In Exercises 15–30, write each number in scientific notation. -317

Verified step by step guidance

1. Identify the given number: -317.
2. Determine the position of the decimal point in the number. For -317, the decimal point is after the 7, i.e., -317.0.
3. Move the decimal point to the right of the first non-zero digit. In this case, move it two places to the left to get -3.17.
4. Count the number of places the decimal point was moved. Here, it was moved 2 places to the left.
5. Express the number in scientific notation as \(-3.17 \times 10^2\).

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 3000 can be expressed as 3.0 x 10^3. This notation simplifies calculations and comparisons of very large or very small values.

Negative Numbers in Scientific Notation

When writing negative numbers in scientific notation, the process is similar to that of positive numbers, but the coefficient remains negative. For instance, -317 can be expressed as -3.17 x 10^2. The negative sign indicates the value is less than zero, and the exponent reflects the position of the decimal point in relation to the base number.

Exponent Rules

Understanding exponent rules is crucial when working with scientific notation. The exponent indicates how many times the base (10) is multiplied by itself. For example, in -3.17 x 10^2, the exponent 2 means that 10 is multiplied by itself twice (10 x 10), which equals 100. This concept is essential for correctly interpreting and manipulating numbers in scientific notation.