Mathematics

Ordering of Decimals

Ordering Decimals

“Could I have a 3.65 and an 0.8, please … ?”
NO, not THAT type of ordering. I mean putting them in order

Ordering Decimals can be tricky. Because often we look at 0.42 and 0.402 and say that 0.402 must be bigger because there are more digits. But no!

We can use this method to see which decimals are bigger:

  • Set up a table with the decimal point in the same place for each number.
  • Put in each number.
  • Fill in the empty squares with zeros.
  • Compare using the first column on the left
  • until one number If the digits are equal move to the next column to the right wins.

If you want ascending order you always pick the smallest first

If you want descending order you always pick the largest first

Example: Put the following decimals in ascending order:

1.506, 1.56, 0.8

In a table they look like this:

Units Decimal
Point
Tenths Hundredths Thousandths
1 . 5 0 6
1 . 5 6
0 . 8

Fill in the empty squares with zeros:

Units Decimal
Point
Tenths Hundredths Thousandths
1 . 5 0 6
1 . 5 6 0
0 . 8 0 0

Compare using the first column (Units)

Two of them are “1”s and the other is a “0”. Ascending order needs smallest first, and so “0” is the winner:

Answer so far: 0.8

Now we can remove 0.8 from the list:

Units Decimal
Point
Tenths Hundredths Thousandths
1 . 5 0 6
1 . 5 6 0
.

Compare the Tenths

Now there are two numbers with the same “Tenths” value of 5, so move along to the “Hundredths” for the tie-breaker

Compare the Hundredths

One of those has a 6 in the hundredths, and the other has a 0, so the 0 wins (remember we are looking for the smallest each time). In other words 1.506 is less than 1.56:

Answer so far: 0.8, 1.506

Remove 1.506 from the list:

Units Decimal
Point
Tenths Hundredths Thousandths
.
1 . 5 6 0
.

Only one number left, it must be the largest:

Answer: 0.8, 1.506, 1.56

Done!

Example: Put the following decimals in DESCENDING order:

0.402, 0.42, 0.375, 1.2, 0.85

In a table they look like this:

Units Decimal
Point
Tenths Hundredths Thousandths
0 . 4 0 2
0 . 4 2  
0 . 3 7 5
1 . 2    
0 . 8 5  

And we want to go from highest to lowest (descending).

Fill in the empty squares with zeros:

Units Decimal
Point
Tenths Hundredths Thousandths
0 . 4 0 2
0 . 4 2 0
0 . 3 7 5
1 . 2 0 0
0 . 8 5 0

Compare using the first column (Units):

There is a 1, all the rest are 0. Descending order needs largest first, so 1.2 must be the highest. (Write it down in your answer and cross it off the table).

Answer so far: 1.2

Units Decimal
Point
Tenths Hundredths Thousandths
0 . 4 0 2
0 . 4 2 0
0 . 3 7 5
0 . 8 5 0

Compare the Tenths.

The 8 is highest, so 0.85 is next in value.

Answer so far: 1.2, 0.85

Units Decimal
Point
Tenths Hundredths Thousandths
0 . 4 0 2
0 . 4 2 0
0 . 3 7 5

Now there are two numbers with the same “Tenths” value of 4, so move along to the “Hundredths” for the tie-breaker

One number has a 2 in the hundredths, and the other has a 0, so the 2 wins. So 0.42 is bigger than 0.402:

Answer so far: 1.2, 0.85, 0.42, 0.402

Units Decimal
Point
Tenths Hundredths Thousandths
0 . 3 7 5

Only 0.375 left, so the answer is:

Answer: 1.2, 0.85, 0.42, 0.402, 0.375

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