Understanding Decimals and Place Value

Decimals are another way to write fractions and mixed numbers, using place value and a decimal point. If you can work with whole numbers, you already have most of what you need — decimals just extend the place-value system to the right of the ones place.

Understanding Place Value

Every digit in a decimal number has a specific place value. The decimal point separates the whole-number part from the fractional part.

For the number 47.385:

• 4 is in the tens place (worth 40)
• 7 is in the ones place (worth 7)
• 3 is in the tenths place (worth 0.3)
• 8 is in the hundredths place (worth 0.08)
• 5 is in the thousandths place (worth 0.005)

$47.385 = 40 + 7 + 0.3 + 0.08 + 0.005$

Reading Decimals

Read the decimal using place value names:

The word “and” marks the decimal point. So 5.7 is “five and seven tenths” — not “five point seven” (though “point” is commonly used in conversation).

Writing Decimals from Words

Example 1: Write “six and twenty-three hundredths” as a decimal

• “Six” is the whole number: 6
• “Twenty-three hundredths” means 23 in the hundredths place: .23

Answer: $6.23$

Example 2: Write “four thousandths” as a decimal

“Thousandths” means the third decimal place. Four thousandths = 0.004

Answer: $0.004$

Decimals and Fractions Are the Same Thing

Every decimal can be written as a fraction, and every fraction can be written as a decimal:

To convert a decimal to a fraction: write the digits over the appropriate power of 10 (10, 100, 1000…) and simplify. For the full conversion guide, see Converting Between Fractions, Decimals, and Percents.

Trailing Zeros

Adding zeros to the right end of a decimal does not change its value:

$0.5 = 0.50 = 0.500$

All three equal one-half. Trailing zeros are useful when you need to line up decimal points for addition or subtraction, or when you need a specific precision (like money — $3.50 instead of $3.5).

However, leading zeros after the decimal point do matter:

$0.5 \neq 0.05 \neq 0.005$

These are five tenths, five hundredths, and five thousandths — very different values.

Terminating vs. Repeating Decimals

Terminating decimals end after a finite number of digits:

$\frac{1}{4} = 0.25 \qquad \frac{3}{8} = 0.375$

Repeating decimals have a pattern of digits that repeats forever:

$\frac{1}{3} = 0.333... = 0.\overline{3} \qquad \frac{2}{11} = 0.1818... = 0.\overline{18}$

The bar notation ($\overline{\phantom{x}}$) indicates the repeating block.

Practice Problems

Test your understanding with these problems. Click to reveal each answer.

Key Takeaways

• Place value extends to the right of the decimal point: tenths, hundredths, thousandths
• “And” marks the decimal point when reading numbers aloud
• Trailing zeros (to the right) do not change a decimal’s value; leading zeros after the decimal point do
• Decimals and fractions are two notations for the same values
• Some fractions produce terminating decimals; others produce repeating decimals

Return to Arithmetic for more foundational math topics.