Montana Math MT.8.EE.3

Math8th GradeExpressions and Equations

The Standard

Represent very large or very small quantities using scientific notation, limited to a single digit times an integer power of ten.

2026 Montana Mathematics Content Standards

Teacher's field guide

What Students Need to Do: Students write large and small numbers as one nonzero digit times a power of ten. They use positive exponents for large numbers and negative exponents for numbers between 0 and 1.
What Mastery Looks Like: A student writes 50,000,000 as 5 × 10^7 and 0.00008 as 8 × 10^-5. They can turn both expressions back into decimals.
Common Misconceptions: Students may write a positive exponent for 0.00008 or think a negative exponent makes the number negative. Some write 50 × 10^6 instead of using a single-digit coefficient.
How to Assess It: On an exit ticket, ask students to write 70,000,000 and 0.00009 using powers of ten and explain how they chose each exponent.

Lesson moves

Use a place-value chart and counters to build 6,000,000 and 0.00006, then write each as a digit times a power of ten.
Ask partners to write why 8 × 10^-5 is positive but less than 1, then check by writing its decimal form.
Give pairs cards showing 2,000,000, 0.00003, 2 × 10^6, and 3 × 10^-5; have them match equivalent values.
Show a microscope label for a bacterium measuring 0.000002 meters; ask students to rewrite its length using a power of ten.

Free download