In Exercises 77–86, write each number in scientific notation. 0.0083

Verified step by step guidance

1. Identify the decimal number that needs to be converted to scientific notation: 0.0083.
2. Move the decimal point to the right until you have a number between 1 and 10. In this case, move the decimal point 3 places to the right to get 8.3.
3. Count the number of places you moved the decimal point. Here, it is 3 places.
4. Since you moved the decimal to the right, the exponent will be negative. Therefore, the exponent is -3.
5. Write the number in scientific notation as \(8.3 \times 10^{-3}\).

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, the number 0.0083 can be expressed as 8.3 x 10^-3, where 8.3 is the coefficient and -3 indicates the decimal point has moved three places to the right.

Standard Form

Standard form refers to the conventional way of writing numbers, where the decimal point is placed after the first non-zero digit. In scientific notation, converting a number to standard form involves identifying the significant figures and adjusting the decimal point accordingly. This helps in simplifying calculations and comparisons between very large or very small numbers.

Exponent Rules

Exponent rules are mathematical guidelines that govern the operations involving powers of ten. Key rules include multiplying powers by adding exponents and dividing powers by subtracting exponents. Understanding these rules is essential when converting numbers into scientific notation, as they help in accurately determining the exponent based on the movement of the decimal point.