Question

1. write 0.00003356 in scientific notation. .3356·10⁻⁴ 33.56·10⁻⁵ 3.356·10⁵ 3.356·10⁻⁵

Explanation:

Step1: Recall scientific notation rules

Scientific notation is in the form \( a \times 10^n \), where \( 1 \leq |a| < 10 \) and \( n \) is an integer. For a number less than 1, we move the decimal point to the right until we get a number between 1 and 10, and the exponent \( n \) is negative (equal to the number of places we moved the decimal).

Step2: Process 0.00003356

Start with 0.00003356. Move the decimal point 5 places to the right to get \( 3.356 \) (since \( 0.00003356 = 3.356 \times 10^{-5} \), because we moved the decimal 5 places right, so the exponent is -5, and \( 3.356 \) is between 1 and 10).

Check other options:

• \( 0.3356 \times 10^{-4} \): \( 0.3356 < 1 \), violates the \( 1 \leq |a| < 10 \) rule.
• \( 33.56 \times 10^{-5} \): \( 33.56 \geq 10 \), violates the \( 1 \leq |a| < 10 \) rule.
• \( 3.356 \times 10^{5} \): This would be a large number (335600), but our original number is small, so the exponent should be negative.

Answer:

D. \( 3.356 \cdot 10^{-5} \) (assuming the last option is D, as it's \( 3.356 \cdot 10^{-5} \))