Significant figures and Decimal Places MCQ Quiz - Objective Question with Answer for Significant figures and Decimal Places - Download Free PDF

The correct answer is Option 4.

Key Points

• Significant figures are the digits in a number that contribute to its precision, excluding leading zeros and trailing zeros without a decimal point.
• The number "1.73" has three significant figures: "1", "7", and "3".
• The presence of the decimal point ensures that all digits are significant.
• Significant figures are used to express measurements accurately and are critical in scientific calculations.
• In this case, the correct number of significant figures is three, corresponding to Option 4.

Additional Information

• Significant Figures Definition: These are the digits in a number that are meaningful in expressing its precision, beginning with the first non-zero digit.
• Rules for Significant Figures:
  • Non-zero digits are always significant.
  • Zeros between non-zero digits are significant.
  • Leading zeros (zeros before the first non-zero digit) are not significant.
  • Trailing zeros are significant if there is a decimal point.
• Applications: Significant figures are essential in scientific experiments, engineering calculations, and data reporting to ensure consistency and accuracy.
• Precision vs. Accuracy: Precision refers to how closely repeated measurements agree, while accuracy measures how close a value is to the true value.
• Rounding Rules: When rounding to a specific number of significant figures, consider the digit immediately after the last significant figure to decide whether to round up or down.

The correct answer is 4.

Key Points

• The number 3.700 has four significant figures.
• Significant figures include all non-zero digits, any zeros between significant digits, and any trailing zeros in the decimal portion.
• In 3.700, all the digits (3, 7, 0, 0) are significant.
• Trailing zeros in the decimal part are considered significant because they indicate the precision of the measurement.

Additional Information

• Significant Figures
  • Significant figures are the digits in a number that contribute to its precision.
  • The rules for determining significant figures help in accurately representing the precision of a measurement.
  • All non-zero numbers (1-9) are always significant.
  • Any zeros between significant digits are significant.
  • Leading zeros are not significant, while trailing zeros in the decimal portion are significant.
• Rounding Significant Figures
  • When rounding a number, keep as many significant figures as are required.
  • In rounding, if the digit immediately to the right of the last significant digit is greater than or equal to 5, round up.
  • If it's less than 5, retain the last significant digit and drop the rest.
• Precision and Accuracy
  • Precision refers to the consistency of repeated measurements, while accuracy refers to how close a measurement is to the true value.
  • Significant figures are a way to communicate the precision of a measurement.
  • Higher precision means more significant figures.
• Applications
  • Significant figures are essential in scientific calculations to ensure that results are not overrepresented.
  • They help in maintaining the integrity and accuracy of data in fields such as chemistry, physics, and engineering.

Concept:

Significant Figures and Rounding Off:

When performing calculations involving significant figures, the final result should be reported using the same number of significant digits as the least precise number used in the calculation.

In this case, since all the digits in the given expression are significant, we round the result to 3 significant figures as the least number of significant figures in the given data is 3.

Calculation:

Given,

Expression: y = (32.3 × 1125) / (27 × 4)

First, calculate the value of y:

⇒ y = (32.3 × 1125) / (27 × 4)

⇒ y = 36262.5 / 108

⇒ y = 1326.186

Since the least number of significant figures in the data is 3, we round off the result to 3 significant figures:

⇒ y = 1330

∴ The value of y is 1330 (rounded to 3 significant figures).

• 0.00456: The leading zeros are not significant. This number has 3 significant figures (4, 5, and 6).
• 45,600: Without a decimal point, the trailing zeros are assumed to be placeholders and not significant. This number has 3 significant figures (4, 5, and 6).
• 5.003: All digits, including the zero, are significant. This number has 4 significant figures (5, 0, 0, and 3).
• 0.0304: The leading zeros are not significant. This number has 3 significant figures (3, 0, and 4).

Key Points:

•  These are the some rules for determining significant figures 
  • Leading zeros are not significant.
  • Captive (or embedded) zeros are always significant.
  • Trailing zeros are significant only if the number contains a decimal point.

Concept Used:

The volume of a cube is calculated using the formula: Volume = side³. Here, the side is given, and the volume can be found by cubing the length of the side.

Calculation:

We have:

⇒ Volume = (1.1 × 10^-2)³

⇒ Volume = 1.1³ × (10^-2)³

⇒ Volume = 1.331 × 10^-6 m³

Since we are asked for the volume up to correct significant figures (the given side length has two significant figures), we should round the result accordingly.

⇒ Volume ≈ 1.3 × 10^-6 m³

∴ The correct answer is: 1.3 × 10^-6

CONCEPT:

• Significant Figures: Significant figures in the measured value of a physical quantity tell the number of digits in which we have confidence.
• The larger the number of significant figures obtained in a measurement, the greater is the accuracy of the measurement and vice-versa.

