Question

Arrange the following from least to greatest: 6,700 meters, 672,000 centimeters, and 6.6 kilometers.

Answer 1

Hint: In this question, given three numbers are in different unit systems. Now, we need to use the conversions given by 1 kilometer is equal to 1000 meters which is further equal to 100000 centimeters and then convert the given numbers accordingly to the same unit. Then on comparing them we get the values accordingly from highest to least.

Complete step by step answer:
Now, as we already know that the relation between kilometers and meters is given by
\[1km=1000m\]
Now, the relation between the meters and centimeters is given by
\[1m=100cm\]
Now, from the given numbers in the question we have
6,700 meters, 672,000 centimeters, and 6.6 kilometers.
Let us now first consider the number which is given in centimeters and convert to meters
672,000 centimeters
Now, let us convert this number in terms of meters.
As we already know that the relation between meters and centimeters is given by
\[1m=100cm\]
Now, on dividing with 100 on both sides in the above conversion we get,
\[1cm=\dfrac{1}{100}m\]
Now, we need to divide the given number with 100 to get its value in meters
\[\Rightarrow 672,000cm=\dfrac{672,000}{100}m\]
Now, on further simplification we get,
\[\therefore 672,000cm=6,720m\]
Let us now consider the number which is given in kilometers and convert it to meters
6.6 kilometers
Now, let us convert this number in terms of meters.
As we already know that the relation between meters and centimeters is given by
\[1km=1000m\]
Now, we need to multiply the given number with 1000 to get its value in meters
\[\Rightarrow 6.6km=6.6\times 1000m\]
Now, on further simplification we get,
\[\therefore 6.6km=6,600m\]
Now, the numbers are to be arranged from least to greatest
6,700 meters, 672,000 centimeters, and 6.6 kilometers.
Now, these can be further written as
6,700 meters, 6,720 meters and 6,600 meters
Let us now arrange them from least to greatest
6,600 meters, 6,700 meters, 6,720 meters
Hence, the numbers from least to highest are 6.6 kilometers, 6,700 meters, 672,000 centimeters.

Note:
Instead of converting all the given numbers into meters and then arranging them from least to highest we can also solve this by converting all of them into either kilometers or centimeters. But, then the comparison would be a little confusing as one case has many zeroes and the other has decimals.
It is important to note that before comparing and arranging them from least to greatest we first need to convert all of them into the same units then only we can compare them. If we do not convert them and arrange then the result will be incorrect.