Instruction's: Convert The Following Number's Into Scientific Notation 1.40,000 2.1,200,000 3.35,000,000 4.960,000 5.103,000,000
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 learn how to convert the given numbers into scientific notation.
What is Scientific Notation?
Scientific notation is a way of expressing numbers in the form a × 10^n, where a is a number between 1 and 10, and n is an integer. This notation is commonly used in science and engineering to express very large or very small numbers in a more compact and manageable form.
Converting Numbers to Scientific Notation
To convert a number to scientific notation, we need to move the decimal point to the left or right until we have a number between 1 and 10. We then multiply the number by 10 raised to the power of the number of places we moved the decimal point.
Converting 1,400,000 to Scientific Notation
To convert 1,400,000 to scientific notation, we need to move the decimal point 6 places to the left to get 1.4. We then multiply 1.4 by 10^6 to get 1.4 × 10^6.
Converting 1,200,000 to Scientific Notation
To convert 1,200,000 to scientific notation, we need to move the decimal point 6 places to the left to get 1.2. We then multiply 1.2 by 10^6 to get 1.2 × 10^6.
Converting 35,000,000 to Scientific Notation
To convert 35,000,000 to scientific notation, we need to move the decimal point 7 places to the left to get 3.5. We then multiply 3.5 by 10^7 to get 3.5 × 10^7.
Converting 960,000 to Scientific Notation
To convert 960,000 to scientific notation, we need to move the decimal point 5 places to the left to get 9.6. We then multiply 9.6 by 10^5 to get 9.6 × 10^5.
Converting 103,000,000 to Scientific Notation
To convert 103,000,000 to scientific notation, we need to move the decimal point 8 places to the left to get 1.03. We then multiply 1.03 by 10^8 to get 1.03 × 10^8.
Examples of Scientific Notation
Here are some examples of numbers in scientific notation:
- 1,400,000 = 1.4 × 10^6
- 1,200,000 = 1.2 × 10^6
- 35,000,000 = 3.5 × 10^7
- 960,000 = 9.6 × 10^5
- 103,000,000 = 1.03 × 10^8
Why Use Scientific Notation?
Scientific notation is useful for expressing very large or very small numbers in a more compact and manageable form. It is commonly used in science and engineering to express numbers that are too large or too small to be expressed in standard decimal notation.
Conclusion
In conclusion, scientific notation is a way of expressing numbers in the form a × 10^n, where a is a number between 1 and 10, and n is an integer. We can convert numbers to scientific notation by moving the decimal point to the left or right until we have a number between 1 and 10, and then multiplying the number by 10 raised to the power of the number of places we moved the decimal point. Scientific notation is useful for expressing very large or very small numbers in a more compact and manageable form.
Practice Problems
Here are some practice problems to help you understand how to convert numbers to scientific notation:
- Convert 2,500,000 to scientific notation.
- Convert 4,800,000 to scientific notation.
- Convert 12,000,000 to scientific notation.
- Convert 65,000,000 to scientific notation.
- Convert 275,000,000 to scientific notation.
Answer Key
- 2.5 × 10^6
- 4.8 × 10^6
- 1.2 × 10^7
- 6.5 × 10^7
- 2.75 × 10^8
Scientific Notation Q&A =========================
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 convert a number to scientific notation?
A: To convert a number to scientific notation, you need to move the decimal point to the left or right until you have a number between 1 and 10. You then multiply the number by 10 raised to the power of the number of places you moved the decimal point.
Q: What is the difference between scientific notation and standard decimal notation?
A: Scientific notation is a way of expressing numbers in the form a × 10^n, where a is a number between 1 and 10, and n is an integer. Standard decimal notation is a way of expressing numbers in the form a.bcd, where a, b, c, and d are digits.
Q: Why is scientific notation useful?
A: Scientific notation is useful for expressing very large or very small numbers in a more compact and manageable form. It is commonly used in science and engineering to express numbers that are too large or too small to be expressed in standard decimal notation.
Q: Can I use scientific notation with negative numbers?
A: Yes, you can use scientific notation with negative numbers. To do this, you need to move the decimal point to the left or right until you have a number between 1 and 10, and then multiply the number by 10 raised to the power of the number of places you moved the decimal point. You also need to include a negative sign in front of the number.
Q: How do I convert a number from scientific notation to standard decimal notation?
A: To convert a number from scientific notation to standard decimal notation, you need to multiply the number by 10 raised to the power of the exponent. For example, to convert 3.5 × 10^7 to standard decimal notation, you need to multiply 3.5 by 10^7.
Q: What are some examples of numbers in scientific notation?
A: Here are some examples of numbers in scientific notation:
- 1,400,000 = 1.4 × 10^6
- 1,200,000 = 1.2 × 10^6
- 35,000,000 = 3.5 × 10^7
- 960,000 = 9.6 × 10^5
- 103,000,000 = 1.03 × 10^8
Q: Can I use scientific notation with fractions?
A: Yes, you can use scientific notation with fractions. To do this, you need to multiply the fraction by 10 raised to the power of the exponent. For example, to convert 1/2 × 10^3 to standard decimal notation, you need to multiply 1/2 by 10^3.
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 (the numbers in front of the 10^n) and keep the same exponent. For example, to add 2.5 × 10^4 and 3.2 × 10^4, you need to add 2.5 and 3.2 to get 5.7, and keep the same exponent of 10^4.
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 (the numbers in front of the 10^n) and add or subtract the exponents. For example, to multiply 2.5 × 10^4 and 3.2 × 10^5, you need to multiply 2.5 and 3.2 to get 8, and add 4 and 5 to get 9, so the result is 8 × 10^9.
Conclusion
In conclusion, scientific notation is a useful way of expressing very large or very small numbers in a more compact and manageable form. It is commonly used in science and engineering to express numbers that are too large or too small to be expressed in standard decimal notation. We hope this article has helped you understand how to convert numbers to and from scientific notation, and how to add, subtract, multiply, and divide numbers in scientific notation.