Exercises 159–161 will help you prepare for the material covered in the next section. If 6.2 is multiplied by 10^3, what does this multiplication do to the decimal point in 6.2?

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 typically written as a product of a number between 1 and 10 and a power of ten. For example, 6.2 can be expressed as 6.2 x 10^0, and multiplying by 10^3 shifts the decimal point three places to the right.

Decimal Point Movement

When multiplying a decimal number by a power of ten, the decimal point moves to the right for positive exponents and to the left for negative exponents. In this case, multiplying 6.2 by 10^3 means moving the decimal point three places to the right, resulting in 6200. This concept is crucial for understanding how multiplication by powers of ten affects the value of decimal numbers.

Place Value

Place value refers to the value of a digit based on its position within a number. In the context of decimal numbers, each position to the left of the decimal point represents increasing powers of ten, while each position to the right represents decreasing powers of ten. Understanding place value helps in visualizing how the movement of the decimal point alters the magnitude of the number.