Decimals: learn and practice

Who this lesson is for

This decimals lesson is for grades 4–6. Grade 4 compares decimals. Grades 5 and 6 add them. The practice link opens decimal addition at grade 5. The page has one address, and the grade 4, 5, and 6 hubs all link here.

The point marks the ones place

A decimal point sits just to the right of the ones digit. In 3.25 the 3 is 3 ones, the 2 is 2 tenths, and the 5 is 5 hundredths. Tenths are slices of one tenth. Hundredths are slices of one hundredth, so ten hundredths make one tenth. Writing 3.25 is the same amount as 3 + 2/10 + 5/100.

Line the points up before you add

Adding decimals uses the same places as whole numbers. Tenths add to tenths, and hundredths add to hundredths. The way to keep the places honest is to write the decimal points in one vertical line. 1.2 is 1.20 if you need a hundredths column. The extra zero does not change the amount. It only gives the empty place a digit so the columns stay straight.

Worked example 1: which decimal is larger

Compare 0.4 and 0.35. Give both numbers hundredths: 0.4 = 0.40. Forty hundredths is more than thirty-five hundredths, so 0.4 > 0.35. The longer number is not automatically larger. 0.35 has more digits and a smaller value. Comparing the first place where the digits differ, after matching the columns, is the whole comparison.

Worked example 2: add one and two tenths

Add 1.2 + 0.35. Rewrite 1.2 as 1.20 so both numbers show hundredths. Line up the decimal points. Hundredths: 0 + 5 = 5. Tenths: 2 + 3 = 5. Ones: 1 + 0 = 1. The sum is 1.55. If the points are not lined up, someone may add the 2 to the 5 and get a sum that is not 1.55. The point in the answer sits in the same column as the points in the addends.

Worked example 3: two halves make a whole

Add 0.5 + 0.5. Five tenths plus five tenths is ten tenths. Ten tenths is one whole, so the sum is 1.0, which is the same amount as 1. You can also think 1/2 + 1/2 = 1. The decimal form and the fraction form agree. A sum of 0.10 would mean the tenths were treated as hundredths. That is the column mistake this example is meant to catch.

Checks before you leave the problem

Match the columns, including a placeholder zero, then add one column at a time. The decimal point in the sum stays in the column of the other points. Estimate first: 1.2 + 0.35 should be a little more than 1.5, and 1.55 is. Then practice decimal addition on the board.

Common questions about decimals

Is 0.4 bigger than 0.35?

Yes. 0.4 is 0.40, and 40 hundredths is more than 35 hundredths. More digits after the point do not make a larger number.

Can I write 1.2 as 1.20?

Yes. The extra zero is in an empty hundredths place. The amount is unchanged, and the zero makes addition columns easier to see.

Where does the decimal point go in a sum?

It stays in the column where you lined the points up. You do not slide it to the end after you finish adding the digits.