8th Grade Math · Scientific Notation
Standard form Worksheets
Fresh practice, ready to print. Answer key included.
Numbers already in scientific notation, written out in the usual way.
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How it works: a quick refresher
The rules this worksheet practices, then one problem worked from start to finish.
| Strategy | How it works |
|---|---|
| One digit before the decimal point | The coefficient is at least 1 and less than 10. 45,000 is 4.5 × 10⁴, not 45 × 10³. |
| Count the move | For a large number, the exponent is how many places the decimal point moves left. 45,000 moves four places. |
| Small numbers use a negative exponent | 0.00032 = 3.2 × 10⁻⁴. The exponent is how many places the point moves right. |
| Multiply coefficients, add exponents | (3 × 10⁴) × (2 × 10³) = 6 × 10⁷. |
| Fix a coefficient that leaves the range | 4 × 5 = 20, so 20 × 10⁵ becomes 2 × 10⁶. A quotient of 0.5 × 10² becomes 5 × 10¹. |
Worked example
Find (4 × 10³) × (5 × 10²).
- 1Multiply the coefficients and add the exponents: 4 × 5 = 20, and 3 + 2 = 5. That is 20 × 10⁵.
- 220 is not between 1 and 10. Write it as 2 × 10¹.
- 32 × 10¹ × 10⁵ = 2 × 10⁶.
- 4Check: 4,000 × 500 = 2,000,000, and 2 × 10⁶ = 2,000,000.
Ready-made versions
Three fixed versions you can link to or share. Each is a PDF with its own answer key.
- Standard form Worksheets, version 1Worksheet PDFAnswer key PDF
- Standard form Worksheets, version 2Worksheet PDFAnswer key PDF
- Standard form Worksheets, version 3Worksheet PDFAnswer key PDF
Grade level and standard
Written for 8th grade math (expressions and equations) and aligned to CCSS 8.EE.A.4. It also works as review in later grades.
Common questions
- Is there an answer key?
- Yes. Every worksheet has a matching answer key with each answer worked on the same grid or layout as the question. The worksheet code printed at the bottom of each page pairs a sheet with its key.
- Why is 45,000 written 4.5 × 10⁴ and not 45 × 10³?
- Scientific notation keeps a single digit before the decimal point. 45 is more than 10, so it is not a finished coefficient. 4.5 is between 1 and 10, and the exponent picks up the extra place.
- What if the coefficient is 20 after multiplying?
- Split off a power of 10. 20 = 2 × 10, so add 1 to the exponent. 20 × 10⁵ is the same number as 2 × 10⁶.
- How many different versions are there?
- About a million per skill. Each time you press the button the problems are generated fresh, so you can print a different version for every student, a retake, or another night of practice.
- Are the worksheets free?
- Yes. They are free to print and copy for your home or classroom, with no sign-up.
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