To rewrite the ratio of black cars to green cars, given as [tex]\( 71:53 \)[/tex], in the form [tex]\( n:1 \)[/tex], where [tex]\( n \)[/tex] is expressed to two decimal places, follow these steps:
1. Understand the Ratio: The problem states that for every 71 black cars, there are 53 green cars. We need to express this ratio in the form [tex]\( n:1 \)[/tex].
2. Find [tex]\( n \)[/tex]: To convert the ratio [tex]\( 71:53 \)[/tex] to the form [tex]\( n:1 \)[/tex], we need to determine [tex]\( n \)[/tex]. This involves dividing the number representing the black cars by the number representing the green cars. Thus, we will calculate [tex]\( \frac{71}{53} \)[/tex].
3. Perform the Division:
[tex]\[
\frac{71}{53} \approx 1.3396226415094339
\][/tex]
4. Round to Two Decimal Places: The value [tex]\( 1.3396226415094339 \)[/tex] must be rounded to two decimal places to achieve the desired precision.
[tex]\[
1.3396226415094339 \approx 1.34
\][/tex]
5. Express the Final Ratio: The ratio of black cars to green cars in the form [tex]\( n:1 \)[/tex] is:
[tex]\[
n = 1.34
\][/tex]
Therefore, the equivalent ratio of [tex]\( 71:53 \)[/tex] in the form [tex]\( n :1 \)[/tex] is [tex]\( 1.34:1 \)[/tex].
