In Exercises 77–86, write each number in scientific notation. 579,000,000,000,000,000

Verified step by step guidance

1. Identify the significant digits in the number, which are 579.
2. Count the number of places the decimal point needs to move to the left to be just after the first significant digit. In this case, it moves 17 places.
3. Express the number as a product of the significant digits and a power of 10. This is done by writing 579 as 5.79 and multiplying by 10 raised to the power of the number of places the decimal moved.
4. Write the number in scientific notation as $5.79\times {10}^{17}$.
5. Ensure the coefficient (5.79) is between 1 and 10, which confirms the number is correctly expressed in scientific notation.

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 579,000,000,000,000,000 can be expressed as 5.79 x 10^17, where 5.79 is the coefficient and 17 is the exponent indicating the number of places the decimal point has moved.

Exponent Rules

Exponent rules are mathematical guidelines that govern the operations involving powers of numbers. Key rules include the product of powers (a^m * a^n = a^(m+n)), the power of a power ( (a^m)^n = a^(m*n)), and the power of a product ( (ab)^n = a^n * b^n). Understanding these rules is essential for manipulating numbers in scientific notation effectively.

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 how many places the decimal point moves when converting a standard number to scientific notation. For instance, in 579,000,000,000,000,000, the placement of digits indicates that the decimal point moves 17 places to the left to form 5.79.