Significant Figures and Measurements - Class-XI

For 786, all three digits are significant. For 0.786, leading zeros are not significant, so there are 3. For 0.0786, leading zeros are not significant, so there are 3.

In the measurement 2.0 cm, the digit 2 is significant, and the trailing zero after the decimal point is also significant, indicating precision to the tenths place.

$7 \times 2.232=15.624$

The number of single digits that are important in the coefficient of an expression in scientific notation is termed as significant number.

The significant digits in the number $0.0384g$ are $3,8$ and $4$. Therefore, the number of significant digits are $3$.

There are three rules on determining how
many significant figures are in a number: Non-zero digits are
always significant. Any zeros between two significant digits
are significant. A final zero or trailing zeros in the decimal portion ONLY
are significant.

We use different equipment to cool the object, before weighting it which save time.

$\text{980 have two non-zero digits ie. with significant figure is 2.}$

Side of a cube$=7.203m$

Any zeros between two significant digits are significant.

Non zero digits are always significant it is a true statement.

$1.53\times 0.9995=1.529=1.53$ .....By applying significant figure rule

Precision $=$ Individual value $-$ mean value

In 0.02300, the leading zeros are not significant. The digits 2, 3, 0, and 0 are significant because the zeros are trailing after a decimal point.

In 0.002930, the leading zeros are not significant. The digits 2, 9, 3, and 0 are significant, as the trailing zero indicates precision.

Count significant zeros (zeros that count as significant figures): 0.00007 has 0, 0.00070 has 1, 20.000 has 3, 0.800 has 2. Option C has the maximum significant zeros (3 trailing zeros after decimal).

Option A has 4 significant figures (1.123). Option B has 2 (1.2). Option C has 3 (0.123). Option D has 1 (2).

When adding numbers, the result should be rounded to the same number of decimal places as the term with the fewest decimal places. Adding 4.523, 2.3, and 6.24 yields 13.063. Since 2.3 has only one decimal place, the sum must be rounded to one decimal place, giving 13.1, which contains 3 significant figures.

In a number with a decimal point, all trailing zeros are significant. Therefore, 314.000 has 6 significant figures.

In 0.00025, the leading zeros are not significant. Only the 2 and 5 are significant, totaling 2.

In the number 2000 x 10^2, the trailing zeros without a decimal point are generally considered ambiguous, but following standard rules for scientific notation conversion or explicit digits, 2000 written without a decimal point has only 1 significant figure (the leading 2), as the zeros are placeholders.

Pi is an irrational, transcendental number with an infinite number of non-repeating digits; therefore, it has an infinite number of significant figures.

The number of single digits that are important in the coefficient of an expression in scientific notation is termed as significant number.

 Statement I: The number $5,007$ has four significant figures
Because
Statement II: Zeros between non-zero digits are significant
Hence, the statement I is false and statement II is true.

      $14.5-3.46=11.04$

In multiplication, the final answer is reported as the same number of decimal places as that of the term with the least number of decimal places.

The significant digits in the number $0.5873g$ are $5,8,7$ and $3$. Therefore, the number of significant digits in the given number are $4$.

After rounding off to $2$ significant digits, weight of sample $1$ can be reported as $3.72$ grams. Therefore, total mass $= (3.72+0.42)=4.14 $ grams.

The significant digits in the number $16.280$ are $1,6,2,8$ and $0$. Therefore, the final significant digit in the given number is $0$.

In multiplication, the final answer is reported as the same number of decimal places as that of the number with the least decimal places.

In addition, the final product is reported as the same number of decimal places as that of the number with least decimal places.

Molecular mass of glucose is $180.162$

In multiplication, the result is reported to the same number of significant figures as the measurement with the fewest significant figures. Here, 3 * 10^14 has 1 significant figure, while 1.23 * 10^23 has 3. Therefore, the product must be rounded to 1 significant figure. Calculating 3.69 * 10^37 and rounding to one significant figure gives 4 * 10^37.

Exact number is the number which does not have uncertainity in measurement and significant figures.

In $A:-$ Significant figures $=6,0,2 \Rightarrow 3$ figures

All the last zero or trailing zero's in the decimal portion and between 2 significant digits only are significant.

To round up a given number, ignore the last digit as such if the digit next to it is less than 5. Then increase it by 1, if the next digit is greater than 5.

(i) 34.216

34.22 { since next digit (6) is greater than 5 }

34.2 {since next digit (2) is less than 5 }

 (ii) 0.04597

0.0460 {since next digit (7) is greater than 5}

(iii) 10.4107

10.411 { since next digit (7) is greater than 5}

10.41 { since next digit (1) is less than 5}

10.4 { since next digit (1) is less than 5}

Thus option B is correct.

Figures in scientific notation will be: