In Exercises 15–30, write each number in scientific notation. 32,000

Verified step by step guidance

1. Identify the significant figures in the number 32,000. In this case, the significant figures are 3.2.
2. Determine the power of 10 needed to express the number in scientific notation. Count how many places you move the decimal point to the left to get from 32,000 to 3.2. This is 4 places.
3. Express the number in the form \( a \times 10^n \), where \( a \) is a number greater than or equal to 1 and less than 10, and \( n \) is an integer. Here, \( a = 3.2 \) and \( n = 4 \).
4. Combine the significant figures and the power of 10 to write the number in scientific notation: \( 3.2 \times 10^4 \).
5. Verify that the scientific notation correctly represents the original number by expanding \( 3.2 \times 10^4 \) back to 32,000.

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 32,000 can be expressed as 3.2 x 10^4, where 3.2 is the coefficient and 10^4 indicates that the decimal point in 3.2 is moved four places to the right.

Standard Form

Standard form refers to the conventional way of writing numbers without exponents. In this context, it is the regular representation of numbers like 32,000. Understanding how to convert from standard form to scientific notation is essential, as it involves identifying the significant figures and the appropriate power of ten.

Exponent Rules

Exponent rules are mathematical guidelines that govern the operations involving powers of numbers. When converting to scientific notation, it is important to understand how to manipulate exponents, such as multiplying or dividing powers of ten. For instance, moving the decimal point to the left increases the exponent, while moving it to the right decreases it.