Mathematics · 4th Grade · Fractions: Equivalence and Operations · Weeks 10-18

Decimal Connections: Tenths and Hundredths

Students will use decimal notation for fractions with denominators 10 or 100.

• Common Core State Standards
• CCSS.Math.Content.4.NF.C.6

About This Topic

Decimal notation is one of the most significant conceptual shifts in elementary mathematics, and its introduction in 4th grade rests entirely on the fraction understanding students have built. CCSS 4.NF.C.6 requires students to read and write decimals as an alternative notation for fractions with denominators 10 or 100. The key insight is that 0.3 and 3/10 are not two different answers , they are two ways of writing the same number.

Place value understanding extends directly into decimal notation: the tenths place is to the right of the decimal point, and the hundredths place is one position further right. Students who know how digits shift in relation to each other on the whole-number side can apply the same logic to the decimal side. Connecting this to the place value work from Unit 1 helps students see decimals as an extension of a system they already know, not an entirely new topic.

Active learning strategies that ask students to translate between forms , fraction to decimal, decimal to fraction, and both to a visual model , are particularly effective here. The act of translating forces students to engage with meaning rather than just copying notation, and pair work surfaces the small confusions (tenths vs hundredths, 0.3 vs 0.03) before they harden into persistent errors.

Key Questions

1. Explain how a decimal is just another way of writing a fraction with a denominator of 10 or 100.
2. Differentiate between the place value of digits to the right of the decimal point.
3. Translate a fraction like 3/10 or 45/100 into its decimal equivalent.

Learning Objectives

• Translate fractions with denominators of 10 or 100 into their equivalent decimal notation.
• Identify the place value of digits to the right of the decimal point, distinguishing between tenths and hundredths.
• Compare and order numbers expressed as fractions (with denominators 10 or 100) and their decimal equivalents.
• Represent decimal numbers to the hundredths place using visual models, such as grids or number lines.

Before You Start

Understanding Fractions: Denominators 10 and 100

Why: Students need to be familiar with representing parts of a whole using fractions with these specific denominators before connecting them to decimals.

Place Value of Whole Numbers

Why: Understanding place value for ones, tens, and hundreds is foundational for extending this concept to the tenths and hundredths places.

Key Vocabulary

Decimal Point	A symbol used to separate the whole number part of a number from the fractional part. It indicates place value.
Tenths Place	The first position to the right of the decimal point, representing values that are one-tenth (1/10) of a whole.
Hundredths Place	The second position to the right of the decimal point, representing values that are one-hundredth (1/100) of a whole.
Equivalent Fractions	Fractions that represent the same value, even though they have different numerators and denominators. For example, 3/10 and 30/100 are equivalent.

Watch Out for These Misconceptions

Common Misconception

Students confuse 0.3 (three tenths) with 0.03 (three hundredths), especially when reading decimals aloud.

What to Teach Instead

Insist on reading decimals using place value names, not as individual digits: '0.3' is 'three tenths,' not 'zero point three.' Pair this with grid shading: three shaded columns in a tenths model vs three shaded squares in a hundredths model makes the size difference concrete and memorable.

Common Misconception

Students think 0.30 is larger than 0.3 because it has more digits.

What to Teach Instead

This error comes from whole-number thinking (30 > 3). Using a hundredths grid where students shade both shows they cover identical areas: 3 columns = 30 squares. Matching card activities that group 0.3, 0.30, and 3/10 as equivalent reinforce this without requiring lengthy explanation.

Common Misconception

Students read the decimal point as 'and' and treat the decimal portion as a separate whole number (e.g., 0.35 is 'zero and thirty-five').

What to Teach Instead

The decimal point separates the whole part from the fractional part. 0.35 means 35 hundredths , not 35 of anything whole. Using fraction notation alongside decimal notation (0.35 = 35/100) consistently until students internalize the connection helps prevent this confusion.

Active Learning Ideas

Matching Game: Three-Way Fraction-Decimal-Model Match

Create sets of cards showing the same quantity in three forms: a fraction (3/10), its decimal (0.3), and a shaded hundredths or tenths grid. Partners sort the cards into matched sets of three and explain each match aloud. Any disagreements are resolved by referring to the visual model as the tie-breaker.

20 min·Pairs

Think-Pair-Share: Decimal Number Line Placement

Provide a number line marked from 0 to 1 with only the endpoints labeled. Give each student three decimals to place on the line. Partners compare placement and explain their reasoning about which benchmarks they used. The class debrief asks two pairs to justify a placement they initially disagreed on.

15 min·Pairs

Inquiry Circle: What Does This Digit Mean?

Give groups a set of decimal cards (e.g., 0.4, 0.04, 0.40, 0.14). For each card, groups must identify the value of each digit to the right of the decimal point, write the equivalent fraction, and shade a grid model. Groups then compare 0.4 and 0.40 , are they the same? , and report their conclusion.

20 min·Small Groups

Gallery Walk: Fraction and Decimal Representation Stations

Set up five stations around the room. Each station shows a visual model (shaded grid, number line segment, or money amount). Students write the fraction and decimal forms at each station on their recording sheet. In a closing discussion, students identify which representation they found most useful and explain why.

20 min·Small Groups

Real-World Connections

• Grocery stores use decimals to represent prices, such as $2.45 for a pound of apples. This connects to understanding numbers with two decimal places (hundredths).
• Sports statistics often use decimals, like a baseball player's batting average (e.g., .300) or a runner's time in seconds (e.g., 10.5 seconds). These represent fractions of a whole.
• Measuring tools, like rulers marked in centimeters and millimeters, can be related to decimals. A measurement of 2.5 cm means 2 whole centimeters and 5 tenths of a centimeter.

Assessment Ideas

Exit Ticket

Provide students with a 10x10 grid. Ask them to shade in 7/10 of the grid and write the corresponding decimal. Then, ask them to write the decimal for 23/100 and shade it on a separate grid.

Quick Check

Write the following on the board: '3/10 = ?' and '0.6 = ?/100'. Have students write their answers on mini-whiteboards. Observe student responses to identify common misconceptions about place value and equivalence.

Discussion Prompt

Pose the question: 'If you have 0.5 dollars, how many cents do you have? Explain your thinking.' Listen for students connecting the tenths place to 50 cents (50/100) and using place value reasoning.

Frequently Asked Questions

How do I introduce decimal notation to 4th graders who already know fractions?

Frame decimals explicitly as a second name for fractions with denominator 10 or 100 , not a new topic. Show 3/10 and 0.3 side by side on the same shaded grid and ask, 'What's different? What's the same?' Students who see both notations representing one shaded region are more likely to treat them as equivalent rather than separate concepts.

What is the difference between the tenths place and the hundredths place in a decimal?

The tenths place is immediately to the right of the decimal point; the hundredths place is one position further right. In 0.35, the 3 is in the tenths place (worth 3/10) and the 5 is in the hundredths place (worth 5/100). Connecting to money helps: tenths are dimes (0.3 = 3 dimes), hundredths are pennies (0.05 = 5 pennies).

How do I help students who confuse tenths and hundredths place value?

Use a place value chart that extends to the right of the decimal point, and require students to name the place before writing the digit. Regular practice reading decimals aloud using place value names ('four tenths,' 'seven hundredths') instead of digit-by-digit reading reinforces the distinction. Money amounts are an effective real-world anchor for this work.

Why does active learning help students learn decimal notation?

Translation tasks , converting the same quantity between fraction, decimal, and visual form , require students to engage with meaning rather than copy notation. When students do this with a partner and explain each conversion, they surface and correct small confusions (like tenths vs hundredths) immediately. Passive copying of examples does not build this flexibility.