Lesson Video: Finding One, Ten, One Hundred, One Thousand, or Ten Thousand More or Less Mathematics

In this video, we will learn how to use place value to add or subtract 1, 10, 100, 1,000, or 10,000 from five-digit numbers and complete number patterns.

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Video Transcript

Finding One, 10, 100, 1,000, or 10,000 More or Less

In this video, we’re going to learn how to use place value to add or subtract one, 10, 100, 1,000, or 10,000 from a given number and how to complete number patterns. In this video, we’re going to work with numbers with four or five digits.

Let’s take a minute to think about the place value of each of these digits. This is the ones digit. The smallest one-digit number we can make is number one, and the largest one-digit number we can have is number nine. If we add one more to the number nine, we’ll have 10. This is the smallest two-digit number we can make. The greatest two-digit number we can make is the number 99. And if we add one more, we need to move into the hundreds column. The smallest three-digit number we can make is 100, and the greatest three-digit number is 999. If we add one more to 999, we have to move into the thousands column. 1,000 is the smallest four-digit number we can make. The greatest four-digit number we can make is 9,999. And if we add one more, we’ll have 10,000, which is the smallest five-digit number we can make. And the largest is 99,999.

The position of each digit tells us its place value. For example, the three digit in the number 95,364 is worth 300. The three is in the hundreds place. But if we change the order of the digits around, the three digit in the number 35,964 is worth 30,000. The three digit is in the ten thousands place.

Let’s see what happens if we add one to this number. The digit in the ones place is a four, worth four ones. So if we add one more, we’ll have five ones. The ones digit has increased by one. If we were to subtract one from the number 35,964, instead of having four ones, we’d have three. The ones digit has decreased by one. And if we were to subtract 1,000 from the number 35,964, the number of thousands would also decrease by one. We had five 1,000s. Now we have four.

Sometimes more than one digit in the number changes. Watch what happens if we add 100 to our number. Now we have 10 hundreds, and we need to regroup. By adding 1,000 into the thousands place, two of our digits have changed, the hundreds digit and the thousands digit. So when we’re adding one, 10, 100, 1,000, or 10,000, sometimes we have to regroup, and more than one digit changes.

How many digits do you think will change if we add one to the number 39,999? All of the digits would change. 39,999 plus one is 40,000. Let’s have a go at answering some questions now, and we can put into practice what we’ve learned about place value.

Find 10,000 more than the number given in the table.

In this question, we’ve been given a five-digit number in a place value table. And we have to find 10,000 more than this number. This number has 62 1,000s. Our number is 62,100. This is the ten thousands digit. The six is worth six 10,000s. 10,000, 20,000, 30,000, 40,000, 50,000, 60,000. If we add one more 10,000, instead of having six 10,000s, we’ll have seven, and the seven digit will be worth 70,000. 10,000 more than 62,100 is 72,100. The ten thousands digit increased by one.

Complete the following table.

In this question, we’re given a four-digit number, 5,666. In this column, we have to write the answer to 5,666 take away one. In the next column, we have to subtract 10 from 5,666 and write the answer here. Next, we need to subtract 100 from our number and write the answer here. And in the last column, we need to subtract 1,000 from our number and write the answer here.

Writing the number in a place value table helps us to understand the value of each digit. The number 5,666 has five 1,000s, six 100s, six 10s, and six ones. What is 5,666 take away one? We already know our number has six ones. If we take one away, we’ll have five ones left. 5,666 take away one is 5,665. The ones digit has decreased by one.

Now we need to take away 10 from our number. The tens digit is also a six, and this is worth 60. If we take away one 10, we’ll have five 10s. The tens digit has decreased by one.

Now we have to take away 100 from our number. The digit in the hundreds place is also a six. If we have six 100s and we take one away, we have five 100s left. 5,666 take away 100 is 5,566. The hundreds digit has decreased by one.

Finally, we need to subtract 1,000 from our number. The digit in the thousands place is a five. And if we take one 1,000 away, we’ll have four 1,000s left. 5,666 take away 1,000 is 4,666. This time, the thousands digit decreased by one.

We completed the table by taking away one, 10, 100, and 1,000 from the number 5,666. The missing numbers are 5,665, 5,656, 5,566, and 4,666. We used our knowledge of place value to help us subtract.

Find the missing numbers in the following pattern: 96,000, what, 76,000, what, 56,000.

In this question, we’re given a number pattern and we have to find the two missing numbers. We can tell from the three numbers we are given that this is a decreasing number pattern: 96,000, 76,000, 56,000. The thousands part of the number is decreasing. What’s the difference between 96,000 and 76,000? The nine digit in 96,000 has decreased by two, to a seven in the number 76,000. The difference between 96,000 and 76,000 is 20,000, and the difference between 76,000 and 56,000 is also 20,000.

The digit in the ten thousands place is decreasing by two: 96,000, 76,000, 56,000. So if the difference between our given numbers is 20,000, the midway point between each pair of numbers must be half that amount. We know that half of 20 is 10, so half of 20,000 is 10,000. So 10,000 less than 96,000 is 86,000; 10,000 less than 86,000 is 76,000; and 10,000 less than 76,000 is 66,000. And we know that 10,000 less than 66,000 is 56,000. Our numbers are decreasing by 10,000 each time: 96,000, 86,000, 76,000, 66,000, and 56,000. The missing numbers in the pattern are 86,000 and 66,000. The rule of the pattern is to subtract 10,000 each time.

What have we learned in this video? We have learned how to find one, 10, 100, 1,000, or 10,000 more or less than a number using our knowledge of place value.

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