What decimals are marked on the number line?
We’re given a number line with four decimals that have been marked. We need to work out, using the information that we’ve been given, what those decimals are. The only numbers that we have to help us have been marked already. And they are 21.67, 21.77, and 21.87. When we look at these numbers closely, we can see that they increase by one-tenth each time. Six-tenths becomes seven-tenths becomes eight-tenths. So, the interval between these two numbers on the number line is worth one-tenth, or 0.1.
And the same is true between 21.77 and 21.87. So, if the distance between the numbers we know already is one-tenth, then what’s the value of each of the small intervals that are marked but not labelled? They’re not worth tenths. Are they worth hundredths? Let’s count in hundredths to see. We’ll start with 21.67, 21.68, 21.69, 21.70. Now if we’re correct and each interval is worth one hundredth, then there should be seven intervals between here and 21.77, one, two, three, four, five, six, seven. We were right. Each interval on the number line is worth one hundredth, or 0.01. We can now use this information to help us.
If this position is 21.77, then the decimal before it will be one hundredth less than 21.77. This decimal is 21.76. Let’s continue to count backwards in hundredths to find the first missing decimal, 21.76, 21.75, 21.74. This must mean that our next missing decimal is 21.73. To find the final two missing decimals, let’s start at 21.77 and count up, 21.78, 21.79, 21.80, 21.81. So, that makes this missing decimal 21.82. 21.83, 21.84, and finally 21.85.
We used the numbers that we can see already and also the number of notches in-between each of them to work out that each interval was worth one hundredth. And we then used this to find the missing decimals. From left to right, they are 21.73, 21.76, 21.82, and finally 21.85.