Which expression represents 0.00052 in scientific notation?

• A. 5.2 x 10^4
• B. 5.2 x 10^-4
• C. 0.052 x 10^-2
• D. 0.00052 x 10^0

Answer: (B)

To write a number in scientific notation, you place the decimal so the coefficient (mantissa) is between 1 and 10, and then multiply by a power of ten that accounts for how far you moved the decimal. For 0.00052, the mantissa becomes 5.2 (placing the decimal after the 5). To keep the value the same, you must multiply by 10 to compensate for moving the decimal, which corresponds to a negative exponent because you’re shrinking the number. Specifically, 5.2 × 10^-4 equals 0.00052, so the correct scientific notation is 5.2 × 10^-4.

Other forms either use a mantissa outside the 1 to 10 range or are not the conventional single-coefficient form, even though some may be mathematically equivalent. For example, a mantissa of 0.052 or a plain decimal with no normalized mantissa doesn’t meet the standard formatting of scientific notation.