number from 1 to under 10, place a decimal point after the 3.

Now you have a number from 1 to less than 10.
3.844

Now count the number of places the decimal point moved left from its original position.
The decimal point was here: 384,400. after the last zero.
The decimal point moved 5 places to the left to be placed after the 3.
Since the decimal point moved 5 places left, the exponent of the 0 is 5.

384,400 = 3.844 * 10^5

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