4th Grade Tenths, Hundredths and Decimal Notation Lesson: Notes and Examples (Free PDF)

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This 4th grade decimals lesson covers tenths, hundredths and decimal notation (Common Core 4.NF.C.5, 4.NF.C.6, 4.NF.C.7), with a free PDF to print.

Key takeaway: This lesson helps fourth grade students read, write, and compare decimals to the hundredths place and connect them to fractions with denominators of 10 and 100.

Topic: Tenths, Hundredths and Decimal Notation (4th grade)
Content: One-page lesson with a definition, a worked example and key facts
Standards: 4.NF.C.5, 4.NF.C.6, 4.NF.C.7
Answers: Explanations included
Format: Free printable PDF, US Letter, black and white

Tenths and hundredths are decimal places. One tenth is 1/10, or 0.1, and one hundredth is 1/100, or 0.01. Ten hundredths make one tenth, so 3/10 = 30/100 = 0.30. To compare decimals, write them to the same place, then compare the digits from left to right.

This lesson helps fourth grade students read, write, and compare decimals to the hundredths place and connect them to fractions with denominators of 10 and 100. It builds on a grid of 100 squares, so each tenth and hundredth is something students can see.

The lesson shows how tenths turn into hundredths, how to add a tenth and a hundredth, how to place decimals on a number line, and how to compare them by looking at place value. Also, money is used as a familiar example. Then, plan about 20 minutes, and shade a hundred grid as you read to see each fraction and decimal.

Grade 4 · Common Core State Standards: 4.NF.C.5, 4.NF.C.6, 4.NF.C.7

Key facts in this 4th grade decimals lesson

Key facts

One tenth = 10 hundredths, so 3/10 = 30/100.
Next, the first digit after the decimal point is tenths and the second is hundredths.
To add tenths and hundredths, rewrite the tenths as hundredths first: 3/10 + 4/100 = 34/100 = 0.34.
Then, compare decimals by writing them to the same place: 0.4 = 0.40, which is greater than 0.38.
Money is hundredths of a dollar: a dime is $0.10 and a penny is $0.01.

What are tenths and hundredths?

Imagine a square cut into 100 equal small squares. One small square is one hundredth, written $\frac{1}{100}$. A column of 10 small squares is one tenth, written $\frac{1}{10}$.

3 columns shaded: 3 tenths, which is 30 hundredths.

Tenths and hundredths

$\frac{1}{10} = \frac{10}{100}$. So $\frac{3}{10} = \frac{30}{100}$. To change tenths to hundredths, multiply the numerator and denominator by 10.

How do you write a fraction as a decimal?

A decimal point separates the ones from the parts smaller than 1. The first place after the point is tenths. The second is hundredths. $\frac{3}{10} = 0.3$ and $\frac{34}{100} = 0.34$.

0.34 has 3 tenths and 4 hundredths.

How do you add tenths and hundredths?

Write the tenths as hundredths first so the denominators match. Example: $\frac{3}{10} + \frac{4}{100}$.

Change tenths to hundredths: $\frac{3}{10} = \frac{30}{100}$.
Add the numerators: $30 + 4 = 34$.
Write the sum: $\frac{30}{100} + \frac{4}{100} = \frac{34}{100} = 0.34$.

3 tenths (blue) and 4 hundredths (orange) make 34 hundredths.

How do you compare decimals?

Compare the digits from left to right, but only when the numbers are written to the same place. Write 0.4 as 0.40. Then compare 40 hundredths with 38 hundredths: $0.40 > 0.38$. So 0.4 is greater than 0.38 even though 38 is a bigger number than 4.

0.36 sits between 0.3 and 0.4.

Money works the same way. A dime is $0.10, which is 10 hundredths of a dollar, and a penny is $0.01, one hundredth of a dollar. Three dimes and four pennies make $0.34.

What mistakes should you avoid?

Thinking a longer decimal is greater. The decimal 0.4 is greater than 0.38, because 0.4 is the same as 0.40.
Adding the digits without place value. In $\frac{3}{10} + \frac{4}{100}$, the answer is 0.34, not 0.7.
Mixing up the places. The digit right after the decimal point is tenths. The next digit is hundredths.

A quick check: draw a 10 by 10 grid. Shade whole columns for the tenths and single squares for the hundredths, then count all the shaded squares to find the number of hundredths.

4th grade decimals lesson: questions and answers

What are tenths and hundredths?

A tenth is one of 10 equal parts of a whole, written 1/10 or 0.1. A hundredth is one of 100 equal parts, written 1/100 or 0.01.

How do you change tenths to hundredths?

Multiply the numerator and the denominator by 10. For example, 3/10 = 30/100, because 3 times 10 is 30 and 10 times 10 is 100.

How do you write a fraction like 34/100 as a decimal?

A fraction with denominator 100 has two decimal places. 34/100 is 0.34, which is 3 tenths and 4 hundredths.

Why is 0.4 greater than 0.38?

Write 0.4 as 0.40. Then 40 hundredths is greater than 38 hundredths. The number of digits does not decide which decimal is greater.

How are decimals used with money?

A dollar is split into 100 cents, so each cent is one hundredth of a dollar. Thirty-four cents is 34/100 of a dollar, written $0.34.

Common mistakes with this 4th grade decimals lesson

Students think 0.4 is less than 0.38 because 4 is less than 38. Compare place by place, or write 0.4 as 0.40, and then 40 hundredths is clearly greater.
Students write three tenths and four hundredths as 0.7. They are different place values, so the sum is 0.34, with 3 in the tenths place and 4 in the hundredths place.
Students drop the zero in a number like 0.05 and write 0.5. The zero holds the tenths place, so 0.05 is five hundredths, not five tenths.

How to study this chapter

Draw a hundred grid for any decimal that feels confusing. Finally, shading 4 columns shows 0.4, and shading 4 extra squares shows 0.44.
Practice writing every tenth as hundredths, such as 0.3 as 0.30. Also, this is the fastest way to compare and add decimals safely.
Parents can use coins. Dimes are tenths of a dollar and pennies are hundredths, so counting money builds the same place value ideas.

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