1Cademy - Dividing $$\frac{9 \times 10^3}{3 \times 10^{-2}}$$ and Converting to Decimal Form

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Scientific Notation

Example

Dividing $\frac{9 \times 10^3}{3 \times 10^{-2}}$ and Converting to Decimal Form

Divide $\frac{9 \times 10^3}{3 \times 10^{-2}}$ and express the result in standard decimal form by separating the coefficients from the powers of $10$ and applying the Quotient Property for Exponents.

Step 1 — Separate into two fractions. Rewrite the single fraction as a product of two fractions — one containing the numerical coefficients and one containing the powers of $10$ :

$\frac{9}{3} \times \frac{10^3}{10^{-2}}$

Step 2 — Divide the coefficients and apply the Quotient Property. Divide the numerical parts: $\frac{9}{3} = 3$ . For the powers of $10$ , both the numerator and denominator share the base $10$ , so subtract the exponents using the Quotient Property for Exponents: $\frac{10^3}{10^{-2}} = 10^{3 - (-2)} = 10^{3 + 2} = 10^5$ . The result in scientific notation is:

$3 \times 10^5$

Step 3 — Convert to decimal form. The exponent is $5$ , so move the decimal point $5$ places to the right: $3 \rightarrow 300{,}000$ .

Therefore, $\frac{9 \times 10^3}{3 \times 10^{-2}} = 300{,}000$ .

This example illustrates the general strategy for dividing numbers in scientific notation: separate the fraction into a coefficient fraction and a power-of- $10$ fraction, divide the coefficients, subtract the exponents on the base $10$ (being careful when subtracting a negative exponent), and then convert the result to the desired form.

Updated 2026-04-21

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OpenStax Elementary Algebra

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