To convert a number into scientific notation by hand, you need to move the decimal point to the right or left until you have a number between 1 and 10. The number of times you move the decimal point will be the exponent in your scientific notation. For example, to convert 250,000 into scientific notation, you would move the decimal point 5 places to the left, making the number 2.5. The exponent would then be 5, since you moved the decimal point 5 places.
Standard notation is the typical way we write numbers, with the decimal point in a fixed position and no exponents. Scientific notation, on the other hand, is a way to express very large or very small numbers in a more compact form. It consists of a number between 1 and 10, multiplied by a power of 10 (represented by an exponent). This allows us to easily compare and perform calculations with numbers that have a lot of zeros.
To multiply numbers in scientific notation, you can simply multiply the numbers in front of the decimal point and add the exponents. For example, (4.5 x 10^3) x (6.2 x 10^2) = (4.5 x 6.2) x (10^3 x 10^2) = 27.9 x 10^5. To divide numbers in scientific notation, you can divide the numbers in front of the decimal point and subtract the exponents. For example, (4.5 x 10^3) ÷ (6.2 x 10^2) = (4.5 ÷ 6.2) x (10^3 ÷ 10^2) = 0.72 x 10^1 = 7.2
The purpose of using scientific notation in science is to represent very large or very small numbers in a more concise and manageable form. This allows scientists to perform calculations and make comparisons more easily. It is also used to express measurements with a high level of precision, as the exponent can represent the number of significant figures in the measurement.
To convert a number from scientific notation back to standard notation, you need to move the decimal point to the right or left based on the exponent. If the exponent is positive, you move the decimal point to the right the same number of places as the exponent. If the exponent is negative, you move the decimal point to the left the same number of places as the exponent. For example, 2.5 x 10^5 would become 250,000 in standard notation, and 3.2 x 10^-2 would become 0.032 in standard notation.