two students are playing a math game. the object of the game is to make the least possible number by arranging the given digits inside absolute value bars on a card. In the first round, each player will use the digits 3, 5, and 7 to fill in the card. One student arranges the numbers on the card as shown. what was the student's mistake? the number read -75.3. thanks
wouldn't abs(.357) be the least?
To determine the student's mistake, let's analyze the given number, -75.3, and compare it to the available digits (3, 5, and 7).
To create the least possible number, the digits should be placed from greatest to least value inside the absolute value bars. In this case, the digit '7' should be placed to the left of '5,' resulting in |-7|. Afterward, the digit '3' should be placed after the decimal point. Therefore, the correct representation of the least possible number using the given digits is -7.53.
Based on this, we can conclude that the student mistakenly placed the digit '7' after the decimal point instead of in the ones place.
To determine the mistake made by the student, let's analyze how the digits 3, 5, and 7 were arranged to form the number -75.3.
The absolute value bars, usually denoted as |x|, are used to indicate the magnitude of a number without considering its sign. In this case, the mathematical expression inside the absolute value bars should result in a positive value.
Given that the student arranged the numbers as -75.3, it appears that the student mistakenly put a negative sign before the number. However, the absolute value function does not consider the sign of a number, so the negative sign is incorrect in this case.
To correctly arrange the digits 3, 5, and 7 inside absolute value bars, you should follow these steps:
1. Begin by placing the number with the highest value (in this case, 7) between the absolute value bars.
2. Next, select the remaining two digits (3 and 5) and arrange them outside the absolute value bars in such a way that the expression inside the bars becomes the smallest possible number.
3. In this case, the correct arrangement would be -753, with the numbers 3 and 5 placed on the left side of the bars to create the smallest possible number inside the bars.
4. The student's mistake was placing a decimal point after the number, resulting in -75.3 instead of the correct value -753.
To summarize, the mistake made by the student was adding a decimal point after the number, resulting in an incorrect value for the math game. The correct value should have been -753.