Write in scientific notation: 8,034,000,000. (Section 1.7, Example 2)

Verified step by step guidance

1. Identify the significant digits in the number: 8,034,000,000.
2. Place the decimal point after the first significant digit to form a number between 1 and 10: 8.034.
3. Count the number of places the decimal point has moved from its original position to its new position. In this case, it moves 9 places to the left.
4. Express the number in scientific notation by multiplying the new number by 10 raised to the power of the number of places moved: 8.034 \times 10^9.
5. Verify that the scientific notation correctly represents the original number by considering the magnitude and significant figures.

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 8,034,000,000 can be expressed as 8.034 x 10^9, where 8.034 is the coefficient and 9 is the exponent.

Place Value

Place value is the value of a digit based on its position within a number. In the context of large numbers, understanding place value helps in identifying how many zeros follow the leading digits. For instance, in 8,034,000,000, the digit '8' is in the billions place, indicating that the number is in the range of billions.

Exponent Rules

Exponent rules are mathematical guidelines that govern the operations involving powers of ten. When converting to scientific notation, one must understand how to manipulate exponents, such as adding or subtracting them when multiplying or dividing numbers. This is crucial for correctly expressing large numbers in scientific notation.