Chapter 3, Problem 58E

(a) 52.20 mL helium, (b) 17.963 g nitrogen, (c) 78.45 mg MSG, (d) 23, 642, 000 mm wavelength, (e) 0.0041962 kg lead.

Interpretation Introduction

(a)

Interpretation:

To round off the given quantity to three significant figure for 52.20 mL helium

Concept introduction:

The significant figures are also known as the significant digits. It is the uncertainty associate with the measurement by rounding the results. Moreover the significant figures are defined in a number of the digits with certainty and first uncertain digit. The measurement is a characteristic number to the object or event that can be compared with other object. The scope of the measurement depends upon the context and event. Measurement is commonly used as the international system of unit as a comparison framework. The system defines seven fundamental units like kilogram, meter, candela, ampere, kelvin and mole. The metric system is a decimal system of the measurement based on the units for the length, meter, the mass, the kilogram. It exists in the several forms with different choices of the basic units. The metric system indicates a single basic unit for the number of physical quantities. Other quantities are derived from the SI units.

Answer to Problem 58E

Round off the quantity to three significant figures for 52.20 mL helium is 52.0 mL helium

Explanation of Solution

To identifying the significant figures;

Number system having all non-zero digits is significant i.e., 1, 2, 3…

Zero between the numbers having non-zero are said to be significant: 102, 2005…

Leading zeros are never significant figures: 0.02, 001.887…

In a number system with a decimal point that is trailing zeros are significant figures: 2.02000, 5.4000….

In a number system without a decimal point that is trailing number zero may or may not said to be a significant figure.

To round the n significant figures

Identify the significant figure before rounding it. If the digit that is coming immediately right side of the final significant number greater than five digit number followed by other non-zero digit. Then add number 1 to the last or final significant figure. If digit that is coming immediately to the right of the last significant figure is a 5 not followed by any other number digits or followed only by number zero then rounding off the number to nearest one.

The three significant figures for 52.20 mL helium is 52.0 mL helium

Conclusion

Thus round off the quantity to three significant figures for 52.20 mL helium is 52.2 mL helium

Interpretation Introduction

(b)

Interpretation:

To round off the given quantity to three significant figure for 17.963 g nitrogen

Concept introduction:

The significant figures are also known as the significant digits. It is the uncertainty associate with the measurement by rounding the results. Moreover the significant figures are defined in a number of the digits with certainty and first uncertain digit. The measurement is a characteristic number to the object or event that can be compared with other object. The scope of the measurement depends upon the context and event. Measurement is commonly used as the international system of unit as a comparison framework. The system defines seven fundamental units like kilogram, meter, candela, ampere, kelvin and mole. The metric system is a decimal system of the measurement based on the units for the length, meter, the mass, the kilogram. It exists in the several forms with different choices of the basic units. The metric system indicates the single basic unit for the number of physical quantities. Other quantities are derived from the SI units.

Answer to Problem 58E

Round off the quantity to three significant figure for 17.963 g nitrogen is 18.9 g nitrogen

Explanation of Solution

To identifying the significant figures;

Number system having all non-zero digits is significant i.e., 1, 2, 3…

Zero between the numbers having non-zero are said to be significant: 102, 2005…

Leading zeros are never significant figures: 0.02, 001.887…

In a number system with a decimal point that is trailing zeros are significant figures: 2.02000, 5.4000….

In a number system without a decimal point that is trailing number zero may or may not said to be a significant figure.

To round the n significant figures

Identify the significant figure before rounding it. If the digit that is coming immediately right side of the final significant number greater than five digit number followed by other non-zero digit. Then add number 1 to the last or final significant figure. If digit that is coming immediately to the right of the last significant figure is a 5 not followed by any other number digits or followed only by number zero then rounding off the number to nearest one.

The three significant figures for 52.20 mL helium is 52.0 mL helium

Conclusion

Thus round off the quantity to three significant figures for 52.20 mL helium is 52.0 mL helium

Interpretation Introduction

(c)

Interpretation:

To round off the given quantity to three significant figure for 78.45 mg MSG

Concept introduction:

The significant figures are also known as the significant digits. It is the uncertainty associate with the measurement by rounding the results. Moreover the significant figures are defined in a number of the digits with certainty and first uncertain digit. The measurement is a characteristic number to the object or event that can be compared with other object. The scope of the measurement depends upon the context and event. Measurement is commonly used as the international system of unit as a comparison framework. The system defines seven fundamental units like kilogram, meter, candela, ampere, kelvin and mole. The metric system is a decimal system of the measurement based on the units for the length, meter, the mass, the kilogram. It exists in the several forms with different choices of the basic units. The metric system indicates the single basic unit for the number of physical quantities. Other quantities are derived from the SI units.

