The temperature was 15 degrees below 0 (in Fahrenheit) today.
Write a signed number to represent this temperature.

The temperature would be -15° Fahrenheit, because it is 15 below 0 degrees.

From using this...

0 - 15 = -15

A signed number is just a term which applies to positive and negative numbers.

The decimal point is moved 4 places (right) to put the number into scientific notation form. That form is usually written

... a. 4.21 × 10⁻⁴ g

The tick mark is a non-standard notation that would need to be described to anyone you intend to communicate with. Usually, some indicator of exponentiation is used with the exponent, so that 10-4 is not taken to mean 6. More conventional text form for the number would be 4.21*10^-4, where an asterisk (*) is used to indicate multiplication and a caret (^) is used to indicate exponentiation.

You can get a clue from the expanded form of the number:

0.000 421 = 0×10⁰ +0×10⁻¹ +0×10⁻² +0×10⁻³ +4×10⁻⁴ +2×10⁻⁵ +1×10⁻⁶