[Applause] math 6 quarter 1 week 8th milk base let's learn about types of decimal numbers lesson one hello kids it's me teacher F don't forget to subscribe like and share and hit the notification Bell for the latest video you can also follow my Facebook page teacher FR [Music] TV for today's lesson in math 6 we will discuss about types of decimal numbers this is lesson one of week 8 for most essential learning competencies differen shate it's terminating from repeating non-terminating decimal quotients after going through this lesson you are expected to differentiate terminating from repeating non-terminating decimal quotients a rational number is a number that when written as decimal either stops or repeats in a pattern all rational numbers can be written as fractions or decimals it can be all integers positive and negative it can also be zero examples are -3 -2 -1 02 1 1 and 111,000 2 3 and 333,000 an irrational number is a number that when written as a decimal does not end and never repeats it can never be written as a fraction and it cannot be written as a quotient of two integers the decimal form of an irrational number either terminates or repeats the square roots of numbers that are not perfect square are called irrational numbers examples are square < TK of 2 Square < TK of 3 Square < TK of 2 and square < TK of 3 and now let us do this activity Learning test one classify each number as a rational number and an irrational number write R for rational number and iir for irrational number in your notebook number one -6 is it rational or irrational number very good the correct answer is R it means rational number number two square OT of 7 is it rational or irrational number very good the answer is I it means irrational number number three 6 and 4800 is it rational or irrational number very good the answer is R it means rational number number four what is this is it rational or irrational number very good the answer is IR it means irrational number and for number five three NES is it rational or irrational number very good the answer is IR it means irrational number the word terminate means end or stop a decimal that end is a terminating decimal a terminating decimal have a finite number of digits or numbers which come to an end after the decimal point it is any rational number when you divide the numerator by the denominator and you end up with a remainder of zero then you have a terminating decimal a repeating or non-terminating decimals have an infinite number of digits it is a decimal number that continues endlessly with no group of digits repeated when you divide the numerator at by the denominator with the remainder that begin to repeat after some point then you have a repeating or non-terminating decimal it can be converted into fraction and now let's do learning test two solve and identify if the decimal quotient is a terminating or repeating or non-terminating decimal write your answer in your notebook number one three ided 20 here is the solution 3 / 20 cannot be put decimal point in the dividend and add 0er so 3 / 20 = 0 0 * 20 = 0 3 - 0 = 3 then bring down 0 then put a decimal point in the quotient same place as in dividend so 30 / by 20 = 1 1 * 20 = 20 0 - 0 = 0 and 3 - 2 = 1 then add zero to the dividend and bring down zero 100 divided 20 = 5 5 * 20 = 100 100 - 100 = 0 so the quotient is 1500s it means this decimal is a terminating decimal number two 9 / 40 here is the solution 9 / 40 cannot be put a decimal point and zero into the dividend 9 / 40 = 0 0 * 40 = 0 9 - 0 equal 9 then bring down zero then put a decimal point in the quotient I 90 / 40 = 2 2 * 40 = 80 then 0 - 0 = 0 9 - 8 = 1 then add 0 to the dividend bring down Zer 100 / 40 = 2 2 * 40 = 80 100 - 80 = 20 then add zero again to the dividend then bring down zero 20 200 / 40 = 5 5 * 40 = 200 200 - 200 = Z the answer is 225,000 so this decimal is a terminating decimal number three 2 / 11 here is the solution 2 / 11 cannot be put decimal point and zero to the div then 2 / 11 is 0 0 * 11 = 0 2 - 0 = 2 bring down zero then put decimal point in the quotient 20 / 11 = 1 1 * 11 = 11 20 - 11 = 9 then add Z to the dividend and bring down zero 90 / 11 = = 8 8 * 11 = 88 90 - 88 = 2 then add zero to the dividend bring down zero 20 / 11 = 1 1 * 11 = 11 20 - 11 = 9 then add zero to the dividend bring down 0 90 / 11 = 8 8 * 11 = 8 8 90 - 88 = 2 so it means so that means the decimal quotient is