Chapter PSS, Problem 39E

Interpretation Introduction

(a)

Interpretation:

The given ordinary number is to be expressed in scientific notation.

Concept introduction:

The ordinary numbers are written as the power of $10$ in the scientific terms. The power of $10$ denotes the position of decimal point in a number. The number as the positive power of $10$ shows that the decimal point is present on the right side of the whole number digits. On the other hand, the negative power shows that the decimal point is present on the left side of the whole number digits.

In scientific notation, the non-zero significant numbers are written along with the power of $10$ which denotes the position of decimal point.

Answer to Problem 39E

The given ordinary number, $80,916,000$ in scientific notation is represented as $8.0916\times {10}^7$.

Explanation of Solution

The given number is $80,916,000$. The number has total of eight digits. The decimal point is placed after the first non-zero significant number which is represented as $8.0916000$. The total digits after the decimal point are $7$. These seven digits have $3$ zeros as significant numbers. Thus, these need not to be written in the scientific notation as these are included in the power of $10$. The decimal point is placed to the left of $7$ digits, therefore the power of $10$ is written as $7$. Thus, the number, $80,916,000$, can be written as $8.0916\times {10}^7$ in scientific notation.

Conclusion

The given ordinary number, $80,916,000$ in scientific notation is represented as $8.0916\times {10}^7$.

Interpretation Introduction

(b)

Interpretation:

The given ordinary number is to be expressed in scientific notation.

Concept introduction:

The ordinary numbers are written as the power of $10$ in the scientific terms. The power of $10$ denotes the position of decimal point in a number. The number as the positive power of $10$ shows that the decimal point is present on the right side of the whole number digits. On the other hand, the negative power shows that the decimal point is present on the left side of the whole number digits.

In scientific notation, the non-zero significant numbers are written along with the power of $10$ which denotes the position of decimal point.

Answer to Problem 39E

The given ordinary number, $0.000000015$ in scientific notation is represented as $1.5\times {10}^{-8}$.

Explanation of Solution

The given number is $0.000000015$. The number has total of nine digits. The decimal point is placed after the first non-zero significant number which is represented as $000000001.5$. The total digits before the decimal point are $8$. These eight digits have zero as significant numbers. Thus, these need not to be written in the scientific notation as these are included in the power of $10$. The decimal point is placed to the right of $8$ digits, therefore the power of $10$ is written as $-8$. Thus, the number, $0.000000015$, can be written as $1.5\times {10}^{-8}$ in scientific notation.

Conclusion

The given ordinary number, $0.000000015$ in scientific notation is represented as $1.5\times {10}^{-8}$.

Interpretation Introduction

(c)

Interpretation:

The given ordinary number is to be expressed in scientific notation.

Concept introduction:

The ordinary numbers are written as the power of $10$ in the scientific terms. The power of $10$ denotes the position of decimal point in a number. The number as the positive power of $10$ shows that the decimal point is present on the right side of the whole number digits. On the other hand, the negative power shows that the decimal point is present on the left side of the whole number digits.

In scientific notation, the non-zero significant numbers are written along with the power of $10$ which denotes the position of decimal point.

Answer to Problem 39E

The given ordinary number, $335,600,000,000,000$ in scientific notation is represented as $3.356\times {10}^{14}$.

Explanation of Solution

The given number is $335,600,000,000,000$. The number has total of fifteen digits. The decimal point is placed after the first non-zero significant number which is represented as $3.35600000000000$. The total digits after the decimal point are $14$. These fourteen digits have $11$ zeros as significant numbers. Thus, these need not to be written in the scientific notation as these are included in the power of $10$. The decimal point is placed to the left of $14$ digits, therefore the power of $10$ is written as $14$. Thus, the number, $335,600,000,000,000$, can be written as $3.356\times {10}^{14}$ in scientific notation.

Conclusion

The given ordinary number, $335,600,000,000,000$ in scientific notation is represented as $3.356\times {10}^{14}$.

Interpretation Introduction

(d)

Interpretation:

The given ordinary number is to be expressed in scientific notation.

Concept introduction:

The ordinary numbers are written as the power of $10$ in the scientific terms. The power of $10$ denotes the position of decimal point in a number. The number as the positive power of $10$ shows that the decimal point is present on the right side of the whole number digits. On the other hand, the negative power shows that the decimal point is present on the left side of the whole number digits.

In scientific notation, the non-zero significant numbers are written along with the power of $10$ which denotes the position of decimal point.

Answer to Problem 39E

The given ordinary number, $0.000000000000927$ in scientific notation is represented as $9.27\times {10}^{-13}$.

Explanation of Solution

The given number is $0.000000000000927$. The number has total of fifteen digits. The decimal point is placed after the first non-zero significant number which is represented as $0000000000009.27$. The total digits before the decimal point are $13$. These thirteen digits have zero as significant numbers. Thus, these need not to be written in the scientific notation as these are included in the power of $10$. The decimal point is placed to the right of $13$ digits, therefore the power of $10$ is written as $-13$. Thus, the number, $0.000000000000927$, can be written as $9.27\times {10}^{-13}$ in scientific notation.

Conclusion

The given ordinary number, $0.000000000000927$ in scientific notation is represented as $9.27\times {10}^{-13}$.