Video: Number Patterns with Decimal Numbers

What are the missing numbers in this sequence: 0, 0.25, _, 0.75, 1, _, _?

03:30

Video Transcript

What are the missing numbers in the sequence, zero, 0.25, what, 0.75, one, what, and what?

To begin with, let’s write out the numbers in our sequence in a row, which will help us compare them. Zero, 0.25, then we have a missing value, then 0.75, followed by one. And then, there are two more missing numbers on the end. To be able to spot the rule for a sequence, we need to compare how numbers change from one to the other.

But if we look at the number sequence we’ve been given, there are several missing numbers. This means there are only two parts that we can compare. We can work out how a number changes to get from 0 to 0.25. And we can also see how a number changes to get from 0.75 to 1. Hopefully, the rule will be the same both times. And then, we’ll have a rule for the whole sequence.

Let’s try to find the rule. First of all, how do we get from 0 to 0.25, or twenty-five hundredths? Well, because we’re starting from zero. We can work this out quickly. We’re adding 0.25. 0.25 is the same as a quarter, or twenty-five hundredths. So, we could say we’re counting in quarters, or even adding twenty-five hundredths every time.

The idea of counting in quarters is important when we get to our next pair of numbers, 0.75 and one. Is the rules still to add 0.25? This is where the idea of adding a quarter comes in useful. 0.75 is the same as three-quarters. And if we add a quarter to three-quarters, we get one whole. So, 0.75 plus 0.25 does equal one. We’ve found the rule to the sequence. Now, let’s apply our rule to find the missing numbers.

Our first missing number is found by adding 0.25 to 0.25. Twenty-five hundredths plus another twenty-five hundredths equals fifty hundredths. We can write this simply as 0.5. Another way of thinking of this is a quarter plus a quarter equals a half.

To find our second missing number, we need to add 0.25 to 1. And the answer is 1.25. In other words, one plus a quarter equals one and a quarter, or one plus twenty-five hundredths equals one and twenty-five hundredths.

And to find our final missing number, we need to add another twenty-five hundredths to 1.25. The answer is one and fifty hundredths, or 1.5. The rule for our sequence was to add 0.25 every time. And so, the three missing numbers, from left to right, are 0.5, 1.25, and 1.5.

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