Negative Exponents • Scientific Notation for Small Numbers
Negative Exponents and Scientific Notation for Small Numbers is a Grade 8 math skill from Saxon Math, Course 3. Students learn that negative exponents represent fractions (a to the power -n equals 1 over a to the n), and apply this to write very small numbers in scientific notation using powers of ten.
Key Concepts
New Concept A negative exponent indicates the reciprocal of the base raised to the positive exponent; it does not make the number negative.
Law of Exponents for Negative Exponents $$ x^{ n} = \frac{1}{x^n} $$ What’s next This card is just the foundation. Soon, you'll see worked examples on simplifying complex expressions and converting very small numbers into scientific notation.
Common Questions
What does a negative exponent mean?
A negative exponent means the reciprocal: a to the power -n equals 1 divided by a to the power n. For example, 10 to the -3 equals 0.001.
How do you write a small number in scientific notation?
Move the decimal point to the right to get a number between 1 and 10, and write a negative exponent to show how many places you moved. For example, 0.0045 = 4.5 times 10 to the -3.
What is scientific notation used for?
Scientific notation makes very small (or very large) numbers easier to read, write, and compute, especially in science and engineering.
How do you convert scientific notation back to a decimal?
Move the decimal point left by the number shown in the negative exponent. For 3.2 times 10 to the -4, move left 4 places to get 0.00032.
What grade covers negative exponents and scientific notation?
Negative exponents and scientific notation are covered in Grade 8 math.