   Chapter 9.3, Problem 10ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# A calculator has an eight-digit display and a decimal point that is located at the extreme right of the number displayed, or at the extreme left, or between any pair of digits. The calculator can also display a minus sign at the extreme left of the number. How many distinct numbers can the calculator display? (Note that certain numbers are equal, such as 1.9, 1.90, and 01.900, and should, therefore, not be counted twice.)

To determine

To find how many distinct numbers can the calculator dispay.

Explanation

Given information:

Consider that a calculator has an eight-digit display with a decimal point on the extreme right of the number displayed.

Concept used:

To calculate the number of distinct numbers the calculator display, add +/ to each number at extreme left.

Calculation:

Consider that a calculator has an eight-digit display with a decimal point on the extreme right of the number displayed.

Also consider that the calculator also display a minus sign at the extreme left of the number. The numbers which are equal should not be counted twice.

The objective is to find the number of distinct numbers the calculator display.

To calculate the number of distinct numbers the calculator display, add +/ to each number at extreme left.

Write each number in 8 digit format as 1=0000001.

There are 8 places and 10 different values that can be in each place of the calculator, the number of possible digits in the display is 108.

By the multiplication rule, the number of integers that can be displayed is 2×108.

The calculator is tilled with 0's to have both signs. So, use the difference rule to take one of those away. Hence, the total number of integers that can be displayed as 2×1081.

The other places of the calculator could be any one of 10 different values, because if they are 0's before the decimal point and before any significant non-zero digits

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