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Operations with numbers in scientific notation
Scientific notation is a way of representing very large or very small numbers in a compact form. It involves writing the number as a product of a coefficient and a power of 10. For example, the number 123,000 can be written in scientific notation as 1.23 x 10^5.
When performing operations with numbers in scientific notation, there are four basic operations: addition, subtraction, multiplication, and division.
Addition and Subtraction in Scientific Notation:
To add or subtract numbers in scientific notation, we must first ensure that they have the same power of 10. If the powers of 10 are different, we can convert one of the numbers so that they have the same power of 10. Then, we can add or subtract the coefficients while keeping the power of 10 the same. For example, to add 2.5 x 10^4 and 1.2 x 10^4, we first convert 1.2 x 10^4 to 0.12 x 10^5, and then add the coefficients to get 2.62 x 10^4.
Multiplication in Scientific Notation:
To multiply numbers in scientific notation, we can multiply the coefficients and add the powers of 10. For example, to multiply 2.5 x 10^4 and 1.2 x 10^2, we would multiply the coefficients to get 3.0, and add the powers of 10 to get 3.0 x 10^6.
Division in Scientific Notation:
To divide numbers in scientific notation, we can divide the coefficients and subtract the powers of 10. For example, to divide 2.5 x 10^4 by 1.2 x 10^2, we would divide the coefficients to get 20.83, and subtract the powers of 10 to get 20.83 x 10
Working with numbers in scientific notation can be a powerful tool for dealing with very large or very small numbers. With practice, students can master these operations and feel more confident in their ability to work with scientific notation.
When performing operations with numbers in scientific notation, there are four basic operations: addition, subtraction, multiplication, and division.
Addition and Subtraction in Scientific Notation:
To add or subtract numbers in scientific notation, we must first ensure that they have the same power of 10. If the powers of 10 are different, we can convert one of the numbers so that they have the same power of 10. Then, we can add or subtract the coefficients while keeping the power of 10 the same. For example, to add 2.5 x 10^4 and 1.2 x 10^4, we first convert 1.2 x 10^4 to 0.12 x 10^5, and then add the coefficients to get 2.62 x 10^4.
Multiplication in Scientific Notation:
To multiply numbers in scientific notation, we can multiply the coefficients and add the powers of 10. For example, to multiply 2.5 x 10^4 and 1.2 x 10^2, we would multiply the coefficients to get 3.0, and add the powers of 10 to get 3.0 x 10^6.
Division in Scientific Notation:
To divide numbers in scientific notation, we can divide the coefficients and subtract the powers of 10. For example, to divide 2.5 x 10^4 by 1.2 x 10^2, we would divide the coefficients to get 20.83, and subtract the powers of 10 to get 20.83 x 10
Working with numbers in scientific notation can be a powerful tool for dealing with very large or very small numbers. With practice, students can master these operations and feel more confident in their ability to work with scientific notation.