Zero The Troublemaker (1972)

[Music] is zero a troublemaker for you we often use zero sometimes we use it with small numbers in doing addition or in doing subtraction and we may use it in working with large numbers let's see how we work with zero zero isn't much different from any other number like four you know that this numeral tells us the number in a set of four here is a set of four trucks now it's a set of three trucks a set of two a set of one truck a set of no trucks this is a set of zero trucks zero is the number of the empty set it tells us there are not any in a set a set of three paper flowers a set of zero paper flowers how many pennies are in this set right how many pennies are in this set right zero is the number of the empty set zero is a number just like 1 2 3 and the others you know because zero is a number it's on the number line Z is a starting place for number lines zero is to the left of one because it's less than one just as two is to the left of three because it is less than three because zero is a number you can usually use it like any other number you can add with it let's look at addition with zero Ed has four trucks his friend Steve was going to bring some of his trucks over to Ed's house but Steve forgot how many trucks do they have to play with well Ed has four trucks and Steve brought no trucks zero trucks so they're still just four when zero is added to another number the answer is that number but is 4 + 0 the same as 0 + 4 let's see Sue is Ed's sister she has no paper flowers zero flowers but a friend gives Sue four flowers flowers now how many flowers does Sue have right 0 + 4 is 4 and with the trucks we saw that 4 + 0 equals 4 adding zero is like adding any number either number can be first the answer is the same 7 + 0 equals 7 the same answer answer as 0 + 7 it doesn't matter which number is first when you add with zero you see let's try another addition problem using zero Ed and Sue's Big Brother Jeff has five pennies he's looking for some more pennies no pennies in his pocket zero pennies no pennies in his bank another zero no pennies in his dad's favorite chair either another zero Jeff even asks his mother if she has any extra pennies but no she doesn't have any pennies for Jeff another zero five + 0+ 0+ 0 + 0 equals how much no matter how many zeros are added to another number the sum can never get larger isn't addition with zero easy well subtraction is just as easy we can learn about subtraction with zero by seeing what Sue does with her four flowers she has taken the flowers home she asks Steve and Ed if they would like to have some how many flowers does she have left she had four flowers gave zero away and still has four flowers left Sue will help us do another subtraction problem this is Sue's mother mothers like flowers so sue gives the four flowers to her mother we can subtract four from the number Sue had which leaves Sue with zero flowers no flowers whenever a number is subtracted from itself that leaves zero zero is an easy number to use an addition and subtraction just remember that zero is the number of the empty set even when zero is used with other numerals it tells us there is an empty set Jeff and his marble collection will help us understand the meaning of zero in the numeral 30 each of these bags has exactly 10 marbles in it this is a set of three bags of marbles right but we have more than three marbles altogether this three shows us that we have three sets of 10 zero in the ones place shows us that we have zero ones 31 and 0 1es if we add four marbles the zero no longer correctly counts the set of ones four is the number number of the set of ones Jeff has a total of 34 marbles no he has more marbles this bag has 100 marbles in it we need to show this in the hundreds place Jeff has another bag of 100 Jeff has a total of 234 Marbles What happens when Jeff takes away the three sets of 10 marbles hey what kind of numeral is this is it 24 there are more than 24 marbles on the table two is not the number of sets of 10 it is the number of sets of 100 what numeral tells us how many sets of 10 there are not the four zero is the number of sets of 10 the 10 set is empty no 10 Z is an easy number to use but it also has a special use that no other number has let's see what that is we saw earlier that Jeff has a total of 234 marbles if someone asked Jeff how many marbles he has he would say 234 but Jeff might also say I have about 200 marbles because there are about 200 marbles in the Box not 2,000 not 20 not two Jeff has about 200 marbles in the box but 200 is not the exact number the zeros are Place holders for the exact numbers in the numeral 200 zeros help us know that the two shows how many sets of 100 using zeros as placeholders is called rounding off numers it's often done the distance you'd have to drive to get from New York to San Francisco is 3,38 MI but people often round it off to about 3,000 mil Man's first trip to the moon took 103 hours but we might also say it took about 100 hours for the trip to the moon it's not exact but it gives a pretty good idea zero is an important number it tells us we have empty sets both by itself and with other numerals and zero has a special use as a placeholder for other numerals when we're rounding off do you think zero is a troublemaker not for for you anymore [Music]