Understanding the display capabilities of a digital voltmeter is key to determining its largest possible reading. The question asks about a \(4\frac{1}{2}\)-digit voltmeter, which has a specific meaning in instrumentation.

Voltmeter Digit Representation

A digital voltmeter's display capacity is described by the number of "digits" it has. This typically refers to the number of full digits that can display any number from 0 through 9, plus an additional "half" digit.

• Full Digits: In a \(4\frac{1}{2}\)-digit voltmeter, there are 4 full digits. Each of these digits can display any number from 0 to 9. To achieve the largest possible reading, these four full digits should all display '9'.
• Half Digit: The "half" digit refers to the most significant (leftmost) digit. This digit is limited in its display capability; it can typically only display a '0' or a '1'. If it displays '0', it is often suppressed (not shown) unless it's the only digit. For the largest possible reading, this half digit must display '1'.

Largest Possible Voltmeter Reading Calculation

To find the largest possible reading for a \(4\frac{1}{2}\)-digit voltmeter, we combine the maximum values of its half digit and its full digits:

1. The half digit (the leftmost digit) can show a maximum value of \(1\).
2. The remaining 4 full digits can each show a maximum value of \(9\).

Combining these maximum values gives us the largest possible reading:

• Half digit: \(1\)
• First full digit: \(9\)
• Second full digit: \(9\)
• Third full digit: \(9\)
• Fourth full digit: \(9\)

Therefore, the largest possible reading is \(19999\).

Comparing with Options

Let's examine the given options based on our understanding:

• Option 1: \(99999\) - This would imply a 5-digit meter or a different configuration where the leading digit is not limited to 1. This is not typical for a \(4\frac{1}{2}\)-digit voltmeter's maximum reading.
• Option 2: \(49999\) - This suggests the half-digit can go up to '4', which is incorrect for a standard "half" digit definition.
• Option 3: \(19999\) - This matches our calculation, where the half digit is \(1\) and the four full digits are \(9\)s. This is the correct representation of the largest possible reading.
• Option 4: \(10000\) - This is the smallest number that uses the half-digit '1' followed by four full digits. While it uses the half-digit, it represents a specific reading, not the largest possible.

Based on the standard definition of a \(4\frac{1}{2}\)-digit voltmeter, the largest possible reading is \(19999\).