Write in scientific notation 0.0042
Understand the Problem
The question is asking to convert the decimal number 0.0042 into scientific notation, which involves expressing the number as a product of a coefficient and a power of ten.
Answer
The scientific notation of 0.0042 is $4.2 \times 10^{-3}$.
Answer for screen readers
The number 0.0042 in scientific notation is:
$$ 4.2 \times 10^{-3} $$
Steps to Solve
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Identify the Significant Figures Identify the significant figures in the decimal number 0.0042, which in this case is 42.
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Adjust the Decimal Point Move the decimal point to the right to obtain a value between 1 and 10. For 0.0042, you move the decimal two places to the right to get 4.2.
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Determine the Power of Ten Count how many places you moved the decimal point. Since we moved it 3 places to the left, this will give us a negative exponent. Therefore, we will have $10^{-3}$.
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Combine the Results Now combine the coefficient and the power of ten to write the number in scientific notation: $$ 0.0042 = 4.2 \times 10^{-3} $$
The number 0.0042 in scientific notation is:
$$ 4.2 \times 10^{-3} $$
More Information
Scientific notation is useful for expressing very large or very small numbers in a concise format. It’s a widely used method in scientific fields to simplify calculations and comparisons.
Tips
- Confusing Positive and Negative Exponents: Remember, moving the decimal to the right results in a negative exponent, while moving it to the left gives a positive exponent.
- Incorrect Significant Figures: Ensure you're correctly identifying the significant figures in the number; all non-zero digits are significant.
