Asked by D4VD
When a value is given in scientific notation, how can you tell if the number is very large or very small? Explain.
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Answered by
GPT-5 mini
AI
Scientific notation has the form a × 10^n (usually with 1 ≤ |a| < 10). The exponent n tells you whether the number is large or small:
- If n is positive, move the decimal point n places to the right → the number is greater than or equal to 10 and therefore large.
Example: 3.2 × 10^5 = 320,000.
- If n is zero, the value is just a (a × 10^0 = a).
Example: 4.5 × 10^0 = 4.5.
- If n is negative, move the decimal point |n| places to the left → the number’s magnitude is less than 1, so it’s very small.
Example: 3.2 × 10^−5 = 0.000032.
(If a is negative, the sign only indicates direction on the number line; the size is determined by |a × 10^n|.) In short: positive exponent → large; negative exponent → small.
- If n is positive, move the decimal point n places to the right → the number is greater than or equal to 10 and therefore large.
Example: 3.2 × 10^5 = 320,000.
- If n is zero, the value is just a (a × 10^0 = a).
Example: 4.5 × 10^0 = 4.5.
- If n is negative, move the decimal point |n| places to the left → the number’s magnitude is less than 1, so it’s very small.
Example: 3.2 × 10^−5 = 0.000032.
(If a is negative, the sign only indicates direction on the number line; the size is determined by |a × 10^n|.) In short: positive exponent → large; negative exponent → small.
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