How to Explain Decimals to Fourth Graders

"Is 0.5 or 0.50 bigger?"

When your fourth grader can confidently answer "they're equal" and explain why, they understand decimals.

Fourth grade introduces decimals formally, connecting them to fractions and extending place value in a new direction. This concept bridges arithmetic and algebra, making it essential to get right.

Why Decimals Matter

Decimals are everywhere:

• Money: $3.75
• Measurement: 2.5 inches
• Sports statistics: 0.333 batting average
• Science: temperature, mass, volume
• Technology: grades, ratings, coordinates

Students who understand decimals can navigate the numerical world around them.

The Big Idea: Extending Place Value

Students already know that place value extends LEFT:

• Ones → Tens → Hundreds → Thousands → ...
• Each place is 10 TIMES the one to its right

Decimals extend place value RIGHT:

• Ones → Tenths → Hundredths → Thousandths → ...
• Each place is 1/10 (one-tenth) of the one to its left

        ←10×    ←10×    ←10×    ←10×    ←10×
Hundreds | Tens | Ones | . | Tenths | Hundredths
   100   |  10  |   1  |   |  0.1   |    0.01
        ÷10→    ÷10→    ÷10→    ÷10→

The decimal point separates wholes from parts.

Understanding Decimal Place Value

The Decimal Point

The decimal point is the anchor:

• Everything LEFT is whole numbers (1 or more)
• Everything RIGHT is parts (less than 1)

In 23.45:

• 2 is in the tens place = 20
• 3 is in the ones place = 3
• 4 is in the tenths place = 0.4 (or 4/10)
• 5 is in the hundredths place = 0.05 (or 5/100)

Tenths: The First Decimal Place

Tenths are the first place after the decimal point.

One whole divided into 10 equal parts:

|█|█|█|█|█|█|█|█|█|█|
 1 2 3 4 5 6 7 8 9 10

Each piece = 1/10 = 0.1 (one tenth)

• 0.1 = 1/10 = one tenth
• 0.3 = 3/10 = three tenths
• 0.7 = 7/10 = seven tenths

Hundredths: The Second Decimal Place

Hundredths are the second place after the decimal point.

One whole divided into 100 equal parts:

10 × 10 = 100 tiny squares
Each tiny square = 1/100 = 0.01 (one hundredth)

• 0.01 = 1/100 = one hundredth
• 0.25 = 25/100 = twenty-five hundredths
• 0.07 = 7/100 = seven hundredths

Reading Decimals

Two ways to read 0.45:

1. "Zero point four five" (reading digits)
2. "Forty-five hundredths" (reading the value)

Both are correct, but understanding the second helps with fraction connections.

Reading 3.7:

• "Three and seven tenths"
• "Three point seven"

The Fraction Connection

Decimals and fractions are two ways to write the same values.

Tenths

Fraction → Decimal
1/10     → 0.1
3/10     → 0.3
7/10     → 0.7
10/10    → 1.0

Hundredths

Fraction → Decimal
1/100    → 0.01
25/100   → 0.25
50/100   → 0.50 = 0.5
75/100   → 0.75
100/100  → 1.00

The Conversion Rule

Fraction to Decimal:

• If denominator is 10: numerator goes in tenths place
  • 7/10 → 0.7
• If denominator is 100: numerator fills tenths and hundredths
  • 45/100 → 0.45
  • 3/100 → 0.03 (need the zero placeholder!)

Decimal to Fraction:

• One decimal place = tenths
  • 0.6 → 6/10
• Two decimal places = hundredths
  • 0.35 → 35/100

The Money Connection

Money provides the most concrete decimal model.

Place Values as Money

• Ones = Dollars ($1.00)
• Tenths = Dimes ($0.10)
• Hundredths = Pennies ($0.01)

Examples

$2.35:

• 2 dollars
• 3 dimes (3 tenths of a dollar)
• 5 pennies (5 hundredths of a dollar)

Why 0.50 = 0.5:

$0.50 = 50 cents = 5 dimes = $0.5

Five dimes and fifty pennies are the same amount!

The Power of Money Comparisons

Students already know:

• 50 cents > 5 cents

This transfers to decimals:

• 0.50 > 0.05

"Would you rather have 5 dimes or 5 pennies?"

Comparing Decimals

Same Number of Decimal Places

Compare 0.47 and 0.52:

Both have two decimal places:

• 0.47 = 47 hundredths
• 0.52 = 52 hundredths
• 47 < 52, so 0.47 < 0.52

Different Number of Decimal Places

Compare 0.6 and 0.45:

Make them the same by adding zeros:

• 0.6 = 0.60 (60 hundredths)
• 0.45 = 45 hundredths
• 60 > 45, so 0.6 > 0.45

Key insight: 0.6 is NOT less than 0.45 even though 6 < 45!

The Left-to-Right Method

Compare digits place by place from left to right:

Compare 3.47 and 3.52:

• Ones: 3 = 3 (equal, continue)
• Tenths: 4 < 5
• Stop! 3.47 < 3.52

Common Comparison Trap

Wrong thinking: "0.9 < 0.12 because 9 < 12"

Right thinking:

• 0.9 = 0.90 = 90 hundredths
• 0.12 = 12 hundredths
• 90 > 12, so 0.9 > 0.12

Always compare place by place, or convert to same decimal places.

Decimals on the Number Line

Number lines help visualize decimal relationships.

