Perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. (66,000×0.001)/(0.003×0.002)

Verified step by step guidance

1. First, rewrite the given expression clearly: \(\frac{66,000 \times 0.001}{0.003 \times 0.002}\).
2. Next, perform the multiplications in the numerator and denominator separately: calculate \$66,000 \times 0.001\( and \)0.003 \times 0.002$.
3. After finding these products, rewrite the expression as a division of the two results: \(\frac{\text{numerator product}}{\text{denominator product}}\).
4. Then, divide the numerator product by the denominator product to get a single decimal number.
5. Finally, convert this decimal number into scientific notation by expressing it as \(a \times 10^n\), where \$1 \leq a < 10\(, and round the decimal factor \)a$ to two decimal places if necessary.

Key Concepts

Scientific Notation

Scientific notation expresses numbers as a product of a decimal factor between 1 and 10 and a power of 10. It simplifies handling very large or small numbers, making calculations and comparisons easier. For example, 66,000 can be written as 6.6 × 10^4.

Order of Operations

The order of operations dictates the sequence in which mathematical operations are performed: parentheses, exponents, multiplication and division (left to right), then addition and subtraction. Correctly applying this ensures accurate computation of expressions like (66,000×0.001)/(0.003×0.002).

Rounding Decimal Factors

Rounding decimal factors involves adjusting a decimal number to a specified number of decimal places for simplicity and clarity. In scientific notation, the decimal factor is often rounded to two decimal places to maintain precision without unnecessary detail, such as rounding 6.6667 to 6.67.