Answer :
The three equivalent numerical expressions are:
[tex](0.0004) . (0.005) = (\frac{4}{10000}).(\frac{5}{1000})[/tex]
[tex](0.0004) . (0.005)= (\frac{1}{2500}).(\frac{1}{200})[/tex]
[tex](0.0004) . (0.005) = (4 \times 10^{-4}).(5 \times 10^{-3})[/tex]
Solution:
We have to write three numerical expressions that are equivalent to (0.0004) . (0.005)
Given expression is:
(0.0004) . (0.005)
First numerical expression:
We know that 0.0004 can be written in fraction as:
[tex]0.0004 = \frac{0.0004 \times 10000}{10000} = \frac{4}{10000}[/tex]
Similarly,
[tex]0.005 = \frac{0.005 \times 1000}{1000} = \frac{5}{1000}[/tex]
Therefore,
[tex](0.0004) . (0.005) = (\frac{4}{10000}).(\frac{5}{1000})[/tex]
Second numerical expression:
The first numerical expression can be simplified to get second numerical expression
[tex](\frac{4}{10000}).(\frac{5}{1000}) = (\frac{1}{2500}).(\frac{1}{200})[/tex]
Third numerical expression:
The given expression can be expressed in scientific notation:
Steps for converting to scientific notation:
Move the decimal point in your number until there is only one non-zero digit to the left of the decimal point. The resulting decimal number is a.
Count how many places you moved the decimal point. This number is b.
If you moved the decimal to the left b is positive.
If you moved the decimal to the right b is negative.
If you did not need to move the decimal b = 0.
Write your scientific notation number as a x 10^b and read it as "a times 10 to the power of b."
Remove trailing 0's only if they were originally to the left of the decimal point.
[tex]0.0004 = 4 \times 10^{-4}\\\\0.005 = 5 \times 10^{-3}[/tex]
Therefore, third equivalent numerical expression is:
[tex](0.0004) . (0.005) = (4 \times 10^{-4}).(5 \times 10^{-3})[/tex]