In Exercises 65–76, write each number in decimal notation without the use of exponents. −3.14×10^−3

Verified step by step guidance

1. Identify the given number in scientific notation: \(-3.14 \times 10^{-3}\).
2. Understand that the exponent \(-3\) indicates a shift of the decimal point 3 places to the left.
3. Start with the number \(-3.14\) and move the decimal point 3 places to the left.
4. Add zeros as placeholders if necessary to complete the shift.
5. Write the final number in decimal notation without exponents.

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 a product of a number (the coefficient) and a power of ten. For example, the number 3.14 can be expressed as 3.14 × 10^0, while 0.00314 can be expressed as 3.14 × 10^−3. Understanding this notation is essential for converting numbers to and from decimal form.

Decimal Notation

Decimal notation is the standard way of writing numbers using the base ten system, which includes digits from 0 to 9. It represents values in a straightforward manner, where the position of each digit indicates its value based on powers of ten. For instance, the number 0.00314 in decimal notation clearly shows the value without any exponents, making it easier to interpret in everyday contexts.

Negative Exponents

Negative exponents indicate that a number is being divided by a power of ten rather than multiplied. For example, 10^−3 means 1 divided by 10^3, or 1/1000. This concept is crucial when converting numbers from scientific notation to decimal notation, as it helps in determining how many places to move the decimal point to the left, thereby accurately representing the value.