Question

Which of the following measurements contains the highest number of significant figures?
A.\[1.123 \times {10^{ - 3}}kg\]
B.$1.2 \times {10^{ - 3}}kg$
C.$0.123 \times {10^3}kg$
D.$2 \times {10^5}kg$

Answer 1

Hint: Significant figures are the number of digits in a value, often a measurement, that contributes to the degree of accuracy of the value. We start counting significant figures at the first non-zero digit. Calculate the number of significant figures for an assortment of numbers.

Complete answer:
Significant figures of a number in positional notation are digits in the number that are reliable and absolutely necessary to indicate the quantity of something. If a number expressing the result of measurement of something (e.g., length, pressure, volume, or mass) has more digits than the digits allowed by the measurement resolution, only the digits allowed by the measurement resolution are reliable and so only these can be significant figures.
To determine the number of significant figures in a number use the following three rules:
-All non-zero numbers are significant.
-Zeros between two non-zero digits are significant.
-Leading zeros are not significant.
-Trailing zeros to the right of the decimal ARE significant.
-Trailing zeros in a whole number with the decimal shown are significant.

So, the correct answer is (A) \[1.123 \times {10^{ - 3}}kg\]

Note:
Numbers are often rounded to avoid reporting insignificant figures. For example, it would create false precision to express a measurement as $12.34525kg$ if the scale was only measured to the nearest gram. In this case, the significant figures are the first $5$ digits from the left-most digit, and the number needs to be rounded to the significant figures so that it will be $12.345kg$ as the reliable value. Numbers can also be rounded merely for simplicity rather than to indicate the precision of measurement.