Quick Answer: 27/64 as a decimal is 0.421875.
It is a terminating decimal, meaning it ends and does not repeat.
Step-by-Step Conversion of 27/64 Into Decimal
To convert the fraction into a decimal, divide the numerator by the denominator:
27 ÷ 64 = 0.421875
Since 64 is a power of 2, the decimal will terminate.
Alternative Method (Using Powers of 2)
64 = 2⁶
To convert to a denominator of 1,000,000 (a power of 10), multiply:
27 × 15625 = 421875
64 × 15625 = 1,000,000
So:
27/64 = 421875 / 1,000,000 = 0.421875
This confirms the decimal result exactly.
For the fraction version of this result, visit: 0.421875 as a Fraction (Simple Step-by-Step Explanation)
How to Verify the Result
Multiply Back
0.421875 × 64 = 27
This confirms the conversion is correct.
Prime Factor Rule
64 = 2 × 2 × 2 × 2 × 2 × 2
Since the denominator contains only the prime factor 2, the decimal must terminate.
Calculator Check
Dividing 27 by 64 gives 0.421875 exactly.
Is 27/64 a Terminating or Repeating Decimal?
27/64 is a terminating decimal.
Why?
A fraction terminates if its denominator contains only prime factors 2 and/or 5.
Since 64 contains only 2, the decimal ends.
Understanding the Size of 27/64
The decimal 0.421875 means:
- The value is less than 1
- It represents approximately 42.1875%
- It lies between 0.4 and 0.5 on the number line
Fraction, Decimal, and Percentage Forms
| Form | Value |
| Fraction | 27/64 |
| Decimal | 0.421875 |
| Percentage | 42.1875% |
To convert to percentage:
0.421875 × 100 = 42.1875%
Compare With Similar Denominator-64 Fractions
| Fraction | Decimal |
| 1/64 | 0.015625 |
| 8/64 | 0.125 |
| 16/64 | 0.25 |
| 32/64 | 0.5 |
| 48/64 | 0.75 |
Fractions with denominator 64 often produce decimals with up to 6 decimal places, because 64 = 2⁶.
Rounding Table for 27/64
| Rounded To | Value |
| 1 decimal | 0.4 |
| 2 decimals | 0.42 |
| 3 decimals | 0.422 |
| 4 decimals | 0.4219 |
| 5 decimals | 0.42188 |
| Exact | 0.421875 |
Exam Tip
If asked to round 27/64:
- To 2 decimal places → 0.42
- To 3 decimal places → 0.422
- For exact value → 0.421875
Always check how many decimal places are required.
Real-Life Applications of 27/64
Although people usually use the decimal form, 27/64 appears in:
Binary-Based Calculations
Since 64 is a power of 2, it is common in computing and digital systems.
Measurement Conversions
Fractions over 64 are common in precision engineering and machining.
Data Scaling
Values divided into 64 equal parts often produce decimals like 0.421875.
Common Student Mistakes
- Writing 0.42187 (truncating early)
- Rounding incorrectly at the 4th or 5th decimal place
- Assuming it repeats
- Forgetting to convert to percentage correctly
FAQs About 27/64 as a Decimal
Is 27/64 a terminating decimal?
Yes. It equals 0.421875 exactly.
Why does 27/64 not repeat?
Because 64 contains only the prime factor 2.
What is 27/64 as a percentage?
It equals 42.1875%.
How many decimal places does 27/64 have?
Six decimal places in its exact form.
Final Summary
- 27/64 as a decimal = 0.421875
- It is a terminating decimal
- It equals 42.1875%
- Denominators that are powers of 2 produce terminating decimals
