Which Answer Shows $9 \times 10^{-6}$ Written In Standard Form?A. − 0.000009 -0.000009 − 0.000009 B. − 0.00009 -0.00009 − 0.00009 C. 0.0009 0.0009 0.0009 D. 0.00009 0.00009 0.00009

What is Standard Form?

Standard form is a way of expressing numbers in a compact and precise manner. It is commonly used in mathematics, science, and engineering to represent very large or very 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.

Expressing Numbers in Standard Form

To express a number in standard form, we need to move the decimal point to the left or right until we have a number between 1 and 10. We then multiply or divide the number by 10 for each place the decimal point was moved.

Example: Expressing 9 × 10^(-6) in Standard Form

Let's consider the given expression: $9 \times 10^{-6}$. To express this in standard form, we need to move the decimal point to the left until we have a number between 1 and 10.

Step 1: Move the Decimal Point

We start by moving the decimal point 6 places to the left. This gives us: $0.000009$.

Step 2: Determine the Power of 10

Since we moved the decimal point 6 places to the left, we need to multiply the number by 10^6 to get the original value.

Step 3: Write the Number in Standard Form

Therefore, the number $9 \times 10^{-6}$ can be written in standard form as: $-0.000009 \times 10^6$.

Comparing the Options

Now, let's compare the options given:

A. $-0.000009$ B. $-0.00009$ C. $0.0009$ D. $0.00009$

Which Option is Correct?

Based on our analysis, option A is the correct answer. The number $9 \times 10^{-6}$ is expressed in standard form as $-0.000009$.

Conclusion

In conclusion, standard form is an important concept in mathematics that allows us to express very large or very small numbers in a compact and precise manner. By understanding how to express numbers in standard form, we can solve problems more efficiently and accurately.

Key Takeaways

• Standard form is a way of expressing numbers in a compact and precise manner.
• To express a number in standard form, we need to move the decimal point to the left or right until we have a number between 1 and 10.
• We then multiply or divide the number by 10 for each place the decimal point was moved.
• The power of 10 is determined by the number of places the decimal point was moved.

Practice Problems

Try the following practice problems to reinforce your understanding of standard form:

1. Express $4 \times 10^3$ in standard form.
2. Express $2 \times 10^{-5}$ in standard form.
3. Express $6 \times 10^2$ in standard form.

Answer Key

1. $4 \times 10^3$ can be expressed in standard form as $4000$.
2. $2 \times 10^{-5}$ can be expressed in standard form as $0.00002$.
3. $6 \times 10^2$ can be expressed in standard form as $600$.

Additional Resources

For more information on standard form, check out the following resources:

• Khan Academy: Standard Form
• Mathway: Standard Form
• Wolfram Alpha: Standard Form

Frequently Asked Questions About Standard Form

Q: What is standard form?

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

Q: How do I express a number in standard form?

A: To express a number in standard form, you need to move the decimal point to the left or right until you have a number between 1 and 10. You then multiply or divide the number by 10 for each place the decimal point was moved.

Q: What is the power of 10 in standard form?

A: The power of 10 in standard form is determined by the number of places the decimal point was moved. If the decimal point was moved to the left, the power of 10 is positive. If the decimal point was moved to the right, the power of 10 is negative.

Q: How do I determine the power of 10?

A: To determine the power of 10, count the number of places the decimal point was moved. If the decimal point was moved 3 places to the left, the power of 10 is 10^3. If the decimal point was moved 2 places to the right, the power of 10 is 10^(-2).

Q: Can I have a negative number in standard form?

A: Yes, you can have a negative number in standard form. If the original number is negative, the power of 10 will also be negative.

Q: Can I have a decimal point in standard form?

A: No, you cannot have a decimal point in standard form. The decimal point must be moved to the left or right until you have a number between 1 and 10.

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

A: To convert a number from standard form to decimal form, you need to multiply the number by 10 raised to the power of the exponent. For example, if you have the number 4 × 10^3, you would multiply 4 by 10^3 to get 4000.

Q: What are some common applications of standard form?

A: Standard form is commonly used in mathematics, science, and engineering to represent very large or very small numbers. It is also used in finance, economics, and other fields where large numbers are encountered.

Q: Can I use standard form with fractions?

A: Yes, you can use standard form with fractions. To express a fraction in standard form, you need to multiply the numerator and denominator by 10 raised to the power of the exponent.

Q: How do I express a decimal number in standard form?

A: To express a decimal number in standard form, you need to move the decimal point to the left or right until you have a number between 1 and 10. You then multiply or divide the number by 10 for each place the decimal point was moved.

