Question

express the following in scientific notation: .000457
457 × 10⁶
4.57 ×10⁴
457 × 10⁻⁶
4.57 × 10⁻⁴

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 0.000457

For \( 0.000457 \), we move the decimal point 4 places to the right to get \( 4.57 \). Since we moved the decimal 4 places to the right, the exponent of 10 is \( -4 \). So in scientific notation, \( 0.000457 = 4.57 \times 10^{-4} \).

Step3: Evaluate the options

• Option 1: \( 457 \times 10^6 \): \( 457 \) is not between 1 and 10, and the exponent is positive, incorrect.
• Option 2: \( 4.57 \times 10^4 \): The exponent is positive, but we moved the decimal to the right (for a number less than 1, exponent should be negative), incorrect.
• Option 3: \( 457 \times 10^{-6} \): \( 457 \) is not between 1 and 10, incorrect.
• Option 4: \( 4.57 \times 10^{-4} \): Matches our calculation.

Answer:

D. \( 4.57 \times 10^{-4} \) (assuming the fourth option is labeled D, if the options are labeled A - D as A. \( 457 \times 10^6 \), B. \( 4.57 \times 10^4 \), C. \( 457 \times 10^{-6} \), D. \( 4.57 \times 10^{-4} \))