What does 5.2×10^-7 represent on a calculator?
A. −5.20000000 B. −52,000,000 C. 0.000000052 D. 0.00000052
The Correct Answer and Explanation is:
The expression (5.2 \times 10^{-7}) is in scientific notation, which is commonly used in mathematics and science to represent very small or very large numbers in a more manageable format. In scientific notation, the number is expressed as a product of a coefficient (in this case, 5.2) and a power of ten (here, (10^{-7})).
To convert (5.2 \times 10^{-7}) into standard decimal form, we need to understand what (10^{-7}) signifies. The exponent (-7) indicates that we are moving the decimal point in the coefficient (5.2) seven places to the left.
- Starting with 5.2, if we visualize it as 5.2000000, we can move the decimal point left:
- Move 1: 0.52 (1 place)
- Move 2: 0.052 (2 places)
- Move 3: 0.0052 (3 places)
- Move 4: 0.00052 (4 places)
- Move 5: 0.000052 (5 places)
- Move 6: 0.0000052 (6 places)
- Move 7: 0.00000052 (7 places)
Thus, when we move the decimal point seven places to the left, we arrive at 0.00000052.
Now, let’s look at the provided options:
- A. −5.20000000: This is a negative number and incorrect.
- B. −52,000,000: This is also negative and incorrect.
- C. 0.000000052: This has too many zeros; it is incorrect.
- D. 0.00000052: This is the correct decimal representation of (5.2 \times 10^{-7}).
Therefore, the correct answer is D. 0.00000052.
Using scientific notation allows for clarity and ease of use, especially when dealing with extremely small or large numbers, making calculations and comparisons more straightforward.