Which of the following represents 31 billion in scientific notation?

• A. 3.1 \times 10^{9}
• B. 3.1 \times 10^{10}
• C. 3.1 \times 10^{11}
• D. 31 \times 10^{9}

Answer: (B)

Verified step by step guidance

1. Understand that 1 billion is equal to \$10^{9}\(, so 31 billion can be expressed as \)31 \times 10^{9}$.
2. Recall that scientific notation requires the coefficient to be a number between 1 and 10, so \$31 \times 10^{9}$ is not in proper scientific notation because 31 is greater than 10.
3. Convert \$31 \times 10^{9}\( to proper scientific notation by moving the decimal point one place to the left, which changes 31 to 3.1 and increases the exponent by 1, resulting in \)3.1 \times 10^{10}$.
4. Verify that the coefficient 3.1 is between 1 and 10, confirming that \$3.1 \times 10^{10}$ is the correct scientific notation for 31 billion.
5. Compare the options given and identify that \$3.1 \times 10^{10}$ correctly represents 31 billion in scientific notation.