How to Teach Place Value with Decimals

If your child understands that in 352, the 3 means 300 (three hundreds), they already know the principle behind decimal place value. Decimals extend the same pattern — each place is one-tenth of the place to its left — past the ones place.

The pattern that extends

Moving left: each place is 10× bigger. Moving right: each place is 10× smaller.

The decimal point simply marks where the ones place ends and the parts-of-one begin.

Key Insight: Decimal place value is not a new system — it is the same place value system extended. If your child grasps that tens are 10 ones and hundreds are 10 tens, then tenths are ones split into 10 parts, and hundredths are tenths split into 10 parts. Same pattern, same logic, smaller pieces.

Connect to money

Money is the best decimal model because children already use it:

• $1.00 = 1 dollar (ones)
• $0.10 = 1 dime = 1 tenth of a dollar
• $0.01 = 1 penny = 1 hundredth of a dollar

$3.47 = 3 dollars + 4 dimes + 7 pennies = 3 ones + 4 tenths + 7 hundredths.

Connect to fractions

Decimals are fractions with denominators of 10, 100, 1000:

• 0.3 = 3/10
• 0.25 = 25/100 = 1/4
• 0.125 = 125/1000 = 1/8

This connection is critical for moving between decimals, fractions, and percents.

Reading decimals correctly

3.47 is "three and forty-seven hundredths" — NOT "three point forty-seven."

The place of the last digit determines the name:

• 0.3 → "three tenths"
• 0.37 → "thirty-seven hundredths"
• 0.375 → "three hundred seventy-five thousandths"

Reading decimals correctly reinforces place value understanding.

Common mistakes

Thinking 0.37 > 0.4: They compare 37 and 4 and pick the bigger number. But 0.37 = 37 hundredths and 0.4 = 40 hundredths. Add a trailing zero: 0.37 vs 0.40. Now it is clear.

Ignoring the decimal point: They treat 3.47 as "347." The decimal point is critical — it marks where ones end and fractions begin.

Confusing tenths and tens: The symmetry around the decimal point can confuse. Tens are to the left of ones. Tenths are to the right. Note: there is no "oneths" place — the ones place and the tenths place are right next to each other.

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Decimal place value extends the base-10 system past the ones place. Each place to the right is 10 times smaller, just as each place to the left is 10 times bigger. Connect to money (dimes and pennies), connect to fractions (denominators of 10 and 100), and the decimal system becomes a natural extension of what your child already knows.

If you want a system that builds decimal understanding on solid whole-number place value — and verifies comprehension before advancing to decimal operations — that is what Lumastery does.