If you’ve ever stared at the decimal 1.6 and wondered how it looks as a fraction, you’re not alone. It’s one of the most common conversion questions in basic math, and thankfully, one of the easiest to solve once you know the trick. In this guide, we’ll break down exactly what 1.6 is as a fraction, walk through the simplification process, and then tackle a trickier cousin: 1.6 repeating as a fraction. Along the way, you’ll find clean infographics and tables that make every step easy to visualize.
| Decimal | Fraction (unsimplified) | Simplified Fraction | Type |
|---|---|---|---|
| 1.6 | 16/10 | 8/5 (or 1 3/5) | Terminating decimal |
| 1.6 repeating (1.6̅) | 15/9 | 5/3 (or 1 2/3) | Repeating decimal |
What is 1.6 as a Fraction?
The decimal 1.6 is a terminating decimal — meaning it has a fixed number of digits after the decimal point and doesn’t go on forever. Converting it to a fraction relies on a simple place-value rule: the digit 6 sits in the tenths place, so 1.6 can be read as “one and six tenths.”
That gives us the fraction 16/10, which simplifies down to 8/5, or as a mixed number, 1 3/5. Here’s the full breakdown, visualized step by step:
Step-by-Step: Converting 1.6 to a Fraction
- Write 1.6 as a fraction over 1: 1.6/1.
- Count the digits after the decimal point. There’s one digit (6), so multiply the top and bottom by 10: (1.6 × 10) / (1 × 10) = 16/10.
- Find the greatest common divisor (GCD) of 16 and 10, which is 2.
- Divide both the numerator and denominator by 2: 16 ÷ 2 = 8, and 10 ÷ 2 = 5.
- The simplified fraction is 8/5, which can also be written as the mixed number 1 3/5.
Quick Check 8/5 as a decimal is 8 ÷ 5 = 1.6 — confirming the conversion is correct. |
Recommended Reading: What is 0.6 as a Fraction
What is 1.6 Repeating as a Fraction?
Things get more interesting when the 6 repeats forever: 1.666…, usually written as 1.6̅ (with a bar over the 6). Because this decimal never terminates, you can’t use the simple “place value” trick from before. Instead, you need a bit of algebra.
Step-by-Step: Converting 1.6 Repeating to a Fraction
- Let x equal the repeating decimal: x = 1.6666…
- Multiply both sides by 10 (because 1 digit repeats): 10x = 16.6666…
- Subtract the original equation from this new one, so the repeating part cancels out: 10x − x = 16.6666… − 1.6666…, which gives 9x = 15.
- Divide both sides by 9: x = 15/9.
- Simplify by dividing numerator and denominator by their GCD, 3: x = 5/3, or as a mixed number, 1 2/3.
Quick Check 5/3 as a decimal is 5 ÷ 3 = 1.6666…, matching the repeating decimal exactly. |
1.6 vs. 1.6 Repeating: Side-by-Side Comparison
These two decimals look almost identical at first glance, but they convert to very different fractions. Here’s a clear comparison:
| Feature | 1.6 | 1.6 Repeating (1.6̅) |
|---|---|---|
| Decimal value | 1.6 exactly | 1.6666... forever |
| Conversion method | Place value (÷10) | Algebra (subtract equations) |
| Raw fraction | 16/10 | 15/9 |
| Simplified fraction | 8/5 | 5/3 |
| Mixed number | 1 3/5 | 1 2/3 |
| Number type | Rational, terminating | Rational, repeating |
Why Does This Method Work?
Every terminating decimal can be written as a fraction with a power of 10 (10, 100, 1000…) as the denominator, because each decimal place represents tenths, hundredths, thousandths, and so on. That’s why multiplying 1.6 by 10 clears the decimal point cleanly.
Repeating decimals need a different approach because no power of 10 will ever make them whole — the digits keep going forever. The algebra trick works because subtracting one equation from another cancels out the infinite repeating tail, leaving a normal whole number you can solve for.
Recommended Reading: How to Use the Sridharacharya Formula to Solve Quadratic Equations
Common Mistakes to Avoid
- Forgetting to simplify: 16/10 is technically correct, but 8/5 is the proper final answer.
- Mixing up 1.6 and 1.6 repeating: they use completely different conversion methods and produce different fractions (8/5 vs. 5/3).
- Multiplying by the wrong power of 10: always match the multiplier to the number of decimal or repeating digits (1 digit = ×10, 2 digits = ×100, and so on).
- Forgetting the whole number: 1.6 is more than one whole, so don’t drop the “1” when converting to a mixed number (1 3/5, not just 3/5).
Practice Problems
Try converting these decimals yourself, then check your answers below.
| Decimal | Your Answer | Correct Fraction |
|---|---|---|
| 1.2 | 6/5 | |
| 1.6 (recap) | 8/5 | |
| 2.4 | 12/5 | |
| 0.6 (repeating) | 2/3 |
Conclusion
Converting 1.6 as a fraction comes down to recognizing place value and simplifying — a quick two-step process that lands you at 8/5. Its repeating cousin, 1.6 repeating as a fraction, takes a little more algebra but follows a reliable pattern that works for any repeating decimal. With the steps and infographics above, you should be able to convert either one confidently, and even tackle similar decimals on your own.
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Frequently Asked Questions (FAQs)
1. What is 1.6 as a fraction in simplest form?
1.6 as a fraction in simplest form is 8/5, or equivalently the mixed number 1 3/5.
2. What is 1.6 repeating as a fraction?
1.6 repeating (1.6666… forever) equals 5/3, or 1 2/3 as a mixed number. It’s found using algebra rather than simple place value, since the decimal never ends.
3. Is 1.6 a rational number?
Yes. Any number that can be written as a fraction of two integers — like 8/5 — is a rational number. Both 1.6 and 1.6 repeating qualify, since they can each be expressed as exact fractions.
4. How do you know if a decimal terminates or repeats?
A decimal terminates if it has a fixed, finite number of digits (like 1.6). It repeats if one or more digits go on forever in a pattern (like 1.6666…, written 1.6̅).
