Question

The length and breadth of a rectangle are 4.5 mm and 5.9 mm. Keeping the number of significant figures in mind, its area in mm²

• A. 27.00
• B. 26.55
• C. 26.6
• D. 27

Answer 1

Answer:

D. 27

Significant figures:

Significant figures in physics are the digits in a number that indicate the precision of a measurement and are the result of an actual measurement.

Every non – zero digits are significant figures.

e.g., 454.76 has 5 (five) significant figures.

All zeroes which lie between two non – zero digits are also significant figures.

e.g., 703.004 has 6 (six) significant figures.

All zeros after decimal but before a non – zero digit is not considered a significant figure.

e.g.,0.00465 has only 3 (three) significant figures.

A number is rounded to the needed number of significant digits by leaving one or more digits to the right.

Note:

• The limiting term is the number with the least decimal places.

• When adding / subtracting, the answer should have the same number of decimal places as the limiting term.

• When multiplying / dividing, the answer should have the same number of significant figures as the limiting term.

Analysing the question,

• Area of rectangle is length multiplied by breadth.

• The area of this rectangle is 4.5×5.9 mm2 = 26.55 mm²

• The number of significant figures will be the same as that in the limiting term.

• Here the limiting term can be either the length or breadth, because both the terms have the same number of significant terms, that is 2.

• The number of significant figures in the product, hence should also be 2.

• Hence, 26.55 mm² when rounded should have 2 significant figures.

• This can be written as 27 mm².

Note:

But the options 27. or 27.0 or 27.00, doesn't comes as the answer, as the number of significant figures will be

• 27. and 27.0 - 3 significant figures

• 27.00 - 4 significant figures