What is meant by the significant figures of a measurement? What are the main points to be kept in mind while determining the significant figures of a measurement?

Difficulty: Hard

Significant figures:

All the accurately known digits and the first doubtful digit in an expression are called significant figures. It reflects the precision of a measured value of a physical quantity.

The accuracy in measuring a physical quantity depends upon various factors:

1. The quantity of the measuring instrument
2. The skill of the observer
3. The number of observations made

For example, a student measures the length of a book as 18cm using a measuring tape. The numbers of significant figures in his/her measured value are two. The left digit 1 is the accurately known digit. While the digit 8 is the doubtful digit for which the student may not be sure.

Rules for determining significant figures:
The following rules help identify significant figures:

1. Non-zero digits are always significant.
2. Zeros between two significant figures are also significant.
3. Final or ending zeros on the right in the decimal fraction are significant.
4. Zeros are written on the left side of the decimal point to space the decimal point is not significant.
5. In whole numbers that end in one or more zeros without a decimal point. These zeros may or may not be significant. In such cases, it is not clear which zeros serve to locate the position value and which are parts of the measurement. In such a case, express the quantity using scientific notation to find the significant zero.

RULES TO FIND THE SIGNIFICANT DIGITS INA MEASUREMENT

• Digits other than zero are always significant.

27 has 2 significant digits.

275 has 3 significant digits.

• Zeros between significant digits are also significant.

2705 has 4 significant digits.

• Final zero or zeros after the decimal are significant

275.00 has 5 significant digits.

• Zeros used for spacing the decimal point are not significant here zeros are placeholders only.

0.03 has 1 significant digit.

0.027 has 2 significant digits.

ROUNDING THE NUMBERS

1. If the last digit is less than 5 then it is simply dropped. This decreases the number of significant digits in the figure.

For example,

1.943 is rounded to 1.94 (3 significant figures)

2. If the last digit is greater than 5, then the digit on its left is increased by one. This also decreases the number of significant digits in the figure.

For example,

1.47 is rounded to two significant digits 1.5

3. If the last digit is 5, then it is rounded to get nearest even number.

For example,

1.35 is rounded to 1.4 and 1.45 is also rounded to 1.4