What Is 1.55 as a Fraction? | Clean Steps, Exact Result

1.55 equals 31/20, and it’s already in lowest terms.

Decimals feel friendly until a worksheet, a recipe scale, or an algebra problem asks for a fraction. If you’re staring at 1.55 and want the fraction form that a teacher will accept, you’re in the right spot. We’ll convert it cleanly, reduce it, and show a couple of fast checks so you can trust the result.

What Is 1.55 as a Fraction? Step-By-Step

The core move is simple: treat 1.55 as “one and fifty-five hundredths.” “Hundredths” tells you the denominator.

Write 1.55 over its place value

Because 1.55 has two digits after the decimal point, it’s in hundredths. Move the decimal two places to the right to make a whole number, and put the same power of 10 in the denominator.

• 1.55 = 155/100

Reduce the fraction

Now simplify 155/100 by dividing the top and bottom by their greatest common factor.

• 155 and 100 are both divisible by 5.
• 155 ÷ 5 = 31
• 100 ÷ 5 = 20

So:

• 155/100 = 31/20

Confirm it’s fully simplified

31 is prime, and 20 factors into 2 × 2 × 5. Since 31 shares no factor with 2 or 5, 31/20 can’t reduce further.

Why this method always works for terminating decimals

A terminating decimal ends after a set number of digits. That means it can be written as an integer over a power of 10. Two digits after the decimal means a denominator of 100, three digits means 1000, and so on. After that, simplification is standard fraction work.

If you want a quick refresher on the same idea with more practice items, Khan Academy’s exercise set on writing decimals as fractions uses tenths and hundredths the same way.

Turn 31/20 into a mixed number

Some classes want mixed numbers when the fraction is greater than 1. Since 31 is larger than 20, 31/20 is an improper fraction.

Divide 31 by 20

• 20 goes into 31 one time, with a remainder of 11.

So the mixed number form is:

• 31/20 = 1 11/20

Quick check back to the decimal

Convert 11/20 to a decimal to confirm the “.55” part. Since 20 = 2 × 2 × 5, you can scale it to 100 by multiplying by 5.

• 11/20 = (11×5)/(20×5) = 55/100 = 0.55

Then 1 + 0.55 = 1.55. Match found.

Ways to sanity-check your answer in seconds

It’s easy to lose trust when you’re moving decimals around. These checks take a few seconds and catch the common slips.

Check 1: Multiply the fraction by 100

If 1.55 = 155/100, then multiplying the fraction by 100 should give 155.

• (155/100) × 100 = 155

Check 2: Convert 31/20 to a decimal

Divide 31 by 20.

• 20 goes into 31 once (1), remainder 11.
• Bring down a 0: 110 ÷ 20 = 5, remainder 10.
• Bring down a 0: 100 ÷ 20 = 5, remainder 0.

That gives 1.55 exactly.

Check 3: Convert 1.55 to percent

Moving the decimal two places right turns a decimal into a percent.

• 1.55 = 155%

Now compare that to the fraction: 31/20 = 1.55, so it lines up with 155% as well.

How to spot the best simplification fast

When you see 155/100, your eyes can hunt for shared factors in a calm order. Start with 10 and 2 only if both numbers are even. Here, 155 is odd, so skip 2 right away. Next, check 5, since any number ending in 0 or 5 is divisible by 5. Both 155 and 100 pass that test, so divide by 5.

If you want to be stricter, break each number into prime factors.

• 155 = 5 × 31
• 100 = 2 × 2 × 5 × 5

You can cancel one 5 from top and bottom, leaving 31 over 20. After that, there’s nothing else to cancel, since 31 doesn’t share factors with 2 or 5.

When you should not cancel

Canceling works only with multiplication, not with addition. If you had (155 + 25)/100, you can’t cancel a 5 across the plus sign. Reduce only after you’ve combined terms into a single numerator.

A quick “decimal-place” shortcut that still stays correct

Because 1.55 has two digits after the decimal, you can also think “155 hundredths.” Writing 155/100 is the same idea with cleaner math symbols. If the decimal had three digits, you’d write /1000, and so on. This shortcut stays safe because you’re matching digits to place value, not guessing.

Reference forms of 1.55 at a glance

The same number shows up in lots of “clothes.” Seeing them side by side helps you spot the pattern and choose the form a problem wants.

Form	Value	Fast check
Decimal	1.55	Two digits after the point
Fraction (from place value)	155/100	Move decimal 2 places → 155
Simplified fraction	31/20	Divide top and bottom by 5
Mixed number	1 11/20	31 ÷ 20 = 1 remainder 11
Percent	155%	Decimal × 100
Ratio form	31:20	Same as 31/20
Scaled fraction	310/200	Multiply both parts by 10
Hundredths wording	1 and 55/100	“Fifty-five hundredths”

Common mistakes that change the answer

Most wrong answers come from one of these slips. Spot them once, and you’ll stop repeating them.

