Question

how is the number 0.000436 written in scientific notation?
a. $0.436 \times 10^{-3}$
b. $0.436 \times 10^{3}$
c. $4.36 \times 10^{-4}$
d. $4.36 \times 10^{4}$

Explanation:

Step1: Recall Scientific Notation Rule

Scientific notation is \( a \times 10^n \), where \( 1 \leq |a| < 10 \) and \( n \) is an integer.

Step2: Adjust 0.000436 to Meet \( a \) Requirement

Move the decimal point in 0.000436 to the right until we get a number between 1 and 10. We move it 4 times to get \( a = 4.36 \).

Step3: Determine the Exponent \( n \)

Since we moved the decimal to the right, \( n \) is negative. The number of places moved is 4, so \( n=-4 \).

Step4: Form Scientific Notation

Combine \( a \) and \( 10^n \): \( 4.36 \times 10^{-4} \).

Answer:

C. \( 4.36 \times 10^{-4} \)