5/4 Fraction to Decimal

What is 5/4 as a Decimal? (Step-by-Step Conversion Explained)

ByWilliam Morris

Quick Answer: When you convert 5/4 to a decimal, the result is 1.25.

This is a terminating decimal, which means the number stops and does not repeat.

How to Convert 5/4 to a Decimal

To convert the fraction into a decimal, divide the numerator by the denominator.

5 ÷ 4 = 1.25

So the decimal form of the fraction is 1.25.

Method 1: Long Division

Since 5 is larger than 4, this is an improper fraction. The result will be greater than 1.

Step 1: Set up 5 ÷ 4.

  • 4 goes into 5 one time (4 × 1 = 4).
  • Write “1” above the division bar.
  • Subtract: 5 – 4 = 1.

Step 2: Add a decimal point and a zero (making it 10).

  • 4 goes into 10 two times (4 × 2 = 8).
  • Write “2” after the decimal point.
  • Subtract: 10 – 8 = 2.

Step 3: Bring down a zero, making it 20.

  • 4 goes into 20 five times (4 × 5 = 20).
  • Write “5” in the quotient.
  • Subtract: 20 – 20 = 0.

Result: 1.25

Method 2: The Fraction Splitting Method

Since 5/4 is an improper fraction, you can split it into a whole number and a proper fraction.

5/4 = 4/4 + 1/4

We know that:

  • 4/4 = 1
  • 1/4 = 0.25

So:

1 + 0.25 = 1.25

This method avoids long division entirely.

Method 3: The Equivalent Fractions Method

Multiply the fraction to get a denominator of 100.

5/4 = (5 × 25) / (4 × 25) = 125/100

Since 125/100 means 125 divided by 100, move the decimal two places left.

125 → 1.25

How to Verify the Answer

Multiply the decimal by the denominator.

1.25 × 4 = 5

Since you get back the original numerator, the conversion is correct.

Does 5/4 Terminate or Repeat?

The decimal terminates.

A fraction produces a terminating decimal when the denominator contains only 2 or 5 as prime factors.

Factor the denominator:

4 = 2 × 2

Because it only contains the factor 2, the decimal ends.

What the Decimal Value Means

The decimal 1.25 shows that the value is:

  • Greater than 1
  • Less than 1.5
  • Exactly halfway between 1 and 1.5? No—it’s 1 and 1/4
  • Equal to 1 whole unit plus 1/4
  • The same as 125%

Fraction, Decimal, and Percentage Forms

FormValue
Fraction5/4
Decimal1.25
Percentage125%

To convert the decimal to a percentage:

1.25 × 100 = 125%

Compare With Other Fractions Over 4

Looking at similar fractions helps you see the pattern.

FractionDecimal
1/40.25
2/40.5
3/40.75
4/41.0
5/41.25
6/41.5
7/41.75
8/42.0
9/42.25
10/42.5

Fractions with denominator 4 increase by 0.25, because:

1/4 = 0.25

Rounding 5/4 as a Decimal

Since 1.25 has two decimal places, rounding is straightforward.

Rounded ToValue
Whole number1
1 decimal1.3
2 decimals1.25
Exact value1.25

If rounding to a whole number, 1.25 rounds down to 1.

If rounding to one decimal, 1.25 rounds up to 1.3 (since the second digit is 5 ≥ 5).

Tip for Students

When working with fractions over 4, it helps to remember:

1/4 = 0.25

Then add or multiply:

  • 3/4 = 0.75
  • 5/4 = 1 + 0.25 = 1.25
  • 7/4 = 1 + 0.75 = 1.75
  • 9/4 = 2 + 0.25 = 2.25

Real-World Uses of 1.25

You encounter 1.25 constantly in daily life:

  • Money: $1.25 (a dollar and a quarter)
  • Measurements: 1.25 inches or centimeters
  • Cooking: 1.25 cups (1 and 1/4 cups)
  • Time: 1.25 hours (1 hour and 15 minutes)
  • Sports: A 1.25 ERA in baseball
  • Grades: A 1.25 GPA (very low)
  • Gas prices: $3.25 per gallon (the 0.25 is 1/4 of a dollar)

Common Mistakes Students Make

Students sometimes make small errors such as:

  • Writing 1.50 instead of 1.25 (confusing with 6/4)
  • Writing 1.2 instead of 1.25 (forgetting the hundredths place)
  • Thinking 5/4 equals 1.4 (confusing with 7/5)
  • Forgetting that 5/4 is greater than 1

Final Summary

  • 5/4 as a decimal = 1.25
  • It is a terminating decimal
  • It equals 125%
  • Fractions with denominator 4 increase by 0.25
  • Three methods to solve: long division, fraction splitting, and equivalent fractions
  • Verification: 1.25 × 4 = 5 ✓
  • Common in money (a dollar and a quarter) and measurements

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