Questions: Simplify the expression 0.039 × 0.0084 / 0.21 × 0.078 using scientific notation and express your answer in scientific notation.

Transcript text: Simplify the expression $\frac{0.039 \times 0.0084}{0.21 \times 0.078}$ using scientific notation and express your answer in scientific notation. Answer

Solution

Solution Steps

Step 1: Convert each number to scientific notation

$a = 0.039 = 3.9 \times 10^{-2}$
$b = 0.0084 = 8.400 \times 10^{-3}$
$c = 0.21 = 2.100 \times 10^{-1}$
$d = 0.078 = 7.8 \times 10^{-2}$

Step 2: Multiply the numbers and combine powers of 10

Numerator: $3.9 \times 8.400 \times 10^{-2-3} = 32.760 \times 10^{-5}$
Denominator: $2.100 \times 7.8 \times 10^{-1-2} = 16.380 \times 10^{-3}$

Step 3: Divide the results

$\frac{ 32.760 \times 10^{-5}}{ 16.380 \times 10^{-3}} = 2 \times 10^{-2}$

Step 4: Simplify the expression

Simplified to $2 \times 10^{-2}$

Final Answer: $2 \times 10^{-2}$

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