The correct answer and explanation is:
The correct answer is 0.723.
To solve the division problem 72.3 ÷ 100, we can utilize a straightforward method related to our base ten number system. Dividing a number by 100 effectively makes its value one hundred times smaller. This can be visualized by shifting the position of the digits relative to the decimal point. The most efficient way to perform this calculation is to move the decimal point to the left. The number of places the decimal point moves is determined by the number of zeros in the divisor. Since we are dividing by 100, which has two zeros, we will move the decimal point two places to the left.
Let’s apply this rule to the number 72.3. The decimal point is initially positioned between the digit 2 and the digit 3.
For the first move, we shift the decimal point one place to the left. This moves it from its position in 72.3 to be between the 7 and the 2, resulting in the number 7.23. This first step is equivalent to dividing the original number by 10.
For the second move, we must shift the decimal point another place to the left. Looking at 7.23, moving the decimal to the left of the 7 requires us to introduce a placeholder. We add a zero in front of the 7 to hold the new tenths place. This gives us .723.
As a standard mathematical convention for clarity, when a decimal number is less than one, we write a zero in the ones place. Therefore, the final answer is written as 0.723.
This process works because each shift of the decimal point to the left represents a division by ten. Moving it two places is the same as dividing by ten twice, or dividing by 100 (10 × 10). This simple trick avoids the need for long division and is a fundamental skill for quick mental calculations.
