Rewriting the Expression in Standard Decimal Form

Oct 13, 2025 by miodeya.com 51 views

Understanding Scientific Notation

Scientific notation is a way of expressing very large or very small numbers in a more manageable form. It consists of a number between 1 and 10 multiplied by a power of 10. The power of 10 is usually written as a small number to the right of the number, with an exponent that indicates the power of 10. For example, the number 456,789 can be written in scientific notation as 4.56789 × 10^5.

Rewriting the Expression in Standard Decimal Form

The given expression is $1.02 \times 10^{-2}$ . To rewrite this expression in standard decimal form, we need to multiply the number by the power of 10 and then move the decimal point to the left by the number of places indicated by the exponent.

Step 1: Multiply the Number by the Power of 10

In this case, the exponent is -2, which means we need to multiply the number by 10^(-2) or 0.01.

Step 2: Move the Decimal Point

To move the decimal point to the left by 2 places, we need to multiply the number by 0.01.

Calculating the Result

Let's calculate the result:

$1.02 \times 10^{-2} = 1.02 \times 0.01 = 0.0102$

Conclusion

Therefore, the expression $1.02 \times 10^{-2}$ can be rewritten in standard decimal form as 0.0102.

Examples of Rewriting Scientific Notation

Here are a few more examples of rewriting scientific notation to standard decimal form:

$4.56789 \times 10^5 = 456,789$
$2.34567 \times 10^{-3} = 0.00234567$
$9.87654 \times 10^2 = 987.654$

Tips for Rewriting Scientific Notation

Here are a few tips to help you rewrite scientific notation to standard decimal form:

Make sure to multiply the number by the power of 10.
Move the decimal point to the left by the number of places indicated by the exponent.
Use a calculator to help you with the calculation if necessary.

Common Mistakes to Avoid

Here are a few common mistakes to avoid when rewriting scientific notation to standard decimal form:

Not multiplying the number by the power of 10.
Not moving the decimal point to the left by the correct number of places.
Not using a calculator to help with the calculation if necessary.

Conclusion

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 consists of a number between 1 and 10 multiplied by a power of 10.

Q: How do I rewrite scientific notation to standard decimal form?

A: To rewrite scientific notation to standard decimal form, you need to multiply the number by the power of 10 and then move the decimal point to the left by the number of places indicated by the exponent.

Q: What is the exponent in scientific notation?

A: The exponent in scientific notation is the power of 10 that the number is multiplied by. It is usually written as a small number to the right of the number.

Q: How do I move the decimal point in scientific notation?

A: To move the decimal point in scientific notation, you need to multiply the number by 10 raised to the power of the exponent. For example, if the exponent is -2, you need to multiply the number by 0.01.

Q: What is the difference between scientific notation and standard decimal form?

A: Scientific notation is a way of expressing very large or very small numbers in a more manageable form, while standard decimal form is a way of expressing numbers in a more familiar and intuitive way.

Q: Why is it important to rewrite scientific notation to standard decimal form?

A: Rewriting scientific notation to standard decimal form is important because it allows you to easily compare and manipulate numbers. It is also useful in many real-world applications, such as science, engineering, and finance.

Q: Can I use a calculator to help me rewrite scientific notation to standard decimal form?

A: Yes, you can use a calculator to help you rewrite scientific notation to standard decimal form. Many calculators have a scientific notation mode that allows you to easily convert between scientific notation and standard decimal form.

Q: What are some common mistakes to avoid when rewriting scientific notation to standard decimal form?

A: Some common mistakes to avoid when rewriting scientific notation to standard decimal form include not multiplying the number by the power of 10, not moving the decimal point to the left by the correct number of places, and not using a calculator to help with the calculation if necessary.

Q: How do I know if a number is in scientific notation?

A: A number is in scientific notation if it is written in the form a × 10^b, where a is a number between 1 and 10 and b is an integer.

Q: Can I rewrite scientific notation to standard decimal form by hand?

A: Yes, you can rewrite scientific notation to standard decimal form by hand. However, it may be more difficult and time-consuming than using a calculator.

Q: What are some real-world applications of rewriting scientific notation to standard decimal form?

A: Some real-world applications of rewriting scientific notation to standard decimal form include science, engineering, finance, and data analysis. It is also useful in many everyday situations, such as calculating tips or converting between units of measurement.

Conclusion

Rewriting scientific notation to standard decimal form is an important skill to have in mathematics. By following the steps outlined above and using a calculator if necessary, you can easily convert scientific notation to standard decimal form.