Answer to Problem 58E

Round off the quantity to three significant figures for 78.45 mg MSG is 78.5 mg MSG

Explanation of Solution

To identifying the significant figures;

Number system having all non-zero digits is significant i.e., 1, 2, 3…

Zero between the numbers having non-zero are said to be significant: 102, 2005…

Leading zeros are never significant figures: 0.02, 001.887…

In a number system with a decimal point that is trailing zeros are significant figures: 2.02000, 5.4000….

In a number system without a decimal point that is trailing number zero may or may not said to be a significant figure.

To round the n significant figures

Identify the significant figure before rounding it. If the digit that is coming immediately right side of the final significant number greater than five digit number followed by other non-zero digit. Then add number 1 to the last or final significant figure. If digit that is coming immediately to the right of the last significant figure is a 5 not followed by any other number digits or followed only by number zero then rounding off the number to nearest one.

The three significant figures for 78.45 mg MSG is 78.5 mg MSG

Conclusion

Thus round off the quantity to three significant figure for 78.45 mg MSG is 78.5 mg MSG

Interpretation Introduction

(d)

Interpretation:

To round off the given quantity to three significant figure for 23, 642, 000 mm wavelength

Concept introduction:

The significant figures are also known as the significant digits. It is the uncertainty associate with the measurement by rounding the results. Moreover the significant figures are defined in a number of the digits with certainty and first uncertain digit. The measurement is a characteristic number to the object or event that can be compared with other object. The scope of the measurement depends upon the context and event. Measurement is commonly used as the international system of unit as a comparison framework. The system defines seven fundamental units like kilogram, meter, candela, ampere, kelvin and mole. The metric system is a decimal system of the measurement based on the units for the length, meter, the mass, the kilogram. It exists in the several forms with different choices of the basic units. The metric system indicates the single basic unit for the number of physical quantities. Other quantities are derived from the SI units.

Answer to Problem 58E

Round off the quantity to three significant figures for 23, 642, 000 mm wavelength is $23.6\times {10}^5$ mm wavelength MSG

Explanation of Solution

To identifying the significant figures;

Number system having all non-zero digits is significant i.e., 1, 2, 3…

Zero between the numbers having non-zero are said to be significant: 102, 2005…

Leading zeros are never significant figures: 0.02, 001.887…

In a number system with a decimal point that is trailing zeros are significant figures: 2.02000, 5.4000….

In a number system without a decimal point that is trailing number zero may or may not said to be a significant figure.

To round the n significant figures

Identify the significant figure before rounding it. If the digit that is coming immediately right side of the final significant number greater than five digit number followed by other non-zero digit. Then add number 1 to the last or final significant figure. If digit that is coming immediately to the right of the last significant figure is a 5 not followed by any other number digits or followed only by number zero then rounding off the number to nearest one.

The three significant figure for 23, 642, 000 mm wavelength is $23.6\times {10}^5$.

Conclusion

Thus round off the quantity to three significant figure for 23, 642, 000 mm wavelength is $23.6\times {10}^5$.

Interpretation Introduction

(e)

Interpretation:

To round off the given quantity to three significant figures for 0.0041962 kg lead.

Concept introduction:

The significant figures are also known as the significant digits. It is the uncertainty associate with the measurement by rounding the results. Moreover the significant figures are defined in a number of the digits with certainty and first uncertain digit. The measurement is a characteristic number to the object or event that can be compared with other object. The scope of the measurement depends upon the context and event. Measurement is commonly used as the international system of unit as a comparison framework. The system defines seven fundamental units like kilogram, meter, candela, ampere, kelvin and mole. The metric system is a decimal system of the measurement based on the units for the length, meter, the mass, the kilogram. It exists in the several forms with different choices of the basic units. The metric system indicates the single basic unit for the number of physical quantities. Other quantities are derived from the SI units.

Answer to Problem 58E

Round off the quantity to three significant figures for 0.0041962 kg lead is $4.20\times {10}^{-5}$ kg lead

Explanation of Solution

To identifying the significant figures;

Number system having all non-zero digits is significant i.e., 1, 2, 3…

Zero between the numbers having non-zero are said to be significant: 102, 2005…

Leading zeros are never significant figures: 0.02, 001.887…

In a number system with a decimal point that is trailing zeros are significant figures: 2.02000, 5.4000….

In a number system without a decimal point that is trailing number zero may or may not said to be a significant figure.

To round the n significant figures

Identify the significant figure before rounding it. If the digit that is coming immediately right side of the final significant number greater than five digit number followed by other non-zero digit. Then add number 1 to the last or final significant figure. If digit that is coming immediately to the right of the last significant figure is a 5 not followed by any other number digits or followed only by number zero then rounding off the number to nearest one.

The three significant figures for 0.0041962 kg lead is $4.20\times {10}^5$ kg lead

Conclusion

Thus round off the quantity to three significant figure for 0.0041962 kg lead is $4.20\times {10}^5$ kg lead