Significant figures and Decimal Places MCQ Quiz in मल्याळम - Objective Question with Answer for Significant figures and Decimal Places - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

The correct answer is option 3) i.e. 0.00538

CONCEPT:

• Significant figures are numbers that add to the precision of the overall value of the number.
  • ​The reliable digits plus the first uncertain digit are known as significant digits or significant figures.
  • ​For example, 23.4 has 2 and 3 as reliable digits and the digit 4 is uncertain.
• ​Rounding off the uncertain digits: The result of computation with approximate numbers, which contain more than one uncertain digit, should be rounded off. The rules for rounding off numbers to the appropriate significant figures are:
  • The preceding digit is raised by 1 if the insignificant digit to be dropped is more than 5, and is left unchanged if the latter is less than 5.
  • When the insignificant digit is 5: if the preceding digit is even, the insignificant digit is simply dropped and, if it is odd, the preceding digit is raised by 1.

EXPLANATION:

• Here, the zeros to the left of the decimal for a number less than 1 are insignificant.
• Up to three significant figures we will have to round off 0.005375.
• The uncertain digit here is 5. Going by the rule for rounding off, the preceding digit is 7 and is odd. So, it is raised by 1.
• Hence, the correct answer is 0.00538.

Additional Information

• The rules to be followed in determining or representing significant figures are as listed:
  1. All non-zero numbers are significant.
  2. Zeros between two non-zero digits are significant.
  3. Trailing zeros to the right of the decimal is significant.
  4. Trailing zeros in a whole number with the decimal shown is significant.
  5. Trailing zeros in a whole number with no decimal shown is not significant.
  6. A choice of change of different units does not change the number of significant digits or figures in a measurement
• Rules for arithmetic operations with significant figures:
  1. ​​In multiplication or division, the final result should retain as many significant figures as are there in the original number with the least significant figures.
  2. In addition or subtraction, the final result should retain as many decimal places as are there in the number with the least decimal places.

CONCEPT:

• RULES FOR SIGNIFICANT FIGURES

1. All non-zero numbers ARE significant. 
2. Zeros between two non-zero digits ARE significant numbers.
3. Leading zeros are NOT significant numbers.
   • The number 0.0032 also has TWO significant figures. All of the zeros are leading.
4. Trailing zeros to the right of a decimal number are significant numbers.
5. Trailing zeros in a whole number with the decimal shown are significant numbers.
6. Trailing zeros in a whole number with no decimal shown is NOT significant numbers.
7. Exact numbers that are definitions have an INFINITE number of significant numbers.
   • For example, 1 kg = 1.00 kg = 1.0000 kg = 1.0000000000000000000 kg, etc.
8. For a number in scientific notation: P x 10^k, "10" and "k" are NOT significant numbers; all digits of the number P ARE significant.

EXPLANATION:

• 4.8000 × 104 = 5 significant digit
  • Trailing zeros to the right of a decimal number are significant numbers.
  • For a number in scientific notation: P x 10k, "10" and "k" are NOT significant numbers; all digits of the number P ARE significant.
• 48000.50 = 7 significant digit
  • Zeros between two non-zero digits ARE significant numbers.
• So the correct answer is option 1.

Concept:

Given,

Area of the square A₁ = 5.29 cm²

Total area = A₁ + A₂ + A₃ + A₄ + A₅ + A₆ + A₇

Since, the areas of all the squares are same, total area A = 7A₁

A = 7 × 5.29 = 37.03 cm²

The result should have two significant figures,

A = 37.03 cm²

Addition of all 7 terms having two significant figures beyond decimal, so final answer must have 1 terms beyond decimal (as per rules of significant digits).

as we take minimum number of significant figures i.e., three.

37.0 cm².

The correct answer is option 4) i.e. None of the above

CONCEPT:

• Significant figures are numbers that add to the precision of the overall value of the number.
  • ​The reliable digits plus the first uncertain digit are known as significant digits or significant figures.
  • ​For example, 23.4 has 2 and 3 as reliable digits and the digit 4 is uncertain.
• The rules to be followed in determining or representing significant figures are as listed:
  1. All non-zero numbers are significant.
  2. Zeros between two non-zero digits are significant.
  3. Trailing zeros to the right of the decimal is significant.
  4. Trailing zeros in a whole number with the decimal shown is significant.
  5. Trailing zeros in a whole number with no decimal shown is not significant.
  6. A choice of change of different units does not change the number of significant digits or figures in a measurement
• Rules for arithmetic operations with significant figures:
  1. ​​In multiplication or division, the final result should retain as many significant figures as are there in the original number with the least significant figures.
  2. In addition or subtraction, the final result should retain as many decimal places as are there in the number with the least decimal places.

EXPLANATION:

• Significant figures add accuracy or precision to the measurement. Hence, more the significant figures, the greater the reliability. 
• Using a mathematical operation cannot affect the significance of a result. However, the result obtained is dependent on the significant figures of the quantities operated.
•  In addition, the final result should have as many decimal places as are there in the number with the least decimal places.
• Hence, none of the given statements is correct.

Concept:

• Arithmetic Mean: The arithmetic mean of a set of values is calculated by summing all the values and dividing by the number of values.
• Significant Figures: The result should be reported with the correct number of significant figures based on the precision of the given measurements.

Calculation:

The least number of significant figures in the original data is 2 (from 4.6). Therefore, the mean should be reported with 2 significant figures.

