- The variable \(d = 10^2 = 100\).
- Dividing a number by \(100\) shifts the decimal point two places to the left.
- Checking each equation:
- \(386.2 \div 100 = 3.862\) (True)
- \(4963.6 \div 100 = 49.636
eq 4.9636\) (False)
- \(0.6 \div 100 = 0.006\) (True)
- \(5.8 \div 100 = 0.058
eq 0.58\) (False)
- \(15.3 \div 100 = 0.153\) (True)
- The true equations are \(\boxed{386.2 \div d = 3.862, 0.6 \div d = 0.006, 15.3 \div d = 0.153}\).
Explanation
- Understanding the Problem
The problem asks us to evaluate five given equations where \(d = 10^2\), which is equal to \(100\). Dividing any number by \(100\) shifts the decimal point two places to the left. We will test each equation by performing this division and comparing the result with the value provided in the equation.
- Testing the Equations
We test each equation one by one:
- \(386.2 \div 100 = 3.862\). Shifting the decimal point of \(386.2\) two places to the left gives \(3.862\). This matches the equation, so it is true.
- \(4963.6 \div 100 = 49.636\). Shifting the decimal point of \(4963.6\) two places to the left gives \(49.636\), which does not match \(4.9636\). This is false.
- \(0.6 \div 100 = 0.006\). Shifting the decimal point of \(0.6\) two places to the left (adding a zero as a placeholder) gives \(0.006\). This matches the equation, so it is true.
- \(5.8 \div 100 = 0.058\). Shifting the decimal point of \(5.8\) two places to the left gives \(0.058\), which does not match \(0.58\). This is false.
- \(15.3 \div 100 = 0.153\). Shifting the decimal point of \(15.3\) two places to the left gives \(0.153\). This matches the equation, so it is true.
- Conclusion
Based on our analysis, the equations that hold true are:
- \(386.2 \div d = 3.862\)
- \(0.6 \div d = 0.006\)
- \(15.3 \div d = 0.153\)
The final answer is the set of these three equations.
Examples
Understanding how to divide by powers of ten is crucial for quick mental calculations and scientific notation. For example, if a measurement of \(525.5\) centimeters is taken and you need to convert it to meters, you divide by \(100\) (since there are \(100\) cm in \(1\) m). By simply moving the decimal point two places to the left, you quickly find that the measurement is \(5.255\) meters. This method is used daily in currency conversions, unit conversions, and data scaling.