Forgetting how many decimal places you have

1.55 has two decimal places, so the first fraction is 155/100. If you wrote 155/10, you treated 1.55 like 15.5.

Reducing by a number that doesn’t divide both parts

If you try to reduce 155/100 by 10, the top won’t divide evenly. Stick to common factors like 5, then check if anything else divides both results.

Stopping early at 155/100

155/100 is correct, yet many teachers still want the reduced fraction. Taking the extra moment to reduce it to 31/20 keeps your work consistent.

Mixing up mixed numbers and decimals

1 11/20 is a mixed number. It is not “1.11/20” and it is not “1.11.” The space matters because it means addition: 1 + 11/20.

How to convert any decimal like 1.55

Once you’ve done 1.55, you’ve learned a repeatable routine. You can use it for 0.07, 2.4, 12.125, and more.

Step 1: Count digits after the decimal point

Call that count n. Your denominator will be 10^n.

Step 2: Remove the decimal point to get the numerator

Write the digits as a whole number.

Step 3: Reduce using common factors

Divide top and bottom by the greatest common factor. If you don’t see it right away, start with 2, 3, 5, and 10.

Step 4: Convert to a mixed number if needed

If the numerator is larger than the denominator, do a division step and write the remainder as a fraction.

OpenStax also walks through decimals and fraction conversions in its free Prealgebra text. The section on Decimals and Fractions matches the same place-value reasoning used here.

Practice set: decimals close to 1.55

These are built to train your eye on place value and reduction. Try doing the first pass without a calculator, then verify by converting back to decimals.

Decimal	Fraction (place value)	Simplified form
1.50	150/100	3/2
1.52	152/100	38/25
1.54	154/100	77/50
1.55	155/100	31/20
1.56	156/100	39/25
1.58	158/100	79/50
1.60	160/100	8/5
0.55	55/100	11/20
2.55	255/100	51/20
12.55	1255/100	251/20

How teachers usually want the final answer written

In most math classes, any equivalent fraction is fine, yet grading keys often show the reduced form. If you hand in 155/100, it represents the same number, still a correct fraction. If the instructions say “simplest form,” turn it into 31/20.

If the question asks for a mixed number, write 1 11/20. When you’re unsure, scan the nearby problems. A page full of mixed numbers is a hint about the expected format.

Neat formatting tips that prevent lost points

• Use a clear fraction bar (or a slash) and keep numerator and denominator aligned.
• Leave a space between the whole number and the fraction in a mixed number: 1 11/20.
• Reduce before converting to a mixed number. It keeps the remainder fraction smaller.

Why 31/20 is a strong “exact value” form

Decimals are exact when they terminate, so 1.55 is exact. The fraction 31/20 is also exact, and it carries that exactness into algebra steps. If you later multiply by 3, add 7/4, or solve an equation, the fraction form keeps every step precise without rounding.

It also makes factoring patterns easier to see. A denominator of 20 tells you the number is built from fifths and quarters, since 20 relates to 5 and 4. That can save time in mental math, especially when you’re scaling measurements or working with common denominators.

Try it yourself with a clean checklist

1. Count the digits after the decimal in 1.55. There are 2.
2. Write the number without the decimal point: 155.
3. Put it over 100: 155/100.
4. Divide top and bottom by 5: 31/20.
5. If a mixed number is requested, divide 31 by 20: 1 11/20.
6. Confirm by converting 11/20 to 0.55, then add 1.

Extra practice: fractions back to decimals

Flipping the skill builds confidence. Take 31/20 and turn it back into a decimal two ways: long division, or scaling to a denominator of 100 by multiplying by 5. Both land on 155/100, then 1.55.

Do the same with 38/25, 77/50, and 51/20 from the table above. After a few rounds, you’ll recognize which denominators scale cleanly to 10, 100, or 1000, and you’ll know right away when a decimal will terminate.

Where the 31/20 form helps in real math

Teachers often push fractions because they’re easier to combine without rounding. When you keep 1.55 as 31/20, you can add, subtract, multiply, or divide with full precision.

Adding and subtracting

Suppose you add 1.55 and 0.45. As fractions, that’s 31/20 + 9/20, which lands on 40/20 = 2. The work stays clean and you don’t risk decimal drift.

Multiplying

Multiplication is also tidy. 1.55 × 4 becomes (31/20) × 4 = 124/20 = 31/5 = 6.2.

Division

Division turns into multiplying by a reciprocal. 1.55 ÷ 0.5 becomes (31/20) ÷ (1/2) = (31/20) × 2 = 31/10 = 3.1.

One last mini-check you can do without long division

When the denominator has only 2s and 5s as factors, the decimal will terminate. Since 20 = 2 × 2 × 5, 31/20 must end. That lines up with 1.55 ending after two digits. It’s a quiet clue that you’ve landed on the right kind of fraction for this decimal.