• Significant figures do not change if we measure a physical quantity in different units.
• Significant figures retained after the mathematical operation (like addition, subtraction, multiplication, and division) should be equal to the minimum significant figures involved in any physical quantity in the given operation.
• Significant figures are the number of digits up to which we are sure about their accuracy.

EXPLANATION:

• Trailing zeros or the zeros placed to the right of the number is significant.
• Therefore, 433.00 has five significant figures. So option 4 is correct.

CONCEPT:

• A significant figure is rounding off a number. It follows some law-
  • All the non-zero digits are always significant.
  • Any zeros between two significant digits are taken as significant.
  • The final zero or trailing zeros in the decimal portion only are significant figure.

EXPLANATION:

• For 42306- Here there are 5 significant figures. Zero between significant digits are taken as significant.
• 0.0007- There is only one significant figure. 

6.5 × 10–3

There are only 2 significant figures.

Concept Used:

• In subtraction, the result should have the same number of decimal places as the term with the fewest decimal places.
• Given values:
  • 9.99 m → 3 significant figures (2 decimal places).
  • 0.0099 m → 2 significant figures (4 decimal places).

Calculation:

Performing the subtraction,

⇒ A - B = 9.99 - 0.0099

⇒ 9.9801 m

Since the result should have 2 decimal places (same as 9.99 m), we round:

⇒ 9.98 m

∴ The correct answer is 9.98 m.

CONCEPT:

• A significant figure is rounding off a number. It follows some law-
  • All the non-zero digits are always significant.
  • Any zeros between two significant digits are taken as significant.
  • The final zero or trailing zeros in the decimal portion only are significant figures.

EXPLANATION:

• The significant figures are 4, therefore, only four digits will be in the value of the mass of the ball.
• The next fifth number is 6 which is greater than 5, hence the number 7 to be rounded off must be increased by one, hence the measurement has value 4.238. So option 3 is correct.

The correct answer is option 3) i.e. The trailing zeros in a number without a decimal point are significant.

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:

• A change of unit of measurement cannot change the number of significant figures. 
  • For example, the length of 2.308 cm has four significant figures. But in different units, the same value can be written as 0.02308 m or 23.08 mm.
• All non-zero digits are significant.
• The trailing zeros in a number without a decimal point are not significant. 
• Thus, option 3) is incorrect.

EXPLANATION:

→Significant figures, are the number of digits in which a value of a physical quantity can be expressed properly.

→More the number of significant figures the more the accuracy of the measurement achieved.

The following rules must be known to find the number of sig. fig. 

1) All non-zero numbers are significant.

2) All zeros are insignificant except if they lie within two sig. numbers. or placed at the end. 

3) In exponential notation, the numerical is the number of significant figures. 

So, here the number is given as 0.06900

"0.0" is insignificant and "6900" is significant.

So, the number of sig. fig. here is 4.

So, the correct answer is option (2).

The correct answer is four.

Key Points

• Significant figures:-
  • These are the digits in a number that carry meaning contributing to its precision and accuracy.
  • The number of significant figures in 0.05800 is four because all non-zero digits are significant, and the trailing zeros after the decimal point are also significant.

CONCEPT:

• A significant figure is rounding off a number. It follows some law-
  • If the digit next to the one rounded is more than 5, the next digit to be rounded is increased by 1.
  • If the digit next to the rounded is less than 5, the next digit is left unchanged.
  • For addition and subtraction first, write the numbers below each other with all the decimal points in one line.

CALCULATION:

14.745 + 0.14750 + 1.4650

After 16.35, there is 7 so, we add one to this

⇒ 16.36

CONCEPT:

A significant figure is rounding off a number. It follows some law-

• All the non-zero digits are always significant.
• Any zeros between two significant digits are taken as significant.
• The final zero or trailing zeros in the decimal portion only are significant figures.

EXPLANATION:

• In the given number 09.09090, the first zero is not a significant figure. But the last zero is a significant figure.
• Similarly, the zero between two 9 will also be a significant figure.
• Thus there are 6 significant figures. So option 2 is correct.

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.
• ​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:

• In 865.78, the uncertain digit to be dropped 8 is greater than 5. Hence, the preceding digit 7 should be raised by 1.
  • So, the correct answer should be 865.8 after rounding off.
• In 10.2, the uncertain digit to be dropped 2 is less than 5. Hence, the preceding digit should be left unchanged.
  • So, the correct answer should be 10 after rounding off.
• In 325.452, the uncertain digit to be dropped is 5 and the preceding digit to it is 4 (even number).
  • Hence, the preceding digit should be left unchanged. So, the correct answer should be 325.4 after rounding off.
• Thus, none of the given options is correct.