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Zorluk: KolayScientific Notation

Arrange the following values from least to greatest.

  1. 1620620
  2. 28,5008,500
  3. 31.2×1041.2 \times 10^4
  4. 43.0×1053.0 \times 10^5

Cevap

The correct sequence from least to greatest is: 620620, 8,5008,500, 1.2×1041.2 \times 10^4, 3.0×1053.0 \times 10^5.
By converting all values to standard form, it is clear that 620620 is the smallest, followed by 8,5008,500, then 12,00012,000 (which is 1.2×1041.2 \times 10^4), and finally 300,000300,000 (which is 3.0×1053.0 \times 10^5).

Adım Adım Çözüm

1
Convert all values to standard numerical form to easily compare their sizes.
The values become: 12,00012,000 (from item 1), 620620 (from item 2), 300,000300,000 (from item 3), and 8,5008,500 (from item 4).
Translating scientific notation into standard form allows for direct visual comparison of digit lengths and magnitudes.
2
Group and compare the numbers by their total number of digits.
620620 has three digits, 8,5008,500 has four digits, 12,00012,000 has five digits, and 300,000300,000 has six digits.
For whole positive numbers, a value with fewer digits is always smaller than a value with more digits.
3
Order the values sequentially starting from the smallest.
The final order is 620620 < 8,5008,500 < 12,00012,000 < 300,000300,000.
This establishes the ascending sequence requested by the question.

Anahtar Kavram

Comparing Magnitudes in Standard and Scientific Notation

Alternatif Yöntem

Instead of using standard form, you can convert all numbers to scientific notation: 6.2×1026.2 \times 10^2, 8.5×1038.5 \times 10^3, 1.2×1041.2 \times 10^4, 3.0×1053.0 \times 10^5. Because the exponents (2,3,4,52, 3, 4, 5) are already in ascending order, you can immediately determine the correct sequence without looking at the coefficients.
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