Complete the pattern. 0.1, 0.8, 1.5, what?
We’ve been given an increasing pattern of decimals. The numbers get larger each time. Let’s think about what each of the decimals represents. If we think about the place value of 0.1, we know that the digit one is in the tenths column. 0.1 is the same as one-tenth. Our second decimal in the pattern, a 0.8, has the digit eight in the tenths place. This represents eight-tenths. We can write this as the fraction eight-tenths.
Let’s pause here for a moment. How do we get from one-tenth to eight-tenths? Well, we add seven-tenths. One-tenth plus seven-tenths equals eight-tenths. And if we want to think about adding seven-tenths as a decimal, we can put a seven in the tenths place. We’ve added 0.7.
Let’s see whether adding 0.7 takes us to the next number in our pattern. If so, we’ve found the rule. So what happens when we add 0.7 to 0.8? Or another way of thinking about the same question, what happens if we add seven-tenths to eight-tenths? Well, eight plus seven equals 15. So eight-tenths plus seven-tenths equals fifteen-tenths. We know that ten-tenth equals one whole. So fifteen-tenths is the same as one whole and five-tenths, or in other words, as we were expecting, 1.5.
So we seem to have found the rule for our pattern. We need to add 0.7 or seven-tenths each time. So to complete the pattern, we need to add 0.7 to 1.5. Let’s do this by using vertical addition. And we can add the two decimals together, 1.5 plus 0.7. Make sure to put the decimal point underneath so that our answer is a decimal. Five-tenths plus seven tenth equals to twelve-tenths. This is the same as two-tenths. And we can exchange ten-tenths for one whole. So it’s the same as 1.2. And then in our ones column, we have one at the top and one that we’ve exchanged. So that’s two altogether. The next number in the pattern is 2.2.
First, we found the rule for the pattern, which we said was to add seven-tenths or 0.7 every time. And then all we had to do was to add 0.7 to 1.5 to find the answer. Notice that we could cover up all the decimal points in this pattern. And it would make sense that we were adding seven every time — one, eight, 15, 22 — as a useful way of checking that our pattern is correct. And so our completed pattern is 0.1, 0.8, 1.5, and our missing number, which is 2.2.