Question

multiply by taking out factors of 10
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multiply.
300 × 900 = \boxed{}

Explanation:

Step1: Factor out 10s from numbers

Rewrite \( 300 \) as \( 3 \times 100 \) (since \( 100 = 10^2 \)) and \( 900 \) as \( 9 \times 100 \). So, \( 300 \times 900=(3\times100)\times(9\times100) \).

Step2: Use associative property of multiplication

Using the associative property \( (a\times b)\times(c\times d)=(a\times c)\times(b\times d) \), we get \( (3\times9)\times(100\times100) \).

Step3: Calculate the products

First, calculate \( 3\times9 = 27 \). Then, calculate \( 100\times100=10000 \) (since \( 10^2\times10^2 = 10^{2 + 2}=10^4 = 10000 \)).

Step4: Multiply the results

Multiply \( 27 \) and \( 10000 \), so \( 27\times10000 = 270000 \).

Answer:

\( 270000 \)