Question

which of these expressions is equivalent to $0.8 \div 0.02$? $0.8 \div 2$ $80 \div 2$ $800 \div 2$ $8,000 \div 2$

Explanation:

Step1: Recall the rule of dividing decimals

To make the division of decimals easier, we can multiply both the dividend and the divisor by the same power of 10 to eliminate the decimal in the divisor. For \(0.8\div0.02\), we multiply both the numerator and the denominator by 100 (because \(0.02\times100 = 2\) and \(0.8\times100=80\)). So the equivalent expression is \(\frac{0.8\times100}{0.02\times100}=\frac{80}{2}\), which is \(80\div2\).

Step2: Check other options (optional but for clarity)

• For \(0.8\div2\): The divisor here is 2, while in the original problem the divisor is 0.02. We didn't multiply the divisor by 100 here (we multiplied by 1 instead), so it's not equivalent.
• For \(800\div2\): If we multiply \(0.8\) by 1000 (not 100) and \(0.02\) by 1000, we get \(800\div20\), not \(800\div2\). So this is incorrect.
• For \(8000\div2\): Similar to the above, the multiplications are not consistent with eliminating the decimal in the divisor of the original problem.

Answer:

\(80\div2\)