In Exercises 15–30, write each number in scientific notation.-5716

Verified step by step guidance

1. Identify the given number: -5716.
2. Determine the sign of the number. Since it is negative, the scientific notation will also be negative.
3. Find the decimal point in the number. For -5716, the decimal point is after the last digit: -5716.0.
4. Move the decimal point to the left until there is only one non-zero digit to its left. For -5716, move the decimal point 3 places to the left to get -5.716.
5. Express the number in scientific notation as \(-5.716 \times 10^3\), where 3 is the number of places the decimal was moved.

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 5,716 can be expressed as 5.716 x 10^3 in scientific notation.

Negative Numbers in Scientific Notation

When dealing with negative numbers in scientific notation, the process remains the same, but the coefficient will also be negative. For instance, -5716 in scientific notation would be written as -5.716 x 10^3, indicating that the value is below zero while maintaining the standard format.

Converting to Scientific Notation

To convert a number to scientific notation, identify the first non-zero digit and place the decimal point after it. Count how many places the decimal has moved to determine the exponent of ten. If the original number is negative, the scientific notation will also reflect this negativity in the coefficient.