Answered

Which of these is the smallest number?


A4,120
B$4.1 \times 10^3$
C$5.3 \times 10 \times 10$
D$4.1289 \times 10^2$
E$3.88 \times 10^3$

F. $59.2 \times 10^1$

Verified Answer :

  • Convert each expression into its equivalent decimal value.
  • Compare the decimal results: \(4120, 4100, 530, 412.89, 3880, 592\).
  • Identify the smallest decimal value, which is \(412.89\).
  • The final answer is \(\boxed{412.89}\).

Explanation

  1. Converting to Decimal Notation

To determine the smallest number among the given options, we first convert each number into standard decimal notation:

  1. \(4,120 = 4120\)
  2. \(4.1 \times 10^3 = 4.1 \times 1000 = 4100\)
  3. \(5.3 \times 10 \times 10 = 5.3 \times 100 = 530\)
  4. \(4.1289 \times 10^2 = 4.1289 \times 100 = 412.89\)
  5. \(3.88 \times 10^3 = 3.88 \times 1000 = 3880\)
  6. \(59.2 \times 10^1 = 59.2 \times 10 = 592\)
  1. Comparing the Values

Now we compare the decimal values obtained:
\(412.89 < 530 < 592 < 3880 < 4100 < 4120\)
By arranging the numbers in increasing order, it is clear that \(412.89\) is the smallest value. This value corresponds to the expression \(4.1289 \times 10^2\).

  1. Conclusion

Based on our comparison, the smallest number in the list is \(4.1289 \times 10^2\), which is equal to \(\boxed{412.89}\).

Examples

In finance and data analysis, correctly identifying the smallest value in a dataset is crucial. For example, if you are comparing interest rates or costs across different providers, converting all values to a common format (like currency or decimal) allows for an accurate comparison, ensuring that you select the most cost-effective or advantageous option. This simple method of standardization is a foundational skill in data-driven decision-making.

Related Questions