To express the ratio [tex]\(1800 \, \text{cm}\)[/tex] to [tex]\(20 \, \text{m}\)[/tex] in its simplest form, we'll follow these steps:
1. First, we need to ensure both quantities are in the same units. Since [tex]\(1800 \, \text{cm}\)[/tex] is already in centimeters, we will convert [tex]\(20 \, \text{m}\)[/tex] to centimeters as well:
[tex]\[
20 \, \text{m} = 20 \times 100\, \text{cm} = 2000 \, \text{cm}
\][/tex]
2. Now, the ratio we have is [tex]\(1800 \, \text{cm} : 2000 \, \text{cm}\)[/tex].
3. To simplify this ratio, we need to find the greatest common divisor (GCD) of the two numbers, [tex]\(1800\)[/tex] and [tex]\(2000\)[/tex].
4. The GCD of [tex]\(1800\)[/tex] and [tex]\(2000\)[/tex] is [tex]\(200\)[/tex].
5. We will divide both quantities by their GCD:
[tex]\[
\frac{1800 \, \text{cm}}{200} = 9
\][/tex]
[tex]\[
\frac{2000 \, \text{cm}}{200} = 10
\][/tex]
6. Therefore, the ratio [tex]\(1800 \, \text{cm} : 2000 \, \text{cm}\)[/tex] simplifies to [tex]\(9 : 10\)[/tex].
So, the simplified form of the ratio [tex]\(1800 \, \text{cm} : 20 \, \text{m}\)[/tex] is [tex]\(9 : 10\)[/tex].
