Question

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

Explanation:

Step1: Calculate the product

First, calculate \((0.0004)\cdot(0.005)\). \(0.0004 = 4\times10^{-4}\) and \(0.005 = 5\times10^{-3}\), so their product is \((4\times10^{-4})\times(5\times10^{-3}) = 20\times10^{-7}=2\times10^{-6}\) or \(0.000002\).

Step2: Find equivalent expressions

Expression 1: Using decimal multiplication

We can also calculate \(0.0004\times0.005\) directly. \(0.0004\times0.005 = 0.000002\).

Expression 2: Using fraction form

\(0.0004=\frac{4}{10000}\) and \(0.005 = \frac{5}{1000}\), so \(\frac{4}{10000}\times\frac{5}{1000}=\frac{20}{10000000}=\frac{2}{1000000}=0.000002\).

Expression 3: Using scientific notation manipulation

We know \(2\times10^{-6}\) is equivalent, and we can also write it as \(20\times10^{-7}\) (by moving the decimal in \(2\times10^{-6}\) one place to the right and decreasing the exponent by 1) or \(0.2\times10^{-5}\) (by moving the decimal in \(2\times10^{-6}\) one place to the left and increasing the exponent by 1). Here we take \(2\times10^{-6}\), \(0.000002\), and \(\frac{4\times5}{10000\times1000}\) as three equivalent expressions.

Answer:

Three numerical expressions equivalent to \((0.0004)\cdot(0.005)\) are \(2\times10^{-6}\), \(0.000002\), and \(\frac{4\times5}{10000\times1000}\) (or other valid equivalent expressions like \(20\times10^{-7}\), \(\frac{2}{1000000}\) etc.).