Question

What does a negative integer exponent tell you when a number is written in scientific notation?


Give an example:

Answer 1

In scientific notation, a number is expressed as a product of a coefficient (a number between 1 and 10) and a power of ten. A negative integer exponent indicates that the decimal point of the coefficient is moved to the left, effectively representing a very small number.

For example, if we have the scientific notation \( 3.2 \times 10^{-3} \), the negative exponent (-3) tells us to move the decimal point in the coefficient (3.2) three places to the left.

Here's how that looks:

1. Start with the coefficient: 3.2
2. Move the decimal point 3 places to the left:
- Move 1: 0.32
- Move 2: 0.032
- Move 3: 0.0032

Thus, \( 3.2 \times 10^{-3} \) is equivalent to \( 0.0032 \). This represents a very small number, specifically \( 0.0032 \).

In general, a negative exponent suggests that the value is a fraction or decimal that is less than 1.