1Cademy - Multiplying $$(4 \times 10^5)(2 \times 10^{-7})$$ and Converting to Decimal Form

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Scientific Notation

Example

Multiplying $(4 \times 10^5)(2 \times 10^{-7})$ and Converting to Decimal Form

Multiply $(4 \times 10^5)(2 \times 10^{-7})$ and express the result in standard decimal form by applying Properties of Exponents and the Commutative Property.

Step 1 — Rearrange the factors. Use the Commutative Property of Multiplication to group the numerical coefficients together and the powers of $10$ together:

$4 \cdot 2 \cdot 10^5 \cdot 10^{-7}$

Step 2 — Multiply the coefficients and apply the Product Property. Multiply the numerical parts: $4 \cdot 2 = 8$ . For the powers of $10$ , both factors share the base $10$ , so add the exponents using the Product Property for Exponents: $10^5 \cdot 10^{-7} = 10^{5 + (-7)} = 10^{-2}$ . The result in scientific notation is:

$8 \times 10^{-2}$

Step 3 — Convert to decimal form. The exponent is $-2$ , so move the decimal point $2$ places to the left: $8 \rightarrow 0.08$ .

Therefore, $(4 \times 10^5)(2 \times 10^{-7}) = 0.08$ .

This example illustrates the general strategy for multiplying numbers in scientific notation: rearrange factors so that the coefficients and powers of $10$ are grouped separately, multiply the coefficients, add the exponents on the base $10$ , and then convert the result to the desired form.

Updated 2026-04-21

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OpenStax Elementary Algebra

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