Decimals

Place value

In

$4$ represents tens, $2$ ones, $3$ tenths, $0$ hundredths, and $7$ thousandths:

Every move one place right divides place value by $10$.

Reading and writing

Read the whole-number part, say “and” for the decimal point, then name the final decimal place. Thus $5.042$ is “five and forty-two thousandths.”

Trailing zeros do not change value: $3.5=3.50$, though they can communicate measurement precision.

Comparing decimals

Align decimal points and add placeholder zeros when helpful:

because $0.700>0.659$. Compare from the greatest place value to the first place that differs.

Rounding and measurement

To round to a place, inspect the digit immediately to its right. If it is $5$ or greater, increase the target digit by one; otherwise keep it.

Round only after calculating when possible. In measurement, do not report more precision than the instrument or context supports.

Common mistakes

Aligning final digits instead of decimal points for addition. Align place values.

Thinking $0.9<0.12$ because $9<12$. Compare $0.90$ with $0.12$.

Placing a product decimal without estimating. Use magnitude as a check.

Changing only the divisor when clearing a decimal division. Scale dividend and divisor equally.

Rounding every intermediate line. This accumulates error.

Quick self-check

• Can I name every digit's place value?
• Are decimal points aligned for addition/subtraction?
• Does multiplication/division preserve reasonable magnitude?
• Were both parts of a quotient scaled equally?
• Can the number be connected to a fraction and percent?
• Is rounding delayed and matched to contextual precision?