Q: Can I have a negative exponent in standard form?

A: Yes, you can have a negative exponent in standard form. If the original number is negative, the exponent will also be negative.

Q: How do I simplify an expression in standard form?

A: To simplify an expression in standard form, you need to combine like terms and eliminate any unnecessary factors.

Q: Can I use standard form with scientific notation?

A: Yes, you can use standard form with scientific notation. Scientific notation is a way of expressing numbers in the form a × 10^b, where a is a number between 1 and 10 and b is an integer.

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 number by 10 raised to the power of the exponent.

Q: Can I use standard form with logarithms?

A: Yes, you can use standard form with logarithms. Logarithms are a way of expressing numbers in terms of their logarithmic properties.

Q: How do I express a logarithmic expression in standard form?

A: To express a logarithmic expression in standard form, you need to use the properties of logarithms to simplify the expression.

Q: Can I use standard form with calculus?

A: Yes, you can use standard form with calculus. Calculus is a branch of mathematics that deals with rates of change and accumulation.

Q: How do I express a calculus expression in standard form?

A: To express a calculus expression in standard form, you need to use the properties of calculus to simplify the expression.

Q: Can I use standard form with statistics?

A: Yes, you can use standard form with statistics. Statistics is a branch of mathematics that deals with data analysis and interpretation.

Q: How do I express a statistical expression in standard form?

A: To express a statistical expression in standard form, you need to use the properties of statistics to simplify the expression.

Q: Can I use standard form with finance?

A: Yes, you can use standard form with finance. Finance is a field that deals with the management of money and investments.

Q: How do I express a financial expression in standard form?

A: To express a financial expression in standard form, you need to use the properties of finance to simplify the expression.

Q: Can I use standard form with economics?

A: Yes, you can use standard form with economics. Economics is a field that deals with the production, distribution, and consumption of goods and services.

Q: How do I express an economic expression in standard form?

A: To express an economic expression in standard form, you need to use the properties of economics to simplify the expression.

Q: Can I use standard form with engineering?

A: Yes, you can use standard form with engineering. Engineering is a field that deals with the design, construction, and operation of systems and structures.

Q: How do I express an engineering expression in standard form?

A: To express an engineering expression in standard form, you need to use the properties of engineering to simplify the expression.

Q: Can I use standard form with science?

A: Yes, you can use standard form with science. Science is a field that deals with the study of the natural world.

Q: How do I express a scientific expression in standard form?

A: To express a scientific expression in standard form, you need to use the properties of science to simplify the expression.

Q: Can I use standard form with technology?

A: Yes, you can use standard form with technology. Technology is a field that deals with the development and use of tools and systems.

Q: How do I express a technological expression in standard form?

A: To express a technological expression in standard form, you need to use the properties of technology to simplify the expression.

Q: Can I use standard form with computer science?

A: Yes, you can use standard form with computer science. Computer science is a field that deals with the study of algorithms and data structures.

Q: How do I express a computer science expression in standard form?

A: To express a computer science expression in standard form, you need to use the properties of computer science to simplify the expression.

Q: Can I use standard form with data analysis?

A: Yes, you can use standard form with data analysis. Data analysis is a field that deals with the interpretation and presentation of data.

Q: How do I express a data analysis expression in standard form?

A: To express a data analysis expression in standard form, you need to use the properties of data analysis to simplify the expression.

Q: Can I use standard form with machine learning?

A: Yes, you can use standard form with machine learning. Machine learning is a field that deals with the development of algorithms that can learn from data.

Q: How do I express a machine learning expression in standard form?

A: To express a machine learning expression in standard form, you need to use the properties of machine learning to simplify the expression.

Q: Can I use standard form with artificial intelligence?

A: Yes, you can use standard form with artificial intelligence. Artificial intelligence is a field that deals with the development of algorithms that can simulate human intelligence.

Q: How do I express an artificial intelligence expression in standard form?

A: To express an artificial intelligence expression in standard form, you need to use the properties of artificial intelligence to simplify the expression.

Q: Can I use standard form with natural language processing?

A: Yes, you can use standard form with natural language processing. Natural language processing is a field that deals with the development of algorithms that can process and understand human language.

Q: How do I express a natural language processing expression in standard form?

A: To express a natural language processing expression in standard form, you need to use the properties of natural language processing to simplify the expression.

Q: Can I use standard form with computer vision?

A: Yes, you can use standard form with computer vision. Computer vision is a field that deals with the development of algorithms that can interpret and understand visual