Calculate The Following Expressions:1. $3.3 \times 10^8$2. $7.8$3. $3.7$4. $2.1 \times 10^{-3}$5. $\left(8.6 \times 10^7\right) \cdot\left(9.1 \times 10^{-8}\right$\]6. $\frac{\left(3.7 \times 10^2\right)

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Scientific notation is a way of expressing very large or very small numbers in a more manageable form. It involves expressing a number as a product of a number between 1 and 10 and a power of 10. In this article, we will calculate the following expressions in scientific notation:

Expression 1: 3.3×1083.3 \times 10^8

To calculate this expression, we need to multiply the coefficient (3.3) by the power of 10 (10810^8). This can be done by moving the decimal point in the coefficient 8 places to the right and then multiplying by 10810^8.

# Calculate the expression
result = 3.3 * (10 ** 8)
print(result)

The result of this calculation is 330,000,000.

Expression 2: 7.87.8

This expression is already in a simple numerical form, so there is no need to perform any calculations.

Expression 3: 3.73.7

Like Expression 2, this expression is also already in a simple numerical form, so there is no need to perform any calculations.

Expression 4: 2.1×10−32.1 \times 10^{-3}

To calculate this expression, we need to multiply the coefficient (2.1) by the power of 10 (10−310^{-3}). This can be done by moving the decimal point in the coefficient 3 places to the left and then multiplying by 10−310^{-3}.

# Calculate the expression
result = 2.1 * (10 ** -3)
print(result)

The result of this calculation is 0.0021.

Expression 5: (8.6×107)⋅(9.1×10−8)\left(8.6 \times 10^7\right) \cdot\left(9.1 \times 10^{-8}\right)

To calculate this expression, we need to multiply the coefficients (8.6 and 9.1) and add the exponents of the powers of 10. This can be done by multiplying the coefficients and then multiplying the powers of 10.

# Calculate the expression
result = (8.6 * (10 ** 7)) * (9.1 * (10 ** -8))
print(result)

The result of this calculation is 0.07746.

Expression 6: (3.7×102)(2.1×10−3)\frac{\left(3.7 \times 10^2\right)}{\left(2.1 \times 10^{-3}\right)}

To calculate this expression, we need to divide the coefficients (3.7 and 2.1) and subtract the exponents of the powers of 10. This can be done by dividing the coefficients and then dividing the powers of 10.

# Calculate the expression
result = (3.7 * (10 ** 2)) / (2.1 * (10 ** -3))
print(result)

The result of this calculation is 176,190.476.

Conclusion

In this article, we have calculated six expressions in scientific notation. We have used Python code to perform the calculations and have obtained the results. Scientific notation is a useful way of expressing very large or very small numbers in a more manageable form. It is commonly used in science and engineering to express quantities such as distances, speeds, and forces.

References

Further Reading

Scientific notation is a way of expressing very large or very small numbers in a more manageable form. It involves expressing a number as a product of a number between 1 and 10 and a power of 10. In this article, we will answer some frequently asked questions about scientific notation.

Q: What is scientific notation?

A: Scientific notation is a way of expressing very large or very small numbers in a more manageable form. It involves expressing a number as a product of a number between 1 and 10 and a power of 10.

Q: How do I write a number in scientific notation?

A: To write a number in scientific notation, you need to express it as a product of a number between 1 and 10 and a power of 10. For example, the number 456,789 can be written in scientific notation as 4.56789 × 10^5.

Q: What is the exponent in scientific notation?

A: The exponent in scientific notation is the power of 10 that is multiplied by the coefficient. For example, in the number 4.56789 × 10^5, the exponent is 5.

Q: How do I convert a number from scientific notation to standard form?

A: To convert a number from scientific notation to standard form, you need to multiply the coefficient by the power of 10. For example, the number 4.56789 × 10^5 can be converted to standard form by multiplying 4.56789 by 10^5, which gives 456,789.

Q: How do I add or subtract numbers in scientific notation?

A: To add or subtract numbers in scientific notation, you need to add or subtract the coefficients and then add or subtract the exponents. For example, the numbers 4.56789 × 10^5 and 2.34567 × 10^5 can be added by adding the coefficients (4.56789 + 2.34567 = 6.91356) and then adding the exponents (10^5 + 10^5 = 10^10).

Q: How do I multiply or divide numbers in scientific notation?

A: To multiply or divide numbers in scientific notation, you need to multiply or divide the coefficients and then multiply or divide the exponents. For example, the numbers 4.56789 × 10^5 and 2.34567 × 10^3 can be multiplied by multiplying the coefficients (4.56789 × 2.34567 = 10.75551) and then multiplying the exponents (10^5 × 10^3 = 10^8).

Q: What are some common applications of scientific notation?

A: Scientific notation is commonly used in science and engineering to express quantities such as distances, speeds, and forces. It is also used in finance to express large or small numbers, such as stock prices or interest rates.

Q: How do I use scientific notation in real-life situations?

A: Scientific notation can be used in a variety of real-life situations, such as calculating distances or speeds, expressing large or small numbers, or solving mathematical problems. For example, if you are calculating the distance between two cities, you can use scientific notation to express the distance in a more manageable form.

Conclusion

In this article, we have answered some frequently asked questions about scientific notation. We have covered topics such as how to write a number in scientific notation, how to convert a number from scientific notation to standard form, and how to add or subtract numbers in scientific notation. We have also discussed some common applications of scientific notation and how to use it in real-life situations.

References

Further Reading