Mrs.D Math · 8th Grade

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Scientific Notation & Standard Form
Scientific Notation
Standard Form
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🔬 Sci → Standard
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🔢 Standard → Sci
🔬 Sci → Standard
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🔢 Scientific Notation

Standard Form → Scientific Notation

Scientific notation is written as c × 10n, where the coefficient c is between 1 and 10.

1
Move the decimal point until only one non-zero digit remains in front of it.
45,000 → 4.5
2
Count how many places you moved the decimal — that's your exponent.
45,000 → moved 4 places left → 10⁴
3
Large numbers (≥1) get a positive exponent. Small numbers (<1) get a negative exponent.
45,000 = 4.5 × 10⁴  |  0.0007 = 7 × 10⁻⁴

Scientific Notation → Standard Form

1
Look at the exponent on the 10. Positive exponent → move the decimal point right. Negative exponent → move it left.
2
Move the decimal that many places, filling in zeros as needed.
3.2 × 10³ → move right 3 → 3,200
3
Negative exponent example:
6 × 10⁻⁵ → move left 5 → 0.00006

Worked Example

Convert 0.00052 to scientific notation.

1
Move the decimal right until one nonzero digit is in front: 5.2
2
Count the places moved: 4 places right
3
Since the original number is small, the exponent is negative: 5.2 × 10⁻⁴
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STANDARD → SCIENTIFIC
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