Given Time Periods: 4.62 s, 4.632 s, 4.6 s, 4.64 s

Sum of the values: = 4.6 + 4.6 + 4.6 + 4.6 = 18.4 

Number of values: 4

Arithmetic Mean: 4.623 s

But the least Significant Figures: 4.6 s

∴ The arithmetic mean of the time periods, in correct significant figures, is 4.6 s.

The correct answer is option 3) i.e. 2.785 m2

CONCEPT:

• Significant figures are numbers that add to the precision of the overall value of the number.
  • ​The reliable digits plus the first uncertain digit are known as significant digits or significant figures.
  • ​For example, 23.4 has 2 and 3 as reliable digits and the digit 4 is uncertain.
• The rules to be followed in determining or representing significant figures are as listed:
  1. All non-zero numbers are significant.
  2. Zeros between two non-zero digits are significant.
  3. Trailing zeros to the right of the decimal is significant.
  4. Trailing zeros in a whole number with the decimal shown is significant.
  5. Trailing zeros in a whole number with no decimal shown is not significant.
  6. A choice of change of different units does not change the number of significant digits or figures in a measurement
• Rules for arithmetic operations with significant figures:
  1. ​​In multiplication or division, the final result should retain as many significant figures as are there in the original number with the least significant figures.
  2. In addition or subtraction, the final result should retain as many decimal places as are there in the number with the least decimal places.

CALCULATION:

Area = length × breadth = 1.325 × 2.102 = 2.78515 m2

• ​​In multiplication, the significant figures in the final result should be the same as in the number with the least decimal places.
• Here, both the numbers 1.325 and 2.102 have the same number of significant figures i.e. four.
• Hence, the result is 2.785 m2

option 2

CONCEPT:

• There are mainly three rules by which we can determine the significant figures in a number containing exponents:
  • Non-zero digits are always significant.
  • Zeros between two significant digits are significant.
  • The exponential number is not considered in the significant figure.
• Don't consider exponents insignificant figures.

EXPLANATION:

• Do not consider a significant number in a power.  

Number = 3.10 × 10-3

• There are 3 significant figures as we did not consider the exponential power.

• When we have to count the significant figure in a number that contains exponents.
• we should be careful that:
  • Apply the significant rule only in numerical value.
  • The significant rule is not valid for numbers in exponents.
• As per some example:

• only 2 significant figures it has.

The correct answer is option 3) i.e. to change a number to its nearest accurate number

CONCEPT:

• Significant figures are numbers that add to the precision of the overall value of the number.
  • ​The reliable digits plus the first uncertain digit are known as significant digits or significant figures.
  • ​For example, 23.4 has 2 and 3 as reliable digits and the digit 4 is uncertain.
• ​Rounding off the uncertain digits: The result of computation with approximate numbers, which contain more than one uncertain digit, should be rounded off. 
• The rules for rounding off numbers to the appropriate significant figures are:
  • The preceding digit is raised by 1 if the insignificant digit to be dropped is more than 5, and is left unchanged if the latter is less than 5.
  • When the insignificant digit is 5: if the preceding digit is even, the insignificant digit is simply dropped and, if it is odd, the preceding digit is raised by 1.

EXPLANATION:

• Rounding off of a number is done to simplify the value, or to keep it intact but closer to the next number.
• It is opted for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.
• Rounding off of a number is done to change a number to its nearest accurate number.

The correct answer is option 3) i.e. 3

CONCEPT:

• Significant figures are numbers that add to the precision of the overall value of the number.
  • ​The reliable digits plus the first uncertain digit are known as significant digits or significant figures.
  • ​For example, 23.4 has 2 and 3 as reliable digits and the digit 4 is uncertain.
• The rules to be followed in determining or representing significant figures are as listed:
  1. All non-zero numbers are significant.
  2. Zeros between two non-zero digits are significant.
  3. Trailing zeros to the right of the decimal is significant.
  4. Trailing zeros in a whole number with the decimal shown is significant.
  5. Trailing zeros in a whole number with no decimal shown is not significant.
  6. A choice of change of different units does not change the number of significant digits or figures in a measurement
• Rules for arithmetic operations with significant figures:
  1. ​​In multiplication or division, the final result should retain as many significant figures as are there in the original number with the least significant figures.
  2. In addition or subtraction, the final result should retain as many decimal places as are there in the number with the least decimal places.

EXPLANATION:

Volume of a cube = side × side × side = 80.1 × 80.1 × 80.1

• Using the rule for multiplication, the number of significant figures in 80.1 is three.
• Hence, the product should also have three significant figures.
• The number of significant figures in the measurement of its volume is 3.

Concept:

Significant figures:

• The significant figures of a given number are those significant or important digits, which convey the meaning according to its accuracy
• Significant figures are helpful in real life because they allow for more accurate results in calculations, especially in sciences, applied mathematics, or technical fields.
• The final number after calculations can represent the measurement more closely.

Rules for calculating Significant figures:

• All non-zero digits are significant.
• Zeroes between non-zero digits are significant.
• A trailing zero or final zero in the decimal portion only are significant.
• Those digits which are non-zero are significant.
• If any zero precedes the non-zero digit then it is not significant. 
• If there is a zero between two non-zero digits then it is also a significant figure.
• Zero's at the end or on the right side of the number are also significant.

Explanation:

Calculating the significant figure of given numbers:

• 28.028: In the first number all digits are significant. Hence, the significant figure is 5.
• 0.0004: In the number second only 4 is significant all other zeroes are before the digit, therefore, are not counted as a significant figure. Hence, the significant figure is 1.
• 1.2 × 10-3 : Numbers in powers are also not counted as a significant number, hence there are only 2 significant digits in the last number.

Hence, the correct option is 1.