a repeating or non-terminating decimal number four 6 divided by 13 here is the solution first put decimal point and add zero to the dividend 6 / 13 is 0 0 * 13 = 0 6 - 0 = 6 bring down 0 then put decimal point in the quotient 60 / 13 = 4 4 * 13 = 52 60 - 52 = 8 then add zero to the dividend bring down zero 80 / 13 = 6 6 * 13 = 78 80 - 78 = 2 add 0er to the dividend bring down zero 20 / 13 = 1 1 * 13 = 13 20 - 13 = 7 then add zero to the dividend bring down 0 70 / 13 = 5 5 * 13 = 65 70 - 65 = 5 so that means the decimal quotient is a repeating or non-terminating decimal and for number five 5 / by 16 first put decimal point to the dividend and add zero 5 / 16 = 0 0 * 16 = 0 5 - 0 = 5 bring down zero then write decimal point in the quotient 50 / by 16 = 3 3 * 16 = 48 50 - 48 = 2 add zero to the dividend then bring down zero 20 / 16 = 1 1 * 16 = 16 20 - 16 = 4 then add zero to the dividend bring down zero 40 / 16 = 2 2 * 16 = 32 40 - 32 = 8 then add 0er to the dividend then bring down zero 80 / 16 = 5 5 * 16 = 80 80 - 80 = 0 so that means the decimal quotient is a terminating decimal now let's proceed to learning test three write the given fraction in decimal numbers or vice versa write your answer in your notebook number one 59 write this fraction in decimal numbers how to write these fractions in decimal numbers we have to divide the numerator to denominator 5 / by 9 put decimal point and add Z to the dividend 5 / 9 = 0 0 * 9 = 0 5 - 0 = 5 bring down 0 then put decimal point in the quotient 50 / 9 = 5 5 * 9 = 45 50 - 45 = 5 then add Zer to the dividend bring down zero 50 / 9 = 5 5 * 9 = 45 50 - 45 = 5 add zero to the dividend bring down zero 50 / 9 = 5 5 * 9 = 45 50 - 45 = 5 so that means the quotient is a repeating or non-terminating decimals so therefore 5 9 in decimal is 555,000 or you can put vinculum or over the decimal numbers it means repeated in the same pattern number two 3 over 20 or 3 ided by 20 first put decimal point and add zero to the dividend 3 / 20 = 0 0 * 20 = 0 3 - 0 = 3 then bring down zero add decimal point to the quotient 30 / 20 = 1 1 * 20 = 20 30 - 20 = 10 then add 0er to the dividend bring down zero 100 / 20 = 5 5 * 20 = 100 100 - 100 = 0 so this quotient is a terminating decimal therefore 3 over 20 is equals to 1500s number three 2 and 34s first divide the fraction 3/4s 3 divided by 4 equal put decimal point and add zero to the dividend 3 / 4 = 0 0 * 4 = 0 3 - 0 = 3 bring down 0 put decimal point to the Cent 30 / 4 = 7 7 * 4 = 28 30 - 28 = 2 add 0 to the dividend then bring down zero 20 / 4 = 5 5 * 4 = 20 20 - 20 = 0 so therefore 3/4s is equivalent to 7500s then write the whole number two so 2 and 34 is equivalent to 2 and 7 2500s number four 2500s in fraction it is 1/4 number five 333,000 in fraction it is 333 over 1,000 vinculum a horizontal line placs over an expression to show that everything below the line is one group for example in a decimal number 333,000 this means that 333 which is under the bar is repeated in the same pattern this is a repeating or non-terminating decimals and for learning task 4 identify what kind of decimal number are the following choose choose the letter of the correct answer write your answer in your notebook number one 375,000 is it a non-re repeating decimals B repeating or non-terminating decimals C terminating decimals what is the answer very good the answer is letter C terminating decimals number two is it letter a non-re repeating decimals B repeating or non-terminating decimals C terminating decimals what is the correct answer very good the answer is letter B repeating or nonterminating decimals number three is it a non-repeating decimals B repeating or non-terminating decimals C terminating decimals what is the correct answer very good the correct answer is letter B repeating or non-terminating decimals number four 1500s is it a non-repeating decimals B repeating or non-terminating decimals C terminating decimals what is the correct answer very good the answer is letter C terminate repeating decimals and for number five is it a non-repeating decimals B repeating or non-terminating decimals C terminating decimals what is the correct answer very good the correct answer is letter B repeating or non-terminating decimals so kids do you understand our lesson for today wow good job kids I hope you learn a lot from this lesson until our next topic bye-bye kids thanks for watching [Music] [Applause]