To write the ratio of [tex]$2.40 to $[/tex]2.00 as a ratio of whole numbers in lowest terms, we'll follow these steps:
1. Convert the dollar amounts to cents: This helps avoid working with decimals and makes the calculations simpler.
[tex]\[
2.40 \text{ dollars } = 2.40 \times 100 = 240 \text{ cents}
\][/tex]
[tex]\[
2.00 \text{ dollars } = 2.00 \times 100 = 200 \text{ cents}
\][/tex]
2. Find the greatest common divisor (GCD) of the two amounts in cents. The GCD is the largest number that divides both amounts without leaving a remainder.
[tex]\[
\text{GCD}(240, 200) = 40
\][/tex]
3. Divide both amounts by their GCD to reduce the ratio to its lowest terms.
[tex]\[
\frac{240}{40} = 6
\][/tex]
[tex]\[
\frac{200}{40} = 5
\][/tex]
4. Write the ratio: Now that we have the whole numbers 6 and 5, we can write the ratio in its simplest form:
[tex]\[
2.40 \text{ to } 2.00 \quad \text{is equivalent to} \quad 6:5
\][/tex]
Therefore, the ratio of [tex]$2.40 to $[/tex]2.00 in lowest terms is [tex]\(\boxed{6:5}\)[/tex].
