In Exercises 87–106, 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. Convert each number to scientific notation: 66,000 as $6.6\times {10}^4$, 0.001 as $1\times {10}^{-3}$, 0.003 as $3\times {10}^{-3}$, and 0.002 as $2\times {10}^{-3}$.
2. Rewrite the expression using scientific notation: $(6.6\times {10}^4)\times (1\times {10}^{-3})/((3\times {10}^{-3})\times (2\times {10}^{-3}))$.
3. Simplify the expression by multiplying the coefficients and adding the exponents: $(6.6\times {10}^1)/(6\times {10}^{-6})$.
4. Divide the coefficients: $6.6/6$ and subtract the exponents: ${10}^1-(-6)$.
5. Express the result in scientific notation, rounding the decimal factor to two decimal places if necessary.

Key Concepts

Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small in a compact form. It is written as the product of a number between 1 and 10 and a power of ten. For example, 66,000 can be expressed as 6.6 × 10^4. This notation simplifies calculations and makes it easier to compare very large or very small values.

Multiplication of Decimals

Multiplying decimals involves multiplying the numbers as if they were whole numbers and then placing the decimal point in the product. The total number of decimal places in the product should equal the sum of the decimal places in the factors. Understanding this process is crucial for accurately performing operations in scientific notation.

Division of Decimals

Dividing decimals requires converting the divisor into a whole number by shifting the decimal point, which also shifts the decimal point in the dividend. The result is then calculated as a whole number division. This concept is essential for simplifying expressions in scientific notation, especially when dealing with very small or very large numbers.