Question

Find (2.2 x 105) ÷ (4.4 x 10-3). When you regroup the factors, what do
you notice about the quotient of the decimal factors? How does this
affect the exponent of the quotient?

Answer 1

Answer:

$\sf 5.0 \times 10^7$

Step-by-step explanation:

Given expression:

$\sf (2.2 \times 10^5) \div (4.4 \times 10^{-3})$

$\implies \sf \dfrac{2.2 \times 10^5}{4.4 \times 10^{-3}}$

$\implies \sf \dfrac{2.2}{4.4} \times \dfrac{10^5}{10^{-3}}$

$\implies \sf (2.2 \div 4.4) \times (10^5 \div 10^{-3})$

$\textsf{Apply exponent rule} \quad a^b \div a^c=a^{b-c}$

$\implies \sf 0.5 \times 10^{5-(-3)}$

$\implies \sf 0.5 \times 10^8$

Write in scientific notation:

$\implies \sf 5.0 \times 10^7$

The quotient of the decimal factors is 0.5 and therefore less than 1.

The first factor in scientific notation must be less than 10 and greater than or equal to 1.  Therefore, 0.5 should be multiplied by 10 to become 5.0, which means the exponent of the quotient will be decreased by 1.

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