Compare and order decimals

What you will learn

• Compare and order decimals

Models used: number sentences, stories, tables.

Before you start

• Tenths, hundredths and thousandths

More digits need not mean more

Shade 4 tenths of the first whole.

1. The whole grid has 100 equal squares. One full row is 10 hundredths, or one tenth.

   Shade 4 tenths of the first whole.

   0.4

   One small square is one hundredth of the whole. Ten small squares make one tenth, so the same shaded amount can be described in more than one way.

   40/100 = 0.4 = 40%

2. The whole grid has 100 equal squares. One full row is 10 hundredths, or one tenth.

   Now shade 35 hundredths of another equal whole. Its coloured area is smaller.

   0.35

   One small square is one hundredth of the whole. Ten small squares make one tenth, so the same shaded amount can be described in more than one way.

   35/100 = 0.35 = 35%

3. Both bars use the same scale. Compare their lengths and read the names beside them.

   Four tenths are 40 hundredths. Compare 40 small squares with 35 small squares.

   0.40 > 0.35

   0.400.4

   0.350.35

   Difference: 0.050000000000000044

Worked example: A new example, together

Compare 4.21 □ 7.04.

1. Compare matching place values. A trailing zero does not change the value. Read each value with the heading above its column.

   Align the decimal points and compare the first place that differs.

   Each decimal column names a unit ten times smaller than the one before it. Matching those units keeps the value clear.

   Compare matching place values. A trailing zero does not change the value.

   First decimal	Second decimal
   4.21	7.04

2. Compare matching place values. A trailing zero does not change the value. Read each value with the heading above its column.

   Align decimal points.

   Compare matching place values. A trailing zero does not change the value.

   First decimal	Second decimal
   4.21	7.04

   Compare 4.21 □ 7.04.

   <

3. Compare matching place values. A trailing zero does not change the value. Read each value with the heading above its column.

   Pad with trailing zeroes if needed; value does not change.

   Compare matching place values. A trailing zero does not change the value.

   First decimal	Second decimal
   4.21	7.04

4. Compare matching place values. A trailing zero does not change the value. Read each value with the heading above its column.

   4.21 < 7.04.

   Compare matching place values. A trailing zero does not change the value.

   First decimal	Second decimal
   4.21	7.04

5. Compare matching place values. A trailing zero does not change the value. Read each value with the heading above its column.

   Check the result against the question we started with.

   Compare the first place where the values differ.

   We found <. Each decimal column names a unit ten times smaller than the one before it. Matching those units keeps the value clear.

   Compare matching place values. A trailing zero does not change the value.

   First decimal	Second decimal
   4.21	7.04

Common mistakes to discuss

• More digits means a larger number. Line up the decimal points and compare tenths first. 0.5 is greater than 0.47, and 0.4 equals 0.40.

Check your understanding

• Compare and order decimals
• compare decimals by value rather than length
• check the answer against the original quantities and units

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.