1Cademy - Writing $$0.0052$$ in Scientific Notation

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Procedure for Converting from Decimal Notation to Scientific Notation

Example

Writing $0.0052$ in Scientific Notation

Convert $0.0052$ to scientific notation by applying the four-step procedure. Since $0.0052$ lies between $0$ and $1$ , the result will involve a negative power of $10$ .

Move the decimal point so the coefficient falls between $1$ and $10$ : Shift the decimal point in $0.0052$ to the right until exactly one nonzero digit appears before it. This produces $5.2$ , which satisfies $1 \leq 5.2 < 10$ .
Count the places moved: The decimal point shifted $3$ places to the right.
Write the result as a product with a power of $10$ : Because the original number is between $0$ and $1$ , the exponent is negative, giving $5.2 \times 10^{-3}$ .
Check: Verify by evaluating the product step by step: $5.2 \times 10^{-3} = 5.2 \times \frac{1}{10^3} = 5.2 \times \frac{1}{1000} = 5.2 \times 0.001 = 0.0052$ ✓

Therefore, $0.0052 = 5.2 \times 10^{-3}$ . This example contrasts with converting a large number like $37{,}000$ : here the decimal point moves to the right (producing a negative exponent), whereas for numbers greater than $1$ it moves to the left (producing a positive exponent).

Updated 2026-04-21

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OpenStax Elementary Algebra

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