Montana Math MT.CORE.NUM.REAL.2

MathGrades 9–12The Real Number System

The Standard

Represent and perform operations within very large and very small numbers using scientific notation.

2026 Montana Mathematics Content Standards · Numeric Reasoning

Teacher's field guide

What Students Need to Do: Write very large and very small numbers using a number from 1 to less than 10 times a power of 10. Add and subtract by matching powers of 10. Multiply and divide by working with the front numbers and exponents.
What Mastery Looks Like: A student can write 0.0000042 as 4.2 × 10⁻⁶ and 650,000,000 as 6.5 × 10⁸. They can multiply those expressions to get 2.73 × 10³ and explain how they adjusted the answer from 27.3 × 10².
Common Misconceptions: Students may think a negative exponent makes the number negative. They may add exponents when adding numbers, instead of matching the powers of 10 first. Some leave an answer like 24 × 10⁴ without rewriting it as 2.4 × 10⁵.
How to Assess It: Exit ticket: Write 600,000,000 and 0.000004 in scientific notation. Multiply them, then give the answer in scientific notation and decimal form.

Lesson moves

Give pairs digit cards and a place-value chart to build 0.0000042, then write it as 4.2 × 10⁻⁶.
Put 3 × 10⁶ + 4 × 10⁵ on the board and ask partners why adding the exponents gives a wrong answer.
Deal cards labeled 0.0000048, 4.8 × 10⁻⁶, and (2 × 10⁸)(2.4 × 10⁻¹⁴); the first pair to match all three wins.
Compare Earth's 1.3 × 10⁷ m diameter with a 2 × 10⁻⁶ m bacterium by calculating how many bacterium lengths fit across.

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