Express the quotient of 0.422 and 0.004 in standard form

Analyze the question: We need to divide 0.422 by 0.004 and write the result in standard form (scientific notation), which means a × 10ⁿ with 1 ≤ a < 10.

Concept: To divide decimals, multiply both numbers by the same power of 10 so the divisor becomes a whole number.

Solution:

0.422 ÷ 0.004 = (0.422 × 1000) ÷ (0.004 × 1000) = 422 ÷ 4 = 105.5

Now write 105.5 in standard form:

105.5 = 1.055 × 10²

(The decimal point moves 2 places to the left, so the power of 10 is 2.)

Checking the options (the exponents appear to have lost their superscripts in the formatting, so "102" means 10²):

• A. 1.055 × 10² = 105.5 ✔
• B. 10.55 × 10¹ = 105.5 in value, but 10.55 is not between 1 and 10, so it is not in standard form.
• C. 105 × 10⁰ = 105 ✘
• D. 10.55 × 10⁻¹ = 1.055 ✘
• E. 1.055 × 10⁻² = 0.01055 ✘

Option A is the only one that has the correct value and is in proper standard form.

Tip: In standard form, the first number must be between 1 and 10. Count how many places the decimal point moves: moving left gives a positive power, moving right gives a negative power. Always check that your answer matches the original value by expanding it back.