What Are Decimals?

For Elementary Students

What Is a Decimal?

A decimal is a way to write numbers that are between whole numbers.

Think about it like this: You know whole numbers like 1, 2, 3. But what about numbers between them? That's where decimals come in!

Example: 2.5 is between 2 and 3 (it's 2 and a half!)

The Decimal Point

The decimal point (the dot) separates the whole number from the part.

Example: 3.7

3  .  7
↑  ↑  ↑
whole point part

• 3 is the whole number part
• . is the decimal point
• 7 is the part (seven tenths)

Decimals in Real Life

You see decimals every day!

Money: $5.25 (5 dollars and 25 cents)

Measurements: 3.5 feet, 1.2 kilograms

Temperature: 98.6 degrees

Prices: $12.99

Understanding Tenths

The first place after the decimal point is tenths.

Think: Divide something into 10 equal pieces. Each piece is one tenth!

Example: 0.3 means 3 tenths

Whole divided into 10 parts:
[█][█][█][ ][ ][ ][ ][ ][ ][ ]
 3 out of 10 parts shaded = 0.3

Understanding Hundredths

The second place is hundredths (even smaller pieces!).

Example: 0.25 means 25 hundredths

Think: Divide into 100 tiny pieces, take 25 of them.

Reading Decimals Out Loud

Simple way: Say "point" for the dot

• 2.5 → "two point five"
• 0.8 → "zero point eight"
• 10.3 → "ten point three"

Formal way: Use place value names

• 2.5 → "two and five tenths"
• 0.8 → "eight tenths"

For Junior High Students

Decimal Place Value

Just like whole numbers have place value, so do decimals!

Going left to right from the decimal point:

    2   .   4   5   6
    ↓   ↓   ↓   ↓   ↓
  ones  •  tenths hundredths thousandths

Example: 4.628

• 4 is in the ones place = 4
• 6 is in the tenths place = 6/10 = 0.6
• 2 is in the hundredths place = 2/100 = 0.02
• 8 is in the thousandths place = 8/1000 = 0.008

Total: 4 + 0.6 + 0.02 + 0.008 = 4.628

Place Value Chart

Converting Decimals to Fractions

Rule: Use the place value as the denominator!

Example 1: 0.3

• 3 is in the tenths place
• So 0.3 = 3/10

Example 2: 0.25

• 25 is in the hundredths place
• So 0.25 = 25/100 = 1/4 (simplified)

Example 3: 0.7

• 0.7 = 7/10

Example 4: 0.05

• 0.05 = 5/100 = 1/20 (simplified)

Converting Fractions to Decimals

Common fractions you should know:

Method: Divide the numerator by the denominator

Example: 3/4 = ?

• 3 ÷ 4 = 0.75

Reading Decimals Properly

Method 1: Say "point" (casual)

• 3.14 → "three point one four"
• 0.625 → "zero point six two five"

Method 2: Use place values (formal)

• 0.5 → "five tenths"
• 0.37 → "thirty-seven hundredths"
• 2.8 → "two and eight tenths"
• 1.009 → "one and nine thousandths"

Mixed Numbers with Decimals

Example: 5.3

• Whole number part: 5
• Decimal part: 0.3 = 3/10

As a mixed number: 5 3/10

Trailing Zeros Don't Change the Value

Adding zeros to the end of a decimal doesn't change it!

Example:

• 0.5 = 0.50 = 0.500 = 0.5000
• 3.1 = 3.10

Why? Because 5 tenths = 50 hundredths = 500 thousandths (same amount!)

Use: This helps when adding decimals with different lengths.

Leading Zeros Are Optional

You can write decimals with or without a leading zero:

• 0.5 or .5 (both correct, but 0.5 is clearer)
• 0.75 or .75

Recommendation: Use the leading zero (0.5) to avoid confusion!

Decimals 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 tick is 0.1 (one tenth).

Example: 0.7 is between 0 and 1, closer to 1.

Real-Life Applications

Money: $24.99 = 24 dollars and 99 cents (99/100 of a dollar)

Measurements:

• Height: 5.8 feet
• Weight: 150.5 pounds
• Distance: 3.2 miles

Science: Temperature, pH levels, measurements

Sports: Times (10.5 seconds), scores (9.8 out of 10)

Grades: 85.7% on a test

Practice