Quick Answer: What Is 1.3 as a Fraction?
What is 1.3 as a fraction is a common math question. The answer is 13/10, or 1 3/10 as a mixed number.
Since 13 and 10 share no common factors other than 1, 13/10 is already in its simplest form.
Because the digit 3 is in the tenths place, 1.3 can be converted into an exact fraction by writing it over 10 and simplifying if necessary.
Decimal-to-fraction conversions are useful in geometry, algebra, recipe scaling, and everyday measurements.
Step-by-Step: How to Convert 1.3 to a Fraction
To understand what is 1.3 as a fraction in simplest form, follow these simple mathematical steps:
Step 1: Write 1.3 as a ratio over 1
Start by placing the decimal over the number 1 to form a starting fraction:
1.3 / 1
Step 2: Eliminate the decimal point
Count the number of decimal places after the decimal point. Since 1.3 has one decimal place (the tenths place), multiply both the numerator (top) and denominator (bottom) by 10:
(1.3 × 10) / (1 × 10) = 13 / 10
Step 3: Simplify to lowest terms
To simplify a fraction, divide both the numerator and denominator by their Greatest Common Divisor (GCD). The number 13 is a prime number, meaning its only factors are 1 and 13. Since 10 is not divisible by 13, the fraction 13/10 cannot be simplified any further.
1.3 as an Improper Fraction vs. Mixed Number
Depending on your math assignment or practical application, you can write the answer in two correct formats:
- Improper Fraction: 13/10 (where the numerator is larger than the denominator)
- Mixed Number: 1 3/10 (where the whole number and fractional part are separated)
To convert the improper fraction 13/10 to a mixed number, divide 13 by 10. You get 1 with a remainder of 3, giving you 1 3/10.
Decimal to Fraction Reference Table
| Decimal | Fraction (Improper) | Mixed Number | Simplest Form? |
|---|---|---|---|
| 1.1 | 11/10 | 1 1/10 | Yes |
| 1.2 | 12/10 | 1 1/5 | Reduced from 12/10 |
| 1.3 | 13/10 | 1 3/10 | Already in Simplest Form |
| 1.4 | 14/10 | 1 2/5 | Reduced from 14/10 |
| 1.5 | 15/10 | 1 1/2 | Reduced from 15/10 |
Conclusion
1.3 as a fraction is 13/10. This is in simplest form already. As a mixed number, it is written as 1 3/10. When you convert a decimal to a fraction, it is easier to compare, calculate, and understand mathematical values.
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