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
- If the digits are equal move to the next column right until one number wins
For ascending order we pick the smallest first
Example: Put the following decimals in ascending order:
1.506, 1.56, 0.8
In a table they look like this:
| Ones | Decimal Point |
Tenths | Hundredths | Thousandths |
| 1 | . | 5 | 0 | 6 |
| 1 | . | 5 | 6 | |
| 0 | . | 8 |
Fill in the empty squares with zeros:
| Ones | Decimal Point |
Tenths | Hundredths | Thousandths |
| 1 | . | 5 | 0 | 6 |
| 1 | . | 5 | 6 | 0 |
| 0 | . | 8 | 0 | 0 |
Compare using the first column (Ones)
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:
| Ones | 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:
| Ones | 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 these in ascending order
$0.45, $0.50, $0.09, $0.53
The money values are these decimals: 0.45, 0.5, 0.09, 0.53
Line up the decimal point, and fill empty places with zeros:
| Ones | Decimal Point |
Tenths | Hundredths |
| 0 | . | 4 | 5 |
| 0 | . | 5 | 0 |
| 0 | . | 0 | 9 |
| 0 | . | 5 | 3 |
Now compare from left to right (tenths, then hundredths):
0.09, 0.45, 0.50, 0.53
As money: $0.09, $0.45, $0.50, $0.53
Example: Put these in DESCENDING order:
0.402, 0.42, 0.375, 1.2, 0.85
In a table they look like this:
| Ones | 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:
| Ones | 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 (Ones):
There's a 1, all the rest are 0. Descending order needs largest first, so 1.2 must be the highest. (Write it down in our answer and cross it off the table).
Answer so far: 1.2
| Ones | 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
| Ones | 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
| Ones | 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
Game
Now, go practice with this special Decimal Ordering Game !