Comparing Decimals Objective: Students should be able to compare decimals to the thousandths based on the meaning of the digits in each place using >, =, and < symbols to record the results of comparisons.

Let’s look at a decimal number… 645,789.231 What do we already know? What happens as we move to the left of the decimal point? What happens as we move to the right of the decimal point? We need to use this information to compare decimals.

645,789.231 Which digit has the greatest value? Why? Which digit has the least value? Why? Which digit represents hundredths? Which digit represents ten-thousands?

Compare to another number 645,789.231 645,759.231 If we want to compare these two numbers, what do we notice is the difference? What place value has a change?

645,789.231 645,759.231 The only difference is in the ten thousands place. We know 80,000 is greater than 50,000 So… 645,789.231 > 645,759.231

We need to keep using our place value and decimal knowledge. Increasing value Decreasing Value 645,789.231 We know that the value furthest left is the greatest. We start comparing numbers from the greatest value.

Let’s look at some other numbers. 3.21 3.22

If first, we line up the numbers by place value, 3.21 3.22

Next, shade each place value. 3.21 3.22 Ones. TenthsHundredths

3.21 3.22 then, compare from the greatest value first… Ones place has no difference.

3.21 3.22 and move to the next place value, Tenths place has no difference.

We can see the difference easier. 3.21 3.22 Hundredths place has different values. 2 hundredths is greater than 1 hundredth.

Now, we can write a relationship for the two numbers we compared. 3.21 < 3.22 Three and twenty-one hundredths is less than three and twenty-two hundredths.

What if the numbers have different place values? 6.724 6.57 Is the number with more digits always the largest?

What is the greatest value that has a difference when we compare? We can follow the same steps: 1)Line up the numbers by place value. 2) Shade each place value. 6.724 6.57 What is the greatest value that has a difference when we compare?

7 tenths is greater than 5 tenths. What do we find? 6.724 6.57 7 tenths is greater than 5 tenths.

Write a relationship for the two numbers. 6.724 > 6.57 Six and seven hundred twenty-four thousandths is greater than six and fifty-seven hundredths.

Now, you can try some on your own!!