In 2014, The United States Discarded A Total Of $5.08 \times 10^9$ Pounds Of Trash.Write This Number In Standard Form.$\square$
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. In the given problem, the number of pounds of trash discarded in 2014 is expressed in scientific notation as $5.08 \times 10^9$.
Converting Scientific Notation to Standard Form
To convert a number from scientific notation to standard form, we need to multiply the number by the corresponding power of 10. In this case, we have $5.08 \times 10^9$. To convert this to standard form, we need to multiply 5.08 by $10^9$.
Multiplying by Powers of 10
When multiplying a number by a power of 10, we can simply move the decimal point of the number to the right by the number of places indicated by the exponent. In this case, we need to move the decimal point of 5.08 to the right by 9 places.
Converting the Number
To convert the number $5.08 \times 10^9$ to standard form, we need to move the decimal point of 5.08 to the right by 9 places. This gives us:
Conclusion
In conclusion, the number of pounds of trash discarded in 2014, expressed in scientific notation as $5.08 \times 10^9$, can be converted to standard form by multiplying the number by the corresponding power of 10. This gives us the number 5,080,000,000.
Key Takeaways
- Scientific notation is a way of expressing very large or very small numbers in a more manageable form.
- To convert a number from scientific notation to standard form, we need to multiply the number by the corresponding power of 10.
- When multiplying a number by a power of 10, we can simply move the decimal point of the number to the right by the number of places indicated by the exponent.
Real-World Applications
Scientific notation is commonly used in various fields such as physics, engineering, and chemistry. It allows us to express very large or very small numbers in a more manageable form, making it easier to perform calculations and analyze data.
Example Problems
- Convert the number $2.5 \times 10^6$ to standard form.
- Convert the number $3.2 \times 10^8$ to standard form.
Solutions
- To convert the number $2.5 \times 10^6$ to standard form, we need to move the decimal point of 2.5 to the right by 6 places. This gives us:
- To convert the number $3.2 \times 10^8$ to standard form, we need to move the decimal point of 3.2 to the right by 8 places. This gives us:
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 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 the corresponding power of 10. This can be done by moving the decimal point of the number to the right 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. For example, in the number $5.08 \times 10^9$, the exponent is 9.
Q: How do I move the decimal point in a number?
A: To move the decimal point in a number, you need to add or subtract zeros to the right of the decimal point. For example, to move the decimal point of 5.08 to the right by 9 places, you would add 8 zeros to the right of the decimal point, resulting in 5,080,000,000.
Q: What if the exponent is negative?
A: If the exponent is negative, you need to move the decimal point of the number to the left by the number of places indicated by the exponent. For example, in the number $5.08 \times 10^{-9}$, the exponent is -9, so you would move the decimal point of 5.08 to the left by 9 places, resulting in 0.00000000508.
Q: Can I convert a number from standard form to scientific notation?
A: Yes, you can convert a number from standard form to scientific notation by expressing the number as a number between 1 and 10 multiplied by a power of 10. For example, the number 5,080,000,000 can be expressed in scientific notation as $5.08 \times 10^9$.
Q: Why is scientific notation useful?
A: Scientific notation is useful because it allows us to express very large or very small numbers in a more manageable form. This makes it easier to perform calculations and analyze data.
Q: What are some real-world applications of scientific notation?
A: Scientific notation is commonly used in various fields such as physics, engineering, and chemistry. It is also used in finance, economics, and computer science.
Q: Can I use a calculator to convert a number from scientific notation to standard form?
A: Yes, you can use a calculator to convert a number from scientific notation to standard form. Most calculators have a button that allows you to enter a number in scientific notation and convert it to standard form.
Q: What if I have a decimal point in the exponent?
A: If you have a decimal point in the exponent, you need to multiply the number by the corresponding power of 10. For example, in the number $5.08 \times 10^{9.5}$, you would multiply 5.08 by $10^{9.5}$, resulting in 5,080,000,000,000,000.
Q: Can I convert a number from scientific notation to standard form with a decimal point in the exponent?
A: Yes, you can convert a number from scientific notation to standard form with a decimal point in the exponent by multiplying the number by the corresponding power of 10. For example, in the number $5.08 \times 10^{9.5}$, you would multiply 5.08 by $10^{9.5}$, resulting in 5,080,000,000,000,000.