Consider the 4-digit number abcd. Putting it in scientific notation is a matter of moving the (invisible) decimal point to the left until you have a number between 1 and 10, then multiplying this number by an appropriate power of 10, equal to the number of positions that the point was moved.
In this case,
abcd = abcd . = a . bcd × 10³
The number of underlined digits is the number of positions you have to move the decimal point. The number a . bcd is called the mantissa.
For a number already containing a decimal point, like abc . def, we do the same thing:
abc . def = a . bcdef × 10²
For a number smaller than 1, such as 0.000abcd, we have to move the decimal to the right:
0.000abcd = 0000a . bcd = a . bcd × 10⁻⁴
As mentioned earlier, the mantissa is typically supposed to be between 1 and 10, which means that if you start with a number larger than 1, that number in scientific notation will involve multiplication by a positive power of 10. On the other hand, if you start with a number smaller than 1, the power of 10 will be negative. You can see this is true for each of the examples I've used here.
