Asked by lutina
vThe height of Angel Falls, the tallest waterfall in the world, is 3,212 feet. How do you write this number in scientific notation?
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Why do very large numbers have positive exponents when written in scientific notation? Explain.
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Write 3,212 in normalized scientific notation as 3.212 × 10^3.
Why: scientific notation writes a number as a × 10^n with 1 ≤ |a| < 10. To get a in that range, move the decimal point in 3212 three places left (3212 → 3.212). Each left move divides by 10, so to keep the value equal you must multiply by 10 three times, i.e. multiply by 10^3:
3.212 × 10^3 = 3.212 × 1000 = 3212.
More generally: for numbers ≥ 10 you move the decimal left k places (k = number of digits − 1), so you multiply by 10^k. That is why very large numbers have positive exponents. (Small numbers < 1 need the decimal moved right and get negative exponents; e.g. 0.004 = 4 × 10^−3.)
Why: scientific notation writes a number as a × 10^n with 1 ≤ |a| < 10. To get a in that range, move the decimal point in 3212 three places left (3212 → 3.212). Each left move divides by 10, so to keep the value equal you must multiply by 10 three times, i.e. multiply by 10^3:
3.212 × 10^3 = 3.212 × 1000 = 3212.
More generally: for numbers ≥ 10 you move the decimal left k places (k = number of digits − 1), so you multiply by 10^k. That is why very large numbers have positive exponents. (Small numbers < 1 need the decimal moved right and get negative exponents; e.g. 0.004 = 4 × 10^−3.)
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