Ordering Decimals and Fractions Intro to Algebra

Ordering Decimals Ordering decimals can be tricky! We often look at 0.42 and and say that must be bigger because there are more digits or because 402 is bigger than 42. But NO!

How can we compare decimals? 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 to the right until one number wins

Important Ascending vs Descending

Ascending If you want ascending order, you always pick the smallest first!

Descending If you want descending order you always pick the largest first!

What should our table look like? UnitsDecimal PointTenthsHundredthsThousandths

Example Put the following decimals in ascending order: 1.506, 1.56, 0.8 What goes first? Smallest or biggest number?

Let’s start our table (Step 1 and 2) UnitsDecimal PointTenthsHundredthsThousandths

Step 3 UnitsDecimal PointTenthsHundredthsThousandths

Step 4 Where do we look first? Answer so far: 0.8

Step 5 Now where do we look? Answer: 0.8, 1.506, 1.56

Example Put the following decimals in descending order: 0.402, 0.42, 0.375, 1.2, 0.85

This is what our table should look like UnitsDecimal PointTenthsHundredthsThousandths

Example Put the following decimals in descending order: 0.402, 0.42, 0.375, 1.2, , 0.85, 0.42, 0.402, 0.375

Example Put the following decimals in ascending order: 0.206, 2.06, 0.026, , 0.206, 0.26, 2.06

What if there are fractions in the mix?

Ordering Fractions and Decimals If we are ordering both fractions and decimals, we will add just one step to the beginning! The first thing to do is to convert all the fractions to decimals.

Example