Write each number in scientific notation. −3829

Verified step by step guidance

1. Identify the original number: -3829.
2. Determine the sign of the number. Since the number is negative, the sign will be negative in the scientific notation.
3. Move the decimal point in the number to create a new number between 1 and 10. For -3829, move the decimal point 3 places to the left to get -3.829.
4. Express the number as the product of the new number and 10 raised to the power of the number of places the decimal was moved. Since the decimal was moved 3 places to the left, the exponent will be positive 3.
5. Write the scientific notation as \(-3.829 \times 10^{3}\).

Key Concepts

Scientific Notation

Scientific notation expresses numbers as a product of a number between 1 and 10 and a power of 10. It simplifies handling very large or small numbers by standardizing their format, such as writing 3829 as 3.829 × 10^3.

Place Value and Decimal Movement

Converting to scientific notation involves moving the decimal point to create a number between 1 and 10. The number of places moved determines the exponent on 10, which is positive if the decimal moves left and negative if it moves right.

Handling Negative Numbers in Scientific Notation

When writing negative numbers in scientific notation, the negative sign is placed in front of the coefficient. The exponent on 10 remains based on decimal movement and is unaffected by the number's sign.