Step by step
The question
Question: put 1 and 3/4, 1.6, 1 and 2/3 in order, from smallest to largest.
1 Write each as a decimal
To compare, we write every number the same way: as a decimal.
1 and 3/4 means 1 plus 3/4.
4 times 25 is 100, so we multiply the top and the bottom by 25.
3/4 is 75 hundredths: 0.75.
So 1 and 3/4 is 1.75.
Careful!
The 3 and the 4 are a fraction, not digits after the point.
3/4 is 0.75.
1 and 2/3 means 1 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 1 and 2/3 is 1.666….
2 Same number of digits
Zeros at the end of a decimal do not change it: 1.75 is the same as 1.750.
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: 1600 < 1666 < 1750.
4 Write the answer
Now we write the numbers as they were given, in the same order: 1.6, 1 and 2/3, 1 and 3/4.
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: 1.6, 1 and 2/3, 1 and 3/4.
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.