Convert The Numbers Below To Standard Form.$\[ \begin{tabular}{|l|l|} \hline $6.334 \times 10^6$ & $2.0057 \times 10^8$ \\ \hline $5.93 \times 10^{-4}$ & $3.402 \times 10^{-5}$ \\ \hline \end{tabular} \\]

Feb 26, 2025 by ADMIN 208 views

What is Standard Form?

Standard form is a way of expressing numbers in a compact and simplified manner. It is commonly used in mathematics, science, and engineering to represent large or small numbers in a more manageable form. In standard form, a number is expressed as a product of a number between 1 and 10, and a power of 10.

Converting Numbers to Standard Form

In this section, we will learn how to convert the given numbers to standard form.

Converting Large Numbers to Standard Form

To convert a large number to standard form, we need to move the decimal point to the left until we have a number between 1 and 10. At the same time, we need to increase the power of 10 by the number of places we moved the decimal point.

Example 1: Converting $6.334 \times 10^6$ to Standard Form

To convert $6.334 \times 10^6$ to standard form, we need to move the decimal point 6 places to the left, resulting in 0.006334. At the same time, we need to increase the power of 10 by 6, resulting in $10^6$ . Therefore, $6.334 \times 10^6$ in standard form is 0.006334 $\times$ $10^6$ .

Converting Small Numbers to Standard Form

To convert a small number to standard form, we need to move the decimal point to the right until we have a number between 1 and 10. At the same time, we need to decrease the power of 10 by the number of places we moved the decimal point.

Example 2: Converting $5.93 \times 10^{-4}$ to Standard Form

To convert $5.93 \times 10^{-4}$ to standard form, we need to move the decimal point 4 places to the right, resulting in 5930. At the same time, we need to decrease the power of 10 by 4, resulting in $10^{-4}$ . Therefore, $5.93 \times 10^{-4}$ in standard form is 5930 $\times$ $10^{-4}$ .

Converting Numbers with Decimal Points to Standard Form

To convert a number with a decimal point to standard form, we need to move the decimal point to the left or right until we have a number between 1 and 10. At the same time, we need to increase or decrease the power of 10 by the number of places we moved the decimal point.

Example 3: Converting $2.0057 \times 10^8$ to Standard Form

To convert $2.0057 \times 10^8$ to standard form, we need to move the decimal point 8 places to the left, resulting in 0.000020057. At the same time, we need to increase the power of 10 by 8, resulting in $10^8$ . Therefore, $2.0057 \times 10^8$ in standard form is 0.000020057 $\times$ $10^8$ .

Example 4: Converting $3.402 \times 10^{-5}$ to Standard Form

To convert $3.402 \times 10^{-5}$ to standard form, we need to move the decimal point 5 places to the right, resulting in 340200. At the same time, we need to decrease the power of 10 by 5, resulting in $10^{-5}$ . Therefore, $3.402 \times 10^{-5}$ in standard form is 340200 $\times$ $10^{-5}$ .

Conclusion

In conclusion, converting numbers to standard form is an essential skill in mathematics, science, and engineering. By following the steps outlined in this article, you can easily convert large and small numbers to standard form. Remember to move the decimal point to the left or right until you have a number between 1 and 10, and increase or decrease the power of 10 by the number of places you moved the decimal point.

Practice Problems

Convert $4.275 \times 10^7$ to standard form.
Convert $9.812 \times 10^{-3}$ to standard form.
Convert $1.002 \times 10^9$ to standard form.
Convert $6.543 \times 10^{-6}$ to standard form.

Answer Key

0.0004275 $\times$ $10^7$
9812 $\times$ $10^{-3}$
0.001002 $\times$ $10^9$
0.000006543 $\times$ $10^6$

References

[1] "Standard Form" by Math Open Reference. Retrieved February 26, 2024, from https://www.mathopenref.com/standardform.html
[2] "Converting Numbers to Standard Form" by Khan Academy. Retrieved February 26, 2024, from https://www.khanacademy.org/math/pre-algebra/pre-algebra-standard-form/v/converting-numbers-to-standard-form
Frequently Asked Questions (FAQs) about Converting Numbers to Standard Form ================================================================================

Q: What is standard form?

A: Standard form is a way of expressing numbers in a compact and simplified manner. It is commonly used in mathematics, science, and engineering to represent large or small numbers in a more manageable form.

Q: How do I convert a large number to standard form?

A: To convert a large number to standard form, you need to move the decimal point to the left until you have a number between 1 and 10. At the same time, you need to increase the power of 10 by the number of places you moved the decimal point.

Q: How do I convert a small number to standard form?

A: To convert a small number to standard form, you need to move the decimal point to the right until you have a number between 1 and 10. At the same time, you need to decrease the power of 10 by the number of places you moved the decimal point.

Q: What if the number has a decimal point? How do I convert it to standard form?

A: To convert a number with a decimal point to standard form, you need to move the decimal point to the left or right until you have a number between 1 and 10. At the same time, you need to increase or decrease the power of 10 by the number of places you moved the decimal point.

Q: Can you give me an example of converting a large number to standard form?

A: Let's say we want to convert $6.334 \times 10^6$ to standard form. To do this, we need to move the decimal point 6 places to the left, resulting in 0.006334. At the same time, we need to increase the power of 10 by 6, resulting in $10^6$ . Therefore, $6.334 \times 10^6$ in standard form is 0.006334 $\times$ $10^6$ .

Q: Can you give me an example of converting a small number to standard form?

A: Let's say we want to convert $5.93 \times 10^{-4}$ to standard form. To do this, we need to move the decimal point 4 places to the right, resulting in 5930. At the same time, we need to decrease the power of 10 by 4, resulting in $10^{-4}$ . Therefore, $5.93 \times 10^{-4}$ in standard form is 5930 $\times$ $10^{-4}$ .

Q: What if I'm not sure how to convert a number to standard form? Can I use a calculator?

A: Yes, you can use a calculator to convert a number to standard form. Most calculators have a function that allows you to convert numbers to standard form. Alternatively, you can use online tools or software to help you with the conversion.

Q: Is standard form only used in mathematics and science?

A: No, standard form is used in many fields, including engineering, finance, and computer science. It is a useful way to represent large or small numbers in a compact and simplified manner.

Q: Can I use standard form to represent negative numbers?

A: Yes, you can use standard form to represent negative numbers. To do this, you need to follow the same steps as for positive numbers, but with a negative sign in front of the number.

Q: Can I use standard form to represent fractions?

A: Yes, you can use standard form to represent fractions. To do this, you need to follow the same steps as for whole numbers, but with a fraction bar or a decimal point in the numerator or denominator.