Introducing Decimals: From Fractions to Place Value

Decimals Are Just Fractions

The key insight: decimals are fractions with denominators of 10, 100, 1000, etc.

• 0.5 = 5/10 = 1/2
• 0.25 = 25/100 = 1/4
• 0.125 = 125/1000 = 1/8

If your child understands fractions, they have a head start on decimals.

Decimals Are Place Value

Decimals extend the place value system:

• Ones . Tenths Hundredths Thousandths
• Each place is 1/10 of the place to its left

In 3.47:

• 3 ones
• 4 tenths (4/10)
• 7 hundredths (7/100)

Start with Money

Money is the perfect decimal introduction:

• $1.00 = 1 dollar
• $0.10 = 1 dime = 1/10 of a dollar
• $0.01 = 1 penny = 1/100 of a dollar
• $3.47 = 3 dollars, 4 dimes, 7 pennies

Reading Decimals Correctly

Teach proper pronunciation:

• 0.5 = "five tenths" (not "point five")
• 0.25 = "twenty-five hundredths"
• 3.47 = "three and forty-seven hundredths"

This reinforces place value understanding.

Common Mistakes

Longer = Bigger (wrong!): Kids think 0.125 > 0.5 because 125 > 5

• Fix: Use place value or convert to fractions

Ignoring the decimal: Writing 3.5 + 2.7 = 5.12

• Fix: Line up the decimal points

Adding zeros changes the value (wrong): 0.5 ≠ 0.50? Actually they're equal!

• Fix: Show with money (50 cents = 5 dimes)

Comparing Decimals

Method 1: Make the same number of decimal places

• Compare 0.5 and 0.35
• 0.5 = 0.50
• 0.50 vs 0.35: 50 hundredths > 35 hundredths

Method 2: Use place value

• Compare digit by digit from left to right
• 0.5 has 5 tenths, 0.35 has 3 tenths
• 5 tenths > 3 tenths, so 0.5 > 0.35

Practice Resources

Build decimal skills:

• Grade 4 Decimals
• Grade 5 Decimals