24. Express the following results with due regard to
significant figure
(i) 3.897 + 15.2
(ii) 19.388 + 0.003
Answers
Explanation:
Scientists have established certain conventions for communicating the degree of precision of a measurement. Imagine, for example, that you are using a meterstick to measure the width of a table. The centimeters (cm) are marked off, telling you how many centimeters wide the table is. Many metersticks also have millimeters (mm) marked off, so we can measure the table to the nearest millimeter. But most metersticks do not have any finer measurements indicated, so you cannot report the table’s width any more exactly than to the nearest millimeter. All you can do is estimate the next decimal place in the measurement (Figure 1.7 "Measuring an Object to the Correct Number of Digits").
Figure 1.7 Measuring an Object to the Correct Number of Digits
How many digits should be reported for the length of this object?
The concept of significant figures takes this limitation into account. The significant figures of a measured quantity are defined as all the digits known with certainty and the first uncertain, or estimated, digit. It makes no sense to report any digits after the first uncertain one, so it is the last digit reported in a measurement. Zeros are used when needed to place the significant figures in their correct positions. Thus, zeros may not be significant figures.
Note
“Sig figs” is a common abbreviation for significant figures.
For example, if a table is measured and reported as being 1,357 mm wide, the number 1,357 has four significant figures. The 1 (thousands), the 3 (hundreds), and the 5 (tens) are certain; the 7 (units) is assumed to have been estimated. It would make no sense to report such a measurement as 1,357.0 or 1,357.00 because that would suggest the measuring instrument was able to determine the width to the nearest tenth or hundredth of a millimeter, when in fact it shows only tens of millimeters and the units have to be estimated.
On the other hand, if a measurement is reported as 150 mm, the 1 (hundreds) and the 5 (tens) are known to be significant, but how do we know whether the zero is or is not significant? The measuring instrument could have had marks indicating every 10 mm or marks indicating every 1 mm. Is the zero an estimate, or is the 5 an estimate and the zero a placeholder?
The rules for deciding which digits in a measurement are significant are as follows:
All nonzero digits are significant. In 1,357, all the digits are significant.
Captive (or embedded) zeros, which are zeros between significant digits, are significant. In 405, all the digits are significant.
Leading zeros, which are zeros at the beginning of a decimal number less than 1, are not significant. In 0.000458, the first four digits are leading zeros and are not significant. The zeros serve only to put the digits 4, 5, and 8 in the correct positions. This number has three significant figures.
Trailing zeros, which are zeros at the end of a number, are significant only if the number has a decimal point. Thus, in 1,500, the two trailing zeros are not significant because the number is written without a decimal point; the number has two significant figures. However, in 1,500.00, all six digits are significant because the number has a decimal point.
Explanation:
3.897+15.2 express the following result with due regard to significant figure