- The "E" notation on a calculator stands for "times 10 raised to the power of", so "a E b" is equivalent to \(a \times 10^b\).
- Applying this rule to the display "5 E -7", we get \(5 \times 10^{-7}\).
- The correct choice is \(5 \times 10^{-7}\).
- The final answer is \(\boxed{5 \times 10^{-7}}\).
Explanation
- Understanding Scientific Notation on a Calculator
The problem asks us to interpret the scientific notation displayed on a calculator, specifically the value "5 E -7". In scientific calculators, the notation "a E b" is a shorthand for \(a \times 10^b\). Here, the number is \(5\) and the exponent is \(-7\). Thus, "5 E -7" represents the value \(5 \times 10^{-7}\).
- Mapping the Notation to the Correct Option
Scientific notation is used to represent very large or very small numbers compactly. It takes the form \(a \times 10^n\), where \(1 \leq |a| < 10\) and \(n\) is an integer. Given the calculator display "5 E -7", we directly translate this into the standard scientific notation format. Comparing this with the provided options:
- \(5+10^{-7}\)
- \(-7 \times 10^5\)
- \(5 \times 10^7\)
- \(5 \times 10^{-7}\)
The interpretation \(5 \times 10^{-7}\) matches the fourth option.
Examples
Scientific notation is essential in fields like astronomy, chemistry, and physics, where we often deal with extremely large or small quantities. For instance, the mass of a single proton is approximately \(1.67 \times 10^{-27}\) kilograms. By using scientific notation, scientists avoid writing out long strings of zeros, which reduces the chance of errors during calculations and makes scientific data much easier to communicate and understand.