Significant Figures after Calculation Multiplication

Description:

The significant figures of product or quotient is kept equal to minimum number of significant figures of the quantities being operated i.e. in multiplication or division, the final result should retain as many significant figures as are there in the original number with the least significant figures.

Example

• Multiplication

  When we multiply two measurements such as 2.14 and 6, then by mathematics we get the answer as 12.84, but while working with measurements in physics we consider the minimum significant figure, for our example it is 1 (6), so the final product is 1 × 10¹

• Division

  When we divide two measurements such as mass = 4.273 g and volume = 2.51 cm³ to find density, then by mathematics we get the answer as 1.68804780876 g/cm³, but while working with measurements in physics we consider the minimum significant figure, for our example it is 3 (2.51), so the final product is 1.69 g/cm³.

When we reduce a number to the required significant figures we drop some of its digits and round off the number, to perform this process we have a set of rules.

Rules of rounding off a number

• If the first digit to be dropped is more than 5, then preceding digit rise by one.

  Example

  • 9.35672 has to be reduced to only 4 significant figures, then we need to drop the digits 7 and 2, as 7 is greater than 5, the final result becomes 9.357

• If the first digit to be dropped is less than 5, then preceding digit remains as it is.

  Example

  • 9.35321 has to be reduced to only 4 significant figures, then we need to drop the digits 2 and 1, as 2 is less than 5, the final result becomes 9.353

• If the digit to be dropped is exactly than 5, then see the preceding digit.

  • If preceding digit is odd, increase it by one and

  • If preceding digit is even, then leave it as it is.

  Example

  • has to be reduced to only 1 significant figures, then we need to drop the digits 5, now we will observe the preceding digit i.e. 3 as it odd, the final result becomes 4.

  • has to be reduced to only 1 significant figures, then we need to drop the digits 5, now we will observe the preceding digit i.e. 4 as it even, the final result becomes 4.