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Find the value of 0.025 m x 5 m in correct significant digits.

Find the value of 0.025 m x 5 m in correct significant digits.

Grade:11

1 Answers

AskIITians Expert Hari Shankar IITD
17 Points
12 years ago

Hi,

  Significant Figure Rules for Multiplication and Division

In multiplication and division, the number of S.F. in the answer is the same as the number of S.F. in the input number that has the fewest. For example, consider Person 3's measurement of the wood. If you wanted to know the area of the wood you would use the formula

     Area = Length x Width
                 = (11.63 cm) x (5.74 cm)

The input number with the smallest number of S.F. is the width measurement, which has 3. So, the answer must also have 3 S.F.:

     Area = 66.8 cm2

The number that comes out of the calculator is 66.7562, but because of rule above the answer has been rounded off to the correct number of S.F.

Now suppose you wanted to know the volume of the wood:

     Volume = Length x Width x Thickness
         = (11.63 cm) x (5.74 cm) x (0.42 cm)
         = 28 cm3

The calculator gives 28.037604, but because the thickness has only 2 S.F., so must the answer.

 

Now, coming to your question, 0.025 has 2 significant digits, and 5 has 1 significant digits. Therefore, only 1 significant digit of 0.025 x 5 will be valid.

Hence, 0.025 x 5 = 0.125 = 0.1 since we can use only 1 significant digit.

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