Units and Dimensions - Significant Digits

Description:

The Concept

• Any measurement can be meaningful only up to certain number of digits.

• We follow certain rules to determine such significant figures (or meaningful figures) and carry out arithmetic on them.

Example −

A standard centi-meter ruler has the least count of 1 mm. Hence, measurements of standard centimeter ruler are significant (or meaningful) up to 1 (one) decimal place.

Rules to determine Significant Figures

• Changing different units does not change the number of significant figures  in a measurement.

• All the non-zero digits are significant.

• All zeros between two non-zero digits are significant irrespective of the position of decimal point.

• For a number, less than 1, all the zero on the left of first non-zero digit are NOT significant.

  • E.g.: 0.002308 (underlined zeros are NOT significant)

• The terminal or trailing zero(s) in a number without a decimal point are not significant.

  • E.g.: 12300 (The last two zeros are NOT significant)

  • Understanding the point, we know that,

    4.7 m = 47 dm = 470 cm = 4700 mm

  • If trailing zeros are considered significant then the number of significant digits will vary by simply changing the unit. Hence, such trailing zeros are considered insignificant.

  • This will be more clear in the next section of Scientific Notation.

• The trailing zeros in a number with decimal point are significant.

  • E.g.: 0.6900 (Four significant figures)

  • Purpose of mentioning trailing zeros in case of a number with decimal point is to indicate the precision. Hence, they are considered significant.

Scientific Notation

Format of Scientific Notation −

a × 10^b

Where, ‘a’ is real number between 1 and 10,

‘b’ is an integer.

Digits in ‘a’ reflect as the significant digits of the measurement.

Exponent is irrelevant to significant digits.

Example −

4.7 m = 47 dm = 470 cm = 4700 mm

The same can be written in scientific notation as −

4.7 m = 4.7 × 10¹dm = 4.7 × 10²cm = 4.7 × 10³mm

In the second way of writing, it is very clear that the measurement contains 2 (two) significant digits. Change of units only affect the exponent.