What is Measuring Length
We know how to measure the length to the nearest whole number. Take the object which you want to measure to a measuring scale and measure the length of the object sideways to the scale at one end, or ‘0’.
Then look for the number on the other end. The number on the other end is the length of the object.
If the object doesn’t exactly coincide with any whole number’s mark, find the line that is just about its end. That will be the length of the object.
For example, the feather shown in this picture reaches from the number 0 to exactly 6. So the length of the feather is 6 centimeters.
In our lessons so far, we have been measuring the lengths and heights of the objects to the whole inch.
Measure Length: Half inch
What will be the length of the object if it ends halfway between any two numbers?
In the above picture, the string starts from the number 0 but ends exactly halfway between 2 and 3.
So, to overcome this problem, we mark the scale further into halves and quarters. The points that are exactly halfway between two numbers are marked half \(\frac{1}{2},\frac{3}{2},\frac{5}{2},\) and so on.
Therefore, the length of the pencil is \(\frac{5}{2}\) inches.
Again, not all objects measured have whole numbers as their length or height. So, the rulers are marked half and quarter to measure the length.
So, we can measure the length of the string as shown,
One end of the string is at 0 and the other end is exactly halfway between 1 and 2.
The thread is \(\frac{3}{2}\) inches long. This length can also be represented as 1 whole inch and one \(\frac{1}{2}\) inch, or simply \({1}\frac{1}{2}\) inches.
Estimation of Length for Half an inch
Again, if a feather is between a half-inch mark and a whole number, then the half-inch mark that is closest to the end of the feather is considered its length.
For example,
The thread is between the halfway mark and 1. But we can see that the halfway mark is closer to the end of the string.
So, the string is about \({1}\frac{1}{2}\) inch long.
Measure length: Quarter inch
What will be the length of the object if the object ends exactly halfway between the half and a whole number?
We can measure the length up to half an inch. Similarly, if the end of the object is in the middle of the half and a whole number, we will change the ruler. Take a ruler which consists of the quarter.
Otherwise, we can mark the quarter as shown on this scale,
For example, the string shown in the picture ends at the middle of \(1\frac{1}{2}\) and 2. So, the length of the string is closer to a quarter inch.
The string is \(\frac{7}{4}\)or \({1}\frac{3}{4}\) inches long. The string length can also be represented as 1 whole and three \(\frac{1}{4}\) inches, or \(1\frac{3}{4}\) inches.
Estimation of Length for Quarter inches
Again, if the string is also between a quarter-inch and a half or a whole number, the quarter-inch marking that is closest to the end of the string is taken as the length of the string.
For example,
The thread shown ends between 0 and \({2}\frac{1}{2}\). But we can see that the length of the pencil ends at a quarter mark and is closer to the end of the string.
So, the string is about \({2}\frac{1}{4}\) inches long.
Solved Examples on Measuring Length
Example 1: Find the length of the pencil shown.
Solution:
The end of the pencil is halfway between the numbers 4 and 5. Therefore, the length of the pencil is four and a half, that is, \({4}\frac{1}{2}\) inches.
Example 2: Find the length of the vegetable shown.
Solution:
The end of the ladies’ finger is between 3 and a half mark after 3. We can see that the end of the ladies’ finger is much closer to the \({3}\frac{1}{2}\) mark.
Therefore, the length of the ladies’ finger is about \({3}\frac{1}{2}\) inches.
Example 3: Find the length of the pencil.
Solution:
The end of the pencil is between the \({4}\frac{1}{2}\) and the number 5. The end is exactly halfway between them.
So, it is a quarter more than \({4}\frac{1}{2}\). Therefore, the length of the pencil is \({4}\frac{3}{4}\) inches.
Example 4: Find the length of the feather shown.
Solution:
The end of the feather is between the numbers 3 and \({3}\frac{1}{2}\). But, the end is near the quarter mark after number 3.
Therefore, the length of the feather is nearly \({3}\frac{1}{4}\) inches.
If the end of an object is halfway between a quarter and a whole number mark, we have to change our scale to one eights\((\frac{1}{8}^{th})\) scale. Otherwise, we can also round the value to the nearest half inch or whole number.
No, the length of the object measured from any scale gives the same length. If we measure the length using different unit scales (centimeters, inches, feet etc.), the magnitude of length may be different but they are equivalent to each other.