What decimals are marked on the number line?
On this number line, we can see that there are four decimals that have been marked. But we don’t know their value. And it’s our job to work out what their value is and to label them correctly. Now, to help us do this, we need to use the decimals that we can see on the number line to help us work out the value of those that we don’t know. So the values that are marked on the number line are 67.424, 67.434, and 67.444. Can you see which digit is changing each time? Let’s sketch a place value grid to help us see how these numbers are changing. There we are, 67.424, 67.434, and 67.444. If we look closely, we can see that the hundredth digit is increasing by one each time. And all the other digits are staying the same. So we know that the numbers are increasing by one hundredth every time. So the jump from here to here is worth one hundredth. And the jump from here to here is also worth one hundredth. If we look carefully, we can see that this gap between the two labelled numbers has been split into 10 equal intervals.
Now, we’ve already said that we’re counting up in hundredths. So what do we need 10 of to make one more hundredth. Well, we know that ten thousandths are equal to one hundredth. So each of these small intervals in between our hundredths that are labelled must be worth one thousandth. So in other words, we can start at 67.424 and count up in thousandths. This way, we can find our missing numbers. 67.424, 67.425, 67.426, 67.427, 67.428, 67.429. And now we’ve reached our first missing number, which we know is 67.430. Now we could continue counting on to find our next missing number. But we can see that it’s only one interval less than 67.434. We know from our place value grid that 67.434 has four thousandths. So if we have one less thousandth than this, we’re going to have three thousandths and not four thousandths. The missing number is 67.433.
If we look at that third missing number, we can see that is halfway between 67.434 and 67.444. In other words, we need to count on five intervals or five thousandths from 67.434. As we’ve said already, 67.434 has got four thousandths. So if we add another five thousandths to this, we’re going to get a number with nine thousandths in it. Our third missing number is 67.439. Our final missing number is two intervals or two thousandths less than 67.444.
Another way of thinking of 67.444 is of 67 and four hundred and forty-four thousandths. Thinking of the number like this as a mixed number can help us count back in thousandths. 67 and four hundred forty-three thousandths and then 67 and four hundred forty-two thousandths. So our final missing decimal has a value of 67 and four hundred forty-two thousandths. So our missing decimal then is 67.442.
Now we could’ve just started at the very beginning of the number line and counted in thousandths all the way along to the end and completed our missing numbers that way. But hopefully you can see by the way that we’ve gone through this video there are several different techniques that we could use. We don’t always have to use the same method. And sometimes our other techniques were quicker.
The missing numbers from left to right are 67.430, which we can write as 67.43, then 67.433, 67.439, and finally 67.442.