Addition is a mathematical operation that combines two or more numbers to find their total or sum. It is one of the fundamental arithmetic operations and is commonly used in various fields, including measurement.

When it comes to measurement, addition is used to combine quantities of the same unit to determine the total or cumulative value. For example, if you have measured the lengths of two objects as 5 centimeters and 8 centimeters, you can find their total length by adding these measurements together: 5 cm + 8 cm = 13 cm.

Similarly, addition is used in other units of measurement, such as time, mass, volume, and more. For instance, if you have measured the durations of two events as 2 hours and 30 minutes, you can add them to find the total duration: 2 hours + 30 minutes = 2 hours 30 minutes.

In scientific and engineering contexts, addition is often employed to sum up multiple measurements or quantities for further analysis. This can be useful in experiments, data analysis, financial calculations, and many other applications.

It's important to note that when performing addition with measurements, it is crucial to ensure that the units are compatible. Adding quantities with different units directly is generally not valid, as the units must be consistent for meaningful results.

Measurement is the process of quantitatively determining the size, length, quantity, or capacity of an object or event. It plays a crucial role in various fields, including science, engineering, mathematics, and everyday life. Addition, as an arithmetic operation, can be applied to measurements in certain contexts. However, it's important to note that addition is not always applicable to all types of measurements, particularly those with different units or incompatible dimensions.

In the simplest case, where two measurements have the same unit and dimension, addition can be performed by simply adding the numerical values. For example, if we have two lengths, 5 meters and 3 meters, their sum is 8 meters.

However, when dealing with measurements that have different units or dimensions, additional considerations are necessary. In such cases, the measurements must be converted to a common unit or dimension before addition can be carried out.

For instance, if we want to add a distance in meters (e.g., 5 meters) to a distance in centimeters (e.g., 300 centimeters), we need to convert one of them to match the other. We can convert 300 centimeters to meters by dividing by 100, yielding 3 meters. Now, we can add 5 meters and 3 meters to get a total distance of 8 meters.

In more complex scenarios, such as adding measurements with different dimensions (e.g., adding a length and a volume), it is not appropriate to perform direct addition. In such cases, additional calculations or conversions are necessary to ensure compatibility between the measurements or to express the result in a meaningful way.

It's essential to consider the nature of the measurements and their units before attempting any addition operations. Always ensure that the measurements being added are of the same type or have been appropriately converted to a common unit or dimension to obtain a meaningful result.

While doing Addition in Measurement we have to express the given measures in the same unit by using the decimal notation and then do Addition as in the case of decimals. But before doing that we need to arrange the given units in their place value chart, putting the digits in their proper places, taking the vacant places as zero.

1) Express in decimal notation and then add :-

a) 6 m 7 dm 2 cm 5 mm, 8 m 8 dm 6 cm 6 mm, 10 m 5 mm

            m   dm   cm   mm

            6    7     2     5    =      6  .  7    2     5 m

            8    8     6     6    =      8  .  8    6     6 m

           10    0     0     5    =  + 1 0 .  0    0     5 m


                                          2 5 .  5    9     6 m

     Answer is 25.596 m      (Ans.)

b) 5 g 6 dg 8 cg 4 mg, 15 g 7 mg, 6 dg 5 mg, 8 g 7 cg 2 mg

           g    dg   cg    mg

           5    6    8     4     =      5    .   6    8    4 g

          15    0    0     7     =    1 5   .   0          7 g

           0    6    0     5     =      0    .   6    0    5 g

           8    0    7     2     =    + 8    .   0    7    2 g


                                        2 9    .   3    6    8 g

Answer is 29.368 g    (Ans.)