Complete the figure shown.
The arrow in this figure tells us that we’re supposed to read it from left to right. The diagram is a little bit like a number machine or an input–output model. We have a column of numbers that show the numbers that go in. Then, like any number machine, something happens to those numbers. And here we can see that they’re divided by 10.
And then finally, we have a column of the outputs. What are the answers after the numbers are divided by 10? We can see that only one of the numbers has been completed. And the question tells us to complete the figure shown, so we need to find out what these two missing numbers are going to be.
The first thing that we can see about all the numbers on the left-hand side, that’s all the inputs, is that they’re all decimal numbers. So, how can we divide a number that’s not a multiple of 10 by 10? In particular, how can we divide these decimals by 10? Let’s look at the one completed calculation that we have. 0.233 divided by 10 equals 0.0233. What can we say about these two decimals?
Well, we can see that they both contain the same digits. The second number has an extra zero as a placeholder, but they both contain the digits two, three, and three in the same order. It’s almost as if those digits have just shifted along. In fact, that’s exactly what’s happened to the digits. Let’s see why.
Our input, that’s the number 0.233, is made up of two-tenths, three hundredths, and three thousandths. And to show that we’re using a decimal, we have a decimal point and a zero in the ones place. Now, when we’re thinking about place value, each digit to the right of another digit is worth 10 times less.
So, for example, ones are 10 times less than tens. Tenths are 10 times less than ones, and so on. So, if we divide our number, 0.233, by 10, each of the digits in this number is now going to be worth 10 times less. Each digit is going to move one place to the right. Three thousandths are going to now become worth three ten thousandths. 10 times less than three hundredths are three thousandths.
And if we make two-tenths 10 times smaller, it’s going to become worth two hundredths. And we need to put in a zero as a placeholder to show that empty tenths column. So, that’s how we find our answer, 0.0233. We’ve shifted all the digits one place to the right. So, to find our missing numbers, we just need to shift some digits.
8.69 is made up of eight ones, six-tenths, and nine hundredths. And to divide this number by 10, we need to shift all the digits, then, one place to the right. Nine hundredths become nine thousandths. Six-tenths become six hundredths. Eight ones are now worth eight-tenths. And to show that we now have no ones in the ones place, we use zero as a placeholder. 8.69 divided by 10 equals 0.869. Notice how those digits, eight, six, and nine, are in exactly the same order.
Finally, 22.3 is made up of two tens, two ones, and three-tenths. This time we’ll shift all the digits in one go. Let’s look at this number and visualise how it’s going to change. 22.3 is going to become 2.23. Each digit is now worth 10 times less. So, we can complete our figure. 22.3 divided by 10 equals 2.23. We found our two missing numbers by dividing by 10. And to divide these decimals by 10, we simply shifted the digits one place to the right. Our two missing numbers from top to bottom are 0.869 and 2.23.