Question

write three numerical expressions that are equivalent to (0.0004) · (0.005).

Explanation:

First, calculate the value of \((0.00004) \cdot (0.005)\).

Step 1: Multiply the numbers

\(0.00004\times0.005 = 0.0000002\)

Step 2: Find equivalent expressions

We can rewrite the original numbers in scientific notation and multiply, or use different decimal representations.

Expression 1:

Rewrite \(0.00004\) as \(4\times10^{-5}\) and \(0.005\) as \(5\times10^{-3}\), then multiply:
\((4\times10^{-5})\cdot(5\times10^{-3}) = 4\times5\times10^{-5 - 3}=20\times10^{-8}=2\times10^{-7}\) (Wait, no, \(0.00004\times0.005 = 0.0000002 = 2\times10^{-7}\)? Wait, no, \(0.00004\) is \(4\times10^{-5}\), \(0.005\) is \(5\times10^{-3}\), multiplying them: \(4\times5 = 20\), \(10^{-5}\times10^{-3}=10^{-8}\), so \(20\times10^{-8}=2\times10^{-7}\)? Wait, no, \(0.00004\times0.005 = 0.0000002\), and \(2\times10^{-7}=0.0000002\), yes.

Expression 2:

We can also write \(0.00004\) as \(0.0004\times0.1\) and \(0.005\) as \(0.05\times0.1\), then \((0.0004\times0.1)\cdot(0.05\times0.1)=0.0004\times0.05\times0.1\times0.1 = 0.00002\times0.01 = 0.0000002\)

Expression 3:

Or \(0.00004 = 0.000004\times10\), \(0.005 = 0.05\times0.1\), then \((0.000004\times10)\cdot(0.05\times0.1)=0.000004\times0.05\times10\times0.1 = 0.0000002\times1 = 0.0000002\)

Wait, maybe a better way. First, calculate \(0.00004\times0.005 = 0.0000002\). Now, find three expressions that equal \(0.0000002\).

1. \(0.00002\times0.01\): \(0.00002\times0.01 = 0.0000002\)
2. \(0.0002\times0.001\): \(0.0002\times0.001 = 0.0000002\)
3. \(0.002\times0.0001\): \(0.002\times0.0001 = 0.0000002\)

Let's verify:

• \(0.00002\times0.01\): \(0.00002\times0.01 = 0.0000002\) (correct)
• \(0.0002\times0.001\): \(0.0002\times0.001 = 0.0000002\) (correct)
• \(0.002\times0.0001\): \(0.002\times0.0001 = 0.0000002\) (correct)

Answer:

1. \(0.00002 \cdot 0.01\)
2. \(0.0002 \cdot 0.001\)
3. \(0.002 \cdot 0.0001\)