Concept 3

Use scientific notation and interpret scale (powers of ten, significant size comparisons).

Compare quantities in scientific notation by separating the coefficient from the power of 10.

Core Idea

Keep the coefficient between 1 and 10 and compare powers of 10 separately from the coefficient when judging scale.

Understanding

Rule: Scientific notation is built to make very large and very small quantities easier to compare.

A difference of one in the exponent changes the size by a factor of 10, so exponent gaps matter fast. When comparing two values, divide the coefficients and then account for the power of 10. That keeps the scale logic clean and prevents place-value mistakes.

Question

Worked Example

One culture contains $3.2 \times 107$ bacteria, and another contains $8.0 \times 105$ bacteria. About how many times as many bacteria are in the first culture as in the second?

Select an answer to see the explanation