Scientific Notation · Grades 8–9
Scientific Notation Worksheets
Count how many places the decimal moves and the exponent follows. Scientific notation worksheets converting both directions, negative exponents included.
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What it is
Scientific notation writes a number as a × 10ⁿ, where the coefficient a is at least 1 and less than 10, and n counts how many places the decimal moves.
Why it matters
From the width of an atom to the distance to a star, scientific notation lets scientists write and calculate with numbers whose zeros would otherwise be impossible to track by hand.
How to do it
- Place the decimal so exactly one non-zero digit sits in front of it, that's the coefficient.
- Count how many places the decimal moved: that number is the exponent.
- Large numbers give a positive exponent; numbers less than 1 give a negative exponent.
Examples by level
- Beginner1.9 × 10² =Answer190
- Intermediate1600 =Answer1.6 × 10³
- Advanced0.0000066 =Answer6.6 × 10⁻⁶
Examples are generated by the same engine as the worksheets, so they're always mathematically correct. Built to avoid repeats, not reshuffle the same handful of questions.
Common mistakes
- Leaving the coefficient outside the 1–10 range (45 × 10³ instead of 4.5 × 10⁴).
- Moving the decimal the wrong direction for the exponent's sign.
- Miscounting the number of places the decimal moved.
Tips
- The coefficient must be at least 1 and less than 10.
- A negative exponent means a small number (less than 1), not a negative number.
For parents
Count how many places the decimal moves: a big number gives a positive exponent, a small number (less than 1) gives a negative one.
For teachers
Have students check that the coefficient is at least 1 and less than 10 before writing the power of ten, it catches most errors.
Key vocabulary
- coefficient
- the number from 1 up to 10 in front of the power of ten
- exponent
- the power of ten, telling how many places the decimal moved
Frequently asked questions
- How do you write a number in scientific notation?
- Move the decimal so one non-zero digit sits in front of it, then use the number of places moved as the power of ten, positive for large numbers, negative for small.
- When is the exponent negative?
- When the number is less than 1 (like 0.0045) the exponent is negative, because you move the decimal to the right.
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