# CLASS-5MULTIPLICATION IN MEASUREMENT

MULTIPLICATION IN MEASUREMENT -

Multiplication is another fundamental arithmetic operation that can be applied to measurements. However, similar to addition and subtraction, there are considerations to keep in mind when multiplying measurements, especially when dealing with different units or dimensions.

When multiplying two measurements with the same unit and dimension, the process is straightforward. You multiply the numerical values. For example, if you have a length of 5 meters and you want to multiply it by 3, the result would be 15 meters.

When multiplying measurements with different units or dimensions, additional conversions may be necessary to ensure compatibility and obtain a meaningful result. Here are a few scenarios:

1. Multiplying measurements with the same dimension but different units: In this case, you need to convert one or both measurements to a common unit before multiplication. For example, if you want to multiply a length of 2 feet by a length of 30 centimeters, you would convert 2 feet to centimeters (since 1 foot is approximately 30.48 centimeters). The result would be 60 centimeters multiplied by 30 centimeters, giving you 1800 square centimeters.
2. Multiplying measurements with different dimensions: Multiplying measurements with different dimensions can be more complex, as the resulting measurement may have a different dimension altogether. In such cases, you may need to perform additional calculations or use conversion factors to obtain a meaningful result. For example, multiplying a length of 5 meters by a width of 2 meters would give you an area of 10 square meters.
3. Multiplying measurements with derived units: In some cases, the multiplication of measurements may result in derived units. For example, multiplying a length of 3 meters by a time of 5 seconds could result in a measurement of 15 meter-seconds, which represents the concept of momentum.

It's important to carefully consider the units and dimensions involved when multiplying measurements. Convert measurements to a common unit or dimension when necessary to ensure compatibility and to obtain a meaningful result.

Multiplication is another arithmetic operation that can be applied to measurements, but it requires careful consideration of units and dimensions to ensure the validity and meaningfulness of the result.

When multiplying two measurements with the same unit, the process is straightforward. You simply multiply the numerical values. For example, if you have a length of 5 meters and a width of 3 meters, the product would be the area, which is 15 square meters.

However, when dealing with measurements that have different units or dimensions, additional conversions are necessary before multiplication can be performed.

For instance, if you want to multiply a length in meters (e.g., 4 meters) by a width in centimeters (e.g., 120 centimeters), you need to convert one of the measurements to match the other. Converting 120 centimeters to meters by dividing by 100 gives you 1.2 meters. Now, you can multiply 4 meters by 1.2 meters to get a product of 4.8 square meters.

When multiplying measurements with different dimensions, such as multiplying a length by a volume, it's important to understand the meaning and implications of the operation. The result may have a different dimension or interpretation altogether.

For example, if you multiply a length of 3 meters by a volume of 5 cubic meters, the resulting product would have the dimension of cubic meters multiplied by meters, which would yield a volume of 15 cubic meters cubed (m^3).

Always consider the units and dimensions involved when multiplying measurements. Ensure that the measurements are of the same type or have been appropriately converted to a common unit or dimension to obtain a meaningful result.

While doing Multiplication in Measurement we have to express the given measures in the same unit by using the decimal notation and then do Multiplication 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.

Express in decimal notation and then multiply :-

a) 7 km 2 hm 7 dam 5 m by 48

Ans.)

km    hm    dam    m

7      2       7      5     =   7   .   2      7      5     km

×              4      8

____________________________

5      8       2      0      0

+ 2     9       1       0      0      ×

_________________________________________

3      4      9    . 2       0      0     km

b)   6 hm 4 dam 6 m by 72 [Answer in metre and km]

km    hm    dam     m

0     6      4       6    =  0 . 6  4   6 km

× 7  2

_______________________________________

1   2   9   2

+ 4   5   2   2   ×

_______________________

4   6 . 5   1   2   km

km     hm     dam     m

46.512  km  =   46      5        1      2     =   46 km 512 m

Answer is 46 km 512 m   (Ans.)