What is 0.67 as a Fraction? A Step-by-Step Calculation
Understanding how to express decimal numbers as fractions is a valuable skill in mathematics and various real-life scenarios. In this guide, we will explore the step-by-step calculation process for the decimal number 0.67 and represent it as a fraction. We'll break down the concept, explain the calculation method, and discuss the significance of knowing how to convert decimals into fractions.
Answer: 0.67 as a Fraction is 67/100
Step 1: Understanding Decimal Notation
For instance, in the decimal 0.67, the"6" represents (6/10), "7" represents (7/20)
Step 2: The Calculation Process
To convert the decimal 0.67 into a fraction, follow these steps:
- Start with the decimal 0.67
- Multiply both the numerator and denominator by 1000000000
- Convert 670000000/1000000000 to its lowest terms using the Euclidean Algorithm
- Find the Greatest Common Divisor (GCD) of 670000000 and 1000000000
- Divide both the numerator and denominator by 10000000 this our GCD now
- The simplified fraction is 67/100
Frequently Asked Questions
Is it always possible to convert a decimal like 0.67 into a fraction?
Yes, it's possible to convert most decimals into fractions. However, some decimals, like irrational numbers, cannot be expressed as simple fractions due to their non-repeating and non-terminating nature.
Is it essential to simplify the fraction 0.67 as 67/100 after converting it from a decimal for accuracy?
Simplification is a common practice to express fractions in their simplest form. In the case of converting 0.67 to 67/100, it's not only accurate but also clearer and easier to work with, making it a recommended step in the conversion process.
Are there shortcuts for converting common decimals, like 0.67, into fractions?
Yes, there are shortcuts for common decimals. For instance, 0.67 can be expressed as 67/100. Familiarity with these shortcuts can save time in conversions, especially for frequently encountered decimal values.
Important results
| 1-10^2 | Result |
|---|---|
| 1^2 | 1 |
| 2^2 | 4 |
| 3^2 | 9 |
| 4^2 | 16 |
| 5^2 | 25 |
| 6^2 | 36 |
| 7^2 | 49 |
| 8^2 | 64 |
| 9^2 | 81 |
| 10^2 | 100 |
| 1-10^3 | Result |
|---|---|
| 1^3 | 1 |
| 2^3 | 8 |
| 3^3 | 27 |
| 4^3 | 64 |
| 5^3 | 125 |
| 6^3 | 216 |
| 7^3 | 343 |
| 8^3 | 512 |
| 9^3 | 729 |
| 10^3 | 1000 |
| 1-10^4 | Result |
|---|---|
| 1^4 | 1 |
| 2^4 | 16 |
| 3^4 | 81 |
| 4^4 | 256 |
| 5^4 | 625 |
| 6^4 | 1296 |
| 7^4 | 2401 |
| 8^4 | 4096 |
| 9^4 | 6561 |
| 10^4 | 10000 |
| 1-10^5 | Result |
|---|---|
| 1^5 | 1 |
| 2^5 | 32 |
| 3^5 | 243 |
| 4^5 | 1024 |
| 5^5 | 3125 |
| 6^5 | 7776 |
| 7^5 | 16807 |
| 8^5 | 32768 |
| 9^5 | 59049 |
| 10^5 | 100000 |