In Exercises 15–30, write each number in scientific notation.638,000,000,000,000,000

Verified step by step guidance

1. Identify the significant figures in the number: 638,000,000,000,000,000.
2. Place the decimal point after the first non-zero digit to form a number between 1 and 10: 6.38.
3. Count the number of places the decimal point has moved from its original position to its new position. In this case, it moves 17 places to the left.
4. Express the number as a product of the significant figure and a power of 10. Since the decimal moved 17 places to the left, the exponent will be positive: \(6.38 \times 10^{17}\).
5. Write the final expression in scientific notation: \(6.38 \times 10^{17}\).

Key Concepts

Scientific Notation

Scientific notation is a way of expressing very large or very small numbers 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 638,000,000,000,000,000 can be expressed as 6.38 x 10^17, where 6.38 is the coefficient and 17 is the exponent.

Exponent Rules

Exponent rules are mathematical guidelines that govern the operations involving powers of numbers. When converting to scientific notation, understanding how to manipulate exponents is crucial, especially when multiplying or dividing numbers in scientific form. For instance, when multiplying two numbers in scientific notation, you add their exponents.

Place Value

Place value refers to the value of a digit based on its position within a number. In the context of scientific notation, recognizing the place value helps in determining the correct coefficient and exponent. For example, in the number 638,000,000,000,000,000, the digit '6' is in the 10^17 place, which is essential for accurate conversion to scientific notation.