Number & Operations—Fractions

Fractions to Decimals

Writing a fraction with denominator 10 or 100 as a decimal.

Intermediate15 min lesson2 min readUpdated August 12, 2026Author not yet attributed

Prerequisites

Equivalent Fractions

A New Way to Write Fractions of Ten and Hundred

A fraction with a denominator of 10 or 100 can be written in a shorter form, using a decimal point instead of a fraction bar. This new notation — decimals — is just another way of writing the exact same value as a fraction.

Definition — Decimal

A number written using a decimal point to show a fractional part based on tens, hundreds, or other powers of ten. The first digit after the decimal point represents tenths; the second digit represents hundredths.

To write a fraction with denominator 10 as a decimal, the numerator becomes the single digit right after the decimal point. To write a fraction with denominator 100 as a decimal, the numerator becomes the two digits right after the decimal point.

Worked Example — Writing Tenths as a Decimal

Write 7/10 as a decimal. The denominator 10 means this is a tenths place value. The numerator, 7, becomes the digit right after the decimal point: 0.7.

Worked Example — Writing Hundredths as a Decimal

Write 43/100 as a decimal. The denominator 100 means this is a hundredths place value, using two digits after the decimal point. The numerator, 43, fills both of those digits: 0.43.

\dfrac{7}{10} = 0.7 \qquad \dfrac{43}{100} = 0.43

Tip

Count the zeros in the denominator to know how many digits belong after the decimal point — one zero (10) means one digit (tenths), two zeros (100) means two digits (hundredths).

Common Mistakes

Writing a hundredths fraction with only one digit after the decimal point, such as writing 43/100 as 0.43 but writing 7/100 as 0.7 instead of 0.07.
A hundredths fraction always needs exactly two digits after the decimal point, filling any missing tens digit with a placeholder 0 — 7/100 is 0.07, not 0.7.
Confusing a tenths decimal with a hundredths decimal because they look similar, such as reading 0.5 and 0.05 as the same value.
Count the digits after the decimal point carefully: 0.5 has one digit (five tenths), while 0.05 has two digits (five hundredths) — a much smaller amount.

Key Takeaways

A decimal is another way to write a fraction based on tenths, hundredths, or another power of ten.
The first digit after the decimal point represents tenths; the second represents hundredths.
The number of zeros in the fraction's denominator matches the number of digits that belong after the decimal point.

Summary

Decimals rewrite tenths and hundredths fractions in a compact new notation. The final lesson in this unit uses that same place-value thinking to compare two decimals.

Track your progress

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