0.006 in scientific notation is 6 × 10⁻³. Scientific notation (also called standard form) expresses any number in the form a × 10ⁿ, where 1 ≤ a < 10 and n is an integer. To convert 0.006, move the decimal point 3 places to the right to get 6.0 — a number between 1 and 10. Since the decimal moved 3 places to the right, the exponent is −3 (negative because the original number is less than 1).
0.006 in scientific notation = 6 × 10⁻³.
Move the decimal 3 places to the right → coefficient = 6, exponent = −3.
Scientific notation form: a × 10ⁿ where 1 ≤ a < 10.
Negative exponent (10⁻ⁿ): the original number is between 0 and 1.
Positive exponent (10ⁿ): the original number is ≥ 10.
Verification: 6 × 10⁻³ = 6/1000 = 0.006 ✓
0.006 = 6 × 10⁻³ = 0.6 × 10⁻² = 60 × 10⁻⁴ (but only 6 × 10⁻³ is correct scientific notation).
Method: Move the decimal point until you get a number ≥ 1 and < 10, then multiply by 10 raised to the appropriate power.
Step 1: Write the number: 0.006
Step 2: Move the decimal point to the right until you get a number between 1 and 10. 0.006 → 0.06 (moved 1 place right) 0.06 → 0.6 (moved 2 places right) 0.6 → 6.0 (moved 3 places right)
Step 3: Count how many places you moved: 3 places to the right.
Step 4: Since you moved RIGHT (number < 1), the exponent is NEGATIVE: n = −3
Step 5: Write in scientific notation: 0.006 = 6 × 10⁻³
Verification: 6 × 10⁻³ = 6 × (1/1000) = 6/1000 = 0.006 ✓
Scientific notation: a × 10ⁿ where 1 ≤ a < 10
Rule 1: The coefficient (a) must be ≥ 1 and < 10. • 6 × 10⁻³ ✓ (6 is between 1 and 10) • 60 × 10⁻⁴ ✗ (60 is not between 1 and 10 — should be 6 × 10⁻³) • 0.6 × 10⁻² ✗ (0.6 is less than 1 — should be 6 × 10⁻³)
Rule 2: The exponent (n) is negative when the number is between 0 and 1. • 0.006 → move decimal RIGHT → negative exponent
Rule 3: The exponent is positive when the number is greater than or equal to 10. • 6000 → move decimal LEFT → positive exponent (6 × 10³)
Rule 4: Numbers between 1 and 10 have exponent 0. • 6 = 6 × 10⁰
Decimal numbers in scientific notation:
Number | Decimal moved | Scientific notation 0.6 | 1 place right | 6 × 10⁻¹ 0.06 | 2 places right | 6 × 10⁻² 0.006 | 3 places right | 6 × 10⁻³ 0.0006 | 4 places right | 6 × 10⁻⁴ 0.00006 | 5 places right | 6 × 10⁻⁵ 0.0025 | 3 places right | 2.5 × 10⁻³ 0.00034 | 4 places right | 3.4 × 10⁻⁴ 0.000007 | 6 places right | 7 × 10⁻⁶
Large numbers in scientific notation (for comparison): 6 | no movement | 6 × 10⁰ 60 | 1 place left | 6 × 10¹ 600 | 2 places left | 6 × 10² 6,000 | 3 places left | 6 × 10³ 0.006 | 3 places right | 6 × 10⁻³
Note: 0.006 and 6000 both have coefficient 6, but opposite signs of exponent (+3 vs −3).
To convert 6 × 10⁻³ back to decimal:
Step 1: The exponent is −3, so move the decimal 3 places to the LEFT. Step 2: Start with 6 → 6.0 6.0 → 0.6 (1 left) 0.6 → 0.06 (2 left) 0.06 → 0.006 (3 left)
Answer: 6 × 10⁻³ = 0.006 ✓
Memory aid: • Negative exponent → small number (between 0 and 1) → decimal point moves LEFT when converting back • Positive exponent → large number (≥ 10) → decimal point moves RIGHT when converting back
0.006 in scientific notation is 6 × 10⁻³. To convert: move the decimal point 3 places to the right to get 6.0 (a number between 1 and 10). Since we moved right and the original number is less than 1, the exponent is −3. Verification: 6 × 10⁻³ = 6/1000 = 0.006 ✓
The exponent is negative because 0.006 is a number between 0 and 1. In scientific notation, whenever the original number is less than 1, you need to move the decimal point to the RIGHT to get a number between 1 and 10, and each rightward move gives a negative exponent. 0.006 requires 3 rightward moves → exponent = −3.
0.0006 in scientific notation is 6 × 10⁻⁴. Move the decimal 4 places right: 0.0006 → 6.0, so the exponent is −4.
Scientific notation (standard form) expresses a number as a × 10ⁿ where a is a number satisfying 1 ≤ a < 10 and n is an integer. It is used to write very large or very small numbers compactly. Examples: 0.006 = 6 × 10⁻³; 6,000,000 = 6 × 10⁶; 0.00025 = 2.5 × 10⁻⁴.
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