To arrange the quantities [tex]\(1.8 \text{ kL}\)[/tex], [tex]\(1400 \text{ L}\)[/tex], and [tex]\(16,400 \text{ dL}\)[/tex] in order from smallest to largest, follow these steps:
Step 1: Convert all quantities to the same unit (liters)
1 kiloliter (kL) is equal to 1000 liters (L), hence:
[tex]\[ 1.8 \text{ kL} = 1.8 \times 1000 = 1800 \text{ L} \][/tex]
1 deciliter (dL) is equal to 0.1 liters (L), hence:
[tex]\[ 16,400 \text{ dL} = 16,400 \times 0.1 = 1640 \text{ L} \][/tex]
So, now we have:
[tex]\[ 1.8 \text{ kL} = 1800 \text{ L} \][/tex]
[tex]\[ 1400 \text{ L} = 1400 \text{ L} \][/tex]
[tex]\[ 16,400 \text{ dL} = 1640 \text{ L} \][/tex]
Step 2: Compare the quantities now all in liters
We have:
[tex]\[ 1800 \text{ L} \][/tex]
[tex]\[ 1400 \text{ L} \][/tex]
[tex]\[ 1640 \text{ L} \][/tex]
Step 3: Arrange them in ascending order from smallest to largest
From smallest to largest:
[tex]\[ 1400 \text{ L} < 1640 \text{ L} < 1800 \text{ L} \][/tex]
Thus, the quantities in order from smallest to largest are:
[tex]\[ 1400 \text{ L}, 16,400 \text{ dL}, 1.8 \text{ kL} \][/tex]
