Scientific Notation
Teaching Guide I. Topic: Scientific Notation II. Objectives:
To be able to fully understand the lesson, the student must learn: a. the definition of scientific notation b. the purpose of scientific notation c. how to make a number in scientific notation and vice versa III. Motivation: Recalling the names of numbers by its number of zeroes IV. Lesson Proper: * A number is in scientific notation when it is written as N x 10n, where 1<N<10 and n is an integer. * Scientific notation is used when a number is too large or too small to be remembered in full or it has no name. * Scientific notation is normally used in science, particularly astronomy and chemistry. * To express a number in scientific notation, you must move the decimal point as many places to the right or left depending if the number is less than or more than zero, until only one digit remains at the left of the decimal point. Then drop all the zeroes to the right of the decimal point (except if it is between two non-zero digits) and multiply it to 10 to the power of n, the number of places the decimal point moved, negative when going to the right, and positive when going to the left. * To add or subtract numbers in scientific notation, you first need to factor the powers of ten. Use the smaller exponent because it’s easier. Divide that power of ten by the other powers of ten (by the law on exponents) and multiply the whole quantity (which involves the addends) by that power of ten. Then convert the scientific notations into real numbers, add or subtract as usual, and change back into scientific notation if necessary. * Another way of adding and subtracting is to change the scientific notations into real numbers, add or subtract as usual, and change it back. * To multiply and divide numbers in scientific notation, just multiply or divide the coefficients, multiply the powers of ten (by the law of exponents), combine and change back into
To be able to fully understand the lesson, the student must learn: a. the definition of scientific notation b. the purpose of scientific notation c. how to make a number in scientific notation and vice versa III. Motivation: Recalling the names of numbers by its number of zeroes IV. Lesson Proper: * A number is in scientific notation when it is written as N x 10n, where 1<N<10 and n is an integer. * Scientific notation is used when a number is too large or too small to be remembered in full or it has no name. * Scientific notation is normally used in science, particularly astronomy and chemistry. * To express a number in scientific notation, you must move the decimal point as many places to the right or left depending if the number is less than or more than zero, until only one digit remains at the left of the decimal point. Then drop all the zeroes to the right of the decimal point (except if it is between two non-zero digits) and multiply it to 10 to the power of n, the number of places the decimal point moved, negative when going to the right, and positive when going to the left. * To add or subtract numbers in scientific notation, you first need to factor the powers of ten. Use the smaller exponent because it’s easier. Divide that power of ten by the other powers of ten (by the law on exponents) and multiply the whole quantity (which involves the addends) by that power of ten. Then convert the scientific notations into real numbers, add or subtract as usual, and change back into scientific notation if necessary. * Another way of adding and subtracting is to change the scientific notations into real numbers, add or subtract as usual, and change it back. * To multiply and divide numbers in scientific notation, just multiply or divide the coefficients, multiply the powers of ten (by the law of exponents), combine and change back into