Q.Fill up the blank: A screw gauge and a spherometer can be used to measure lengths as less as to _____ m.

The Problem: How Fine Can You Measure?

Imagine you have a standard 15 cm ruler. You look at the markings — there's a line for every centimetre, and between those, smaller lines for every millimetre. Now try to measure the thickness of a single sheet of paper. You place it against the ruler. Does it line up exactly with a millimetre mark? Almost certainly not. It falls somewhere between two millimetre lines.

What do you report? You can't say "2.3 mm" because your ruler doesn't show tenths of a millimetre. The best you can honestly say is "about 2 mm" or "between 2 and 3 mm". That limitation — the smallest change in the quantity that your instrument can reliably detect and display — is its least count.

The Precise Definition

Least count is the smallest value of a physical quantity that can be measured accurately using a given instrument. It is the resolution of the measuring device.

For a simple scale (like a ruler, voltmeter, or thermometer) with equally spaced markings, the least count is:

For instruments without a vernier (like a plain ruler), the least count is simply the value of the smallest division on the scale.

Examples you already know:

Why This Matters in Exams

When you record a measurement, you must write it to the correct number of decimal places — the least count determines that. If a ruler has a least count of 1 mm, you cannot report a length as 12.35 cm. The correct recording is 12.3 cm or 12.4 cm (the last digit is uncertain, but it must be at the place of the least count).

The Core Intuition …