In Exercises 77–86, write each number in scientific notation. −3829

Verified step by step guidance

1. Identify the significant digits in the number, which are 3829.
2. Determine the position of the decimal point in the original number. Since it's a whole number, the decimal is after the last digit: 3829.
3. Move the decimal point to the left until only one non-zero digit remains to the left of the decimal. For 3829, move the decimal 3 places to the left to get 3.829.
4. Count the number of places the decimal point was moved. In this case, it was moved 3 places.
5. Express the number in scientific notation as \(-3.829 \times 10^3\), where the exponent is positive because the original number is greater than 1.

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 3829 can be expressed as 3.829 × 10^3 in scientific notation.

Negative Numbers in Scientific Notation

When writing negative numbers in scientific notation, the process is similar to positive numbers, but the coefficient remains negative. For instance, the number -3829 would be expressed as -3.829 × 10^3, indicating that it is a negative value while still adhering to the scientific notation format.

Standard Form Conversion

Converting a number to scientific notation involves identifying the significant figures and determining the appropriate power of ten. This requires moving the decimal point in the number until only one non-zero digit remains to its left, which helps in simplifying calculations and comparisons in scientific contexts.