Converting a Simple Decimal

Convert $0.4$ to a fraction.

Identify the place value: The 4 is in the tenths place = Denominator will be $10$

Write as a fraction: $0.4 = \frac{4}{10}$ = $\frac{4}{10}$

Find the GCF: GCF of $4$ and $10$ is $2$ = GCF $= 2$

Simplify: $\frac{4 \div 2}{10 \div 2} = \frac{2}{5}$ = $\frac{2}{5}$

Answer: $0.4 = \frac{2}{5}$

Converting a Hundredths Decimal

Convert $0.75$ to a fraction.

Identify the place value: The last digit (5) is in the hundredths place = Denominator will be $100$

Write as a fraction: $0.75 = \frac{75}{100}$ = $\frac{75}{100}$

Find the GCF: GCF of $75$ and $100$ is $25$ = GCF $= 25$

Simplify: $\frac{75 \div 25}{100 \div 25} = \frac{3}{4}$ = $\frac{3}{4}$

Answer: $0.75 = \frac{3}{4}$

Converting a Thousandths Decimal

Convert $0.125$ to a fraction.

Identify the place value: The last digit (5) is in the thousandths place = Denominator will be $1000$

Write as a fraction: $0.125 = \frac{125}{1000}$ = $\frac{125}{1000}$

Find the GCF: GCF of $125$ and $1000$ is $125$ = GCF $= 125$

Simplify: $\frac{125 \div 125}{1000 \div 125} = \frac{1}{8}$ = $\frac{1}{8}$

Answer: $0.125 = \frac{1}{8}$

Converting a Decimal Greater Than 1

Convert $2.35$ to a mixed number.

Separate whole and decimal parts: $2.35 = 2 + 0.35$ = Whole part: $2$, Decimal part: $0.35$

Convert decimal to fraction: $0.35 = \frac{35}{100}$ = $\frac{35}{100}$

Find the GCF and simplify: GCF of $35$ and $100$ is $5$: $\frac{35 \div 5}{100 \div 5} = \frac{7}{20}$ = $\frac{7}{20}$

Combine with whole number: $2 + \frac{7}{20} = 2\frac{7}{20}$ = $2\frac{7}{20}$

Answer: $2.35 = 2\frac{7}{20}$

Mistake: Using the wrong denominator (e.g., writing $0.25$ as $\frac{25}{10}$)

Why: The denominator depends on the place value of the LAST digit. In $0.25$, the 5 is in the hundredths place, not tenths.

Correct: Count the decimal places: 2 places = 100, so $0.25 = \frac{25}{100}$

Mistake: Forgetting to simplify the fraction

Why: While $\frac{25}{100}$ is technically correct, fractions should be in lowest terms.

Correct: Always check if the numerator and denominator share common factors. $\frac{25}{100} = \frac{1}{4}$

Mistake: Dropping leading zeros in the numerator

Why: For $0.05$, writing $\frac{5}{10}$ instead of $\frac{5}{100}$ gives the wrong value.

Correct: $0.05$ has 2 decimal places, so: $\frac{5}{100} = \frac{1}{20}$

Cooking and Recipes

Many measuring cups show both decimal and fraction measurements.

If a digital scale shows $0.375$ kg of flour, that equals $\frac{3}{8}$ kg.

Shopping Discounts

Sales often show discounts as decimals that are easier to understand as fractions.

A $0.20$ discount means you save $\frac{1}{5}$ of the price.

Q: How do I convert a repeating decimal like $0.333...$ to a fraction?

A: Repeating decimals require a different method. For $0.333...$, this equals $\frac{1}{3}$. In general, for a single repeating digit, put it over 9: $0.777... = \frac{7}{9}$.

Q: Why does the number of decimal places matter?

A: Each decimal place represents a power of 10. Tenths = 10, hundredths = 100, thousandths = 1000. The position tells you the denominator.

Q: What if my fraction doesn't simplify?

A: Some fractions are already in lowest terms. For example, $0.17 = \frac{17}{100}$ cannot be simplified because 17 is prime and doesn't divide 100.