Final answer:
In standard notation, '5.0780 x 10^6 g' is written as 5,078,000 which is option (a), and there are six significant digits in the original scientific notation, as all zeros in '5.0780' are significant.
Step-by-step explanation:
To express the scientific notation '5.0780 x 10^6 g' in standard notation and identify the significant digits, we first convert the value by multiplying the decimal number by 10 raised to the power of 6. Thus, we get:
5.0780 x 1,000,000 = 5,078,000 g.
In standard notation, the number is 5,078,000, which is option (a).
The significant digits in '5.0780 x 10^6' are all the non-zero digits and any zeros between them or following them since the value is in scientific notation. Therefore, the number of significant digits in this example is six, as each digit in the coefficient 5.0780 is significant. Leading zeros in standard notation are not considered significant, but trailing zeros to the right of the decimal point are significant, thus in '5.0780' all zeros are significant.