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Scientific notation is a way to express very large or very small numbers compactly using powers of 10. A number in scientific notation has the form a × 10^n, where 'a' (the coefficient or mantissa) is a number between 1 and 10, and 'n' (the exponent) is an integer. This notation makes calculations with extreme values easier and shows significant figures clearly.
Accepts: 12345, 0.00045, 4.5e4, 4.5E-3, 4.5 × 10^4
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Scientific notation expresses numbers as a × 10^n where 1 ≤ |a| < 10. To convert: move the decimal point until you have one non-zero digit before it, then count the moves as the exponent. Moving right = negative exponent, moving left = positive. Example: 45000 = 4.5 × 10^4, and 0.0023 = 2.3 × 10^-3.
Scientific notation is a standardized way to write very large or very small numbers. It has the form a × 10^n, where "a" (the coefficient) is a number between 1 and 10, and "n" (the exponent) is an integer. For example, 300,000,000 becomes 3 × 10^8, and 0.000045 becomes 4.5 × 10^-5. This makes extreme numbers easier to read, write, and calculate.
Step 1: Move the decimal point until you have exactly one non-zero digit to its left. Step 2: Count how many places you moved the decimal. Step 3: If you moved left (large number), the exponent is positive. If you moved right (small number), the exponent is negative. Example: 45000 → 4.5000 → moved 4 left → 4.5 × 10^4.
E notation is how calculators and computers display scientific notation. The "E" means "times 10 to the power of." So 4.5E4 means 4.5 × 10^4 = 45000, and 3.2E-6 means 3.2 × 10^-6 = 0.0000032. Some calculators use lowercase "e" instead. This format is also used in programming languages.
Negative exponents indicate numbers between -1 and 1 (not including zero). When the original number is small, you move the decimal right to get a coefficient between 1 and 10, and each rightward move gives a negative exponent. Example: 0.00056 → move decimal 4 places right → 5.6 × 10^-4.
Multiply the coefficients and add the exponents. (a × 10^m) × (b × 10^n) = (a × b) × 10^(m+n). Example: (3 × 10^4) × (2 × 10^5) = 6 × 10^9. If the coefficient result is ≥ 10, adjust by moving the decimal and adding 1 to the exponent.
Divide the coefficients and subtract the exponents. (a × 10^m) ÷ (b × 10^n) = (a ÷ b) × 10^(m-n). Example: (8 × 10^6) ÷ (2 × 10^2) = 4 × 10^4. Adjust the coefficient to be between 1 and 10 if necessary.
Engineering notation is a variant of scientific notation where the exponent is always a multiple of 3 (like 10^3, 10^6, 10^-9). This aligns with metric prefixes: kilo (10^3), mega (10^6), milli (10^-3), micro (10^-6). The coefficient can be from 1 to 999. Example: 45000 = 45 × 10^3 in engineering notation.
Scientific notation clearly shows significant figures through the coefficient. In 4.50 × 10^3, there are 3 significant figures (the trailing zero is significant). In standard form (4500), it's ambiguous whether trailing zeros are significant. Writing 4.5 × 10^3 shows only 2 sig figs, while 4.500 × 10^3 shows 4.