Tenths on a Number Line

0    0.1   0.2   0.3   0.4   0.5   0.6   0.7   0.8   0.9   1.0
|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|

Each small segment = 0.1

Hundredths on a Number Line

Zoom in between 0 and 0.1:

0   0.01  0.02  0.03  0.04  0.05  0.06  0.07  0.08  0.09  0.1
|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|

Each tiny segment = 0.01

Locating Decimals

Place 0.75 on a number line:

1. It's between 0 and 1
2. It's between 0.7 and 0.8 (closer to 0.8)
3. It's exactly at 0.75 (halfway between 0.7 and 0.8)

Visual Models for Decimals

Base-10 Blocks (Reinterpreted)

In whole number work:

• Unit cube = 1
• Rod = 10
• Flat = 100

For decimals, redefine the flat as 1 whole:

• Flat = 1 (one whole)
• Rod = 0.1 (one tenth)
• Unit cube = 0.01 (one hundredth)

Build 1.35:

• 1 flat (1 whole)
• 3 rods (3 tenths = 0.30)
• 5 unit cubes (5 hundredths = 0.05)

Hundredths Grids

A 10 × 10 grid represents 1 whole (100 squares):

• Each square = 0.01 (one hundredth)
• Each row or column = 0.10 (one tenth)

Shade 0.45:
Shade 45 squares = 4 full columns + 5 extra squares

Decimal Squares

Divide a square into tenths (vertically) and hundredths (both ways):

Tenths:     |_|_|_|_|_|_|_|_|_|_|  (10 strips)

Hundredths: |█|█|█|█| | | | | | |
            |█|█|█|█| | | | | | |
            |█|█|█|█| | | | | | |  (0.30 shaded)
            ... (10 × 10 grid)

Hands-On Activities

Decimal Concentration

Make cards with matching pairs:

• 0.5 matches 5/10
• 0.75 matches 75/100
• 0.3 matches 3/10

Play memory/concentration to reinforce equivalence.

Grocery Store Decimals

Use grocery receipts or ads:

• Find prices and compare
• Order items from cheapest to most expensive
• Round prices to estimate totals

Build-a-Number

Give digit cards (0-9) and a decimal point. Students create numbers and compare:

• "Make the largest possible decimal under 1"
• "Make two equivalent decimals"
• "Make a decimal between 0.3 and 0.4"

Decimal Number Lines

Draw number lines and place decimals:

• Start simple: Place 0.5 between 0 and 1
• Get precise: Place 0.35 between 0.3 and 0.4
• Challenge: Order 0.4, 0.37, 0.42 on a number line

Money Counting

Practice with real or play money:

• "Show me $0.75 using only dimes and pennies"
• "How many ways can you make $0.50?"
• Connect each representation to decimal notation

Common Mistakes and How to Fix Them

Mistake 1: More Digits = Larger Number

Wrong: 0.125 > 0.5 because 125 > 5

Fix: Add zeros to compare: 0.125 vs 0.500. Or use money: Would you rather have $0.125 (12½ cents) or $0.50 (50 cents)?

Mistake 2: Ignoring Zero Placeholders

Wrong: Writing 0.3 as 0.03, or thinking they're equal

Fix: Use place value charts. 0.3 = 3 tenths = 30 hundredths. 0.03 = 3 hundredths. Very different!

Mistake 3: Reading Decimals as Whole Numbers

Wrong: Reading 0.45 as "zero point forty-five" and thinking it means 45 somethings

Fix: Emphasize "forty-five HUNDREDTHS" - small parts of one whole. Use visuals to show how small hundredths are.

Mistake 4: Fraction-Decimal Conversion Errors

Wrong: 3/100 = 0.3

Fix: Count decimal places. 100 needs TWO decimal places. 3/100 = 0.03 (the 3 goes in the hundredths place).

Connecting Decimals to Everyday Life

Sports Statistics

• Batting average: 0.325
• Field goal percentage: 0.85
• Marathon time: 3.5 hours

Measurements

• Height: 4.5 feet
• Temperature: 98.6 degrees
• Gas mileage: 32.5 miles per gallon

Grades and Scores

• GPA: 3.75
• Test score: 87.5%
• Rating: 4.8 stars

Technology

• File size: 2.4 MB
• Phone battery: 0.45 (45%)
• GPS coordinates use decimals

Building Toward Future Concepts

Decimals prepare students for:

Adding and Subtracting Decimals (Fifth Grade)

Understanding place value makes lining up decimal points sensible.

Decimal Multiplication and Division

Knowing what decimals represent helps students make sense of results.

Percentages

Percent means "per hundred" - directly connected to hundredths: 75% = 0.75 = 75/100

Scientific Notation

Writing very small numbers uses decimal understanding.

Practice Ideas for Home

Shopping Math

"This costs $4.75. If you have $5.00, how much change?"

Measurement Practice

Use rulers marked in tenths of inches. Measure objects and record as decimals.

Comparison Games

"Which is more: 0.8 or 0.75?" Discuss reasoning.

Decimal of the Day

Pick a decimal. Find its fraction equivalent. Locate it on a number line. Use it in a sentence.

Recipe Scaling

"This recipe needs 0.5 cups of sugar. If we double it, how much do we need?"

The Bottom Line

Decimals extend the place value system students already know, but in the opposite direction. The same pattern applies: each place is ten times (or one-tenth of) the one next to it.

The key to decimal understanding is connecting to what students know:

• Money (dimes and pennies)
• Fractions (tenths and hundredths)
• Visual models (grids and number lines)
• Place value (the organizing principle)

When your fourth grader sees 0.45 and understands it as "45 hundredths" or "4 dimes and 5 pennies" or "between 0.4 and 0.5 on a number line," they have a solid foundation for all the decimal work to come.

Decimals aren't a new system—they're the same system extended. Help students see that connection, and decimals make sense.