To determine which number is equivalent to \( 5.1 \times 10^{-2} \), follow these steps:
1. Understand the meaning of the notation \( 5.1 \times 10^{-2} \). This is scientific notation, which is used to express numbers that are too big or too small to be conveniently written in decimal form. The number \( 10^{-2} \) means \( 10 \) raised to the power of \(-2\).
2. When a number is raised to a negative exponent, it means that it is a fraction. Specifically, \( 10^{-2} \) is equal to \( \frac{1}{10^2} \) or \( \frac{1}{100} \).
3. Multiply the base number 5.1 by the value of \( 10^{-2} \) to find its equivalent decimal form:
[tex]\[
5.1 \times 10^{-2} = 5.1 \times \frac{1}{100} = 5.1 \times 0.01
\][/tex]
4. Perform the multiplication:
[tex]\[
5.1 \times 0.01 = 0.051
\][/tex]
Thus, the number equivalent to \( 5.1 \times 10^{-2} \) is \( 0.051 \).
Therefore, the correct answer is:
B. [tex]\( 0.051 \)[/tex]
