Chapter 3, Problem 57E

Interpretation Introduction

(a)

Interpretation:

To round off the given quantity to three significant figure for $6.398\times {10}^{-3}$ km rope

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 57E

Round off the quantity to three significant figure for $6.398\times {10}^{-3}$ km rope is $6.40\times {10}^{-3}$.

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 $6.398\times {10}^{-3}$ km rope is $6.40\times {10}^{-3}$.

Conclusion

Thus round off the quantity to three significant figure for $6.398\times {10}^{-3}$ km rope is $6.40\times {10}^{-3}$.

Interpretation Introduction

(b)

Interpretation:

To round off the given quantity to three significant figure for 0.0178 g silver nitrate.

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 57E

Round off the quantity to three significant figure for 0.0178 g silver nitrate is 0.0178 g.

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 0.0178 g silver nitrate is 0.0178 g

Conclusion

Thus round off the quantity to three significant figure for 0.0178 g silver nitrate is 0.0178 g.

Interpretation Introduction

(c)

Interpretation:

To round off the given quantity to three significant figure for 79, 000 m cable

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 57E

Round off the quantity to three significant figure for 79, 000 m cable is $7.94\times {10}^4\text{m}$.

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 79, 000 m cable is $7.94\times {10}^4\text{m}$.

Conclusion

Thus round off the quantity to three significant figure for 79, 000 m cable is $7.94\times {10}^4\text{m}$.

Interpretation Introduction

(d)

Interpretation:

To round off the given quantity to three significant figure for 42, 150 tons fertilizer

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 57E

Round off the quantity to three significant figure for 42, 150 tons fertilizer is $4.22\times {10}^4$ ton.

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 42, 150 tons fertilizer is $4.22\times {10}^4$ ton

Conclusion

Thus round off the quantity to three significant figures for 42, 150 tons fertilizer is $4.22\times {10}^4$ ton.

Interpretation Introduction

(e)

Interpretation:

To round off the given quantity to three significant figure for $649.85

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 57E

Round off the quantity to three significant figure for $649.85 is $6.50\times {10}^2$ dollars.

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 $649.85 is $6.50\times {10}^2$ dollars

Conclusion

Thus round off the quantity to three significant figures for $649.85 is $6.50\times {10}^2$ dollars.