Step by step
The question
Question: put 3 and 2/3, 3.6, 3 and 4/5, −3.7, 3.67 in order, from smallest to largest.
1 Write each as a decimal
To compare, we write every number the same way: as a decimal.
3 and 2/3 means 3 plus 2/3.
For 2/3 we divide.
20 divided by 3 is 6, with 2 left.
2 left again: the 6 repeats for ever.
So 3 and 2/3 is 3.666….
Careful!
The 2 and the 3 are a fraction, not digits after the point.
2/3 is 0.666….
3 and 4/5 means 3 plus 4/5.
5 times 2 is 10, so we multiply the top and the bottom by 2.
4/5 is 8 tenths: 0.8.
So 3 and 4/5 is 3.8.
2 Same number of digits
Zeros at the end of a decimal do not change it: 3.6 is the same as 3.600.
A repeating decimal goes on for ever, so we can write as many of its digits as we need.
So we give every number 3 digits after the point.
3 Compare
Now they all have 3 digits after the point.
So we can forget the point and compare them like whole numbers: 3600 < 3666 < 3670 < 3800.
Negative numbers are smaller than every positive number.
So they come first.
4 Write the answer
Now we write the numbers as they were given, in the same order: −3.7, 3.6, 3 and 2/3, 3.67, 3 and 4/5.
5 Check
Let's check on a number line.
Smaller numbers are further to the left.
We put a dot for each number.
From left to right: −3.7, 3.6, 3 and 2/3, 3.67, 3 and 4/5.
The same order.
So the answer is right!
Let's look back.
First: write each as a decimal.
Then: same number of digits.
Then: compare.
Then: write the answer.
Last: check.