Convert Decimal 4.6 to Its Equivalent Fraction Form

Q: Why do I multiply by 10 and not 100?

Count the decimal places! Since 4.6 has one decimal place, multiply by 101 = 10. If it were 4.66, you'd multiply by 102 = 100.

Q: How do I find the GCD of 46 and 10?

List the factors: 46: 1, 2, 23, 46 and 10: 1, 2, 5, 10. The largest number that appears in both lists is 2, so GCD = 2.

Q: Can I convert 4.6 differently?

Yes! You can think of it as 4 and 6 tenths: $ 4 + \frac{6}{10} = \frac{40}{10} + \frac{6}{10} = \frac{46}{10} $. Then simplify to $ \frac{23}{5} $.

Decimal Conversion with Simplification Required

Write 4.6 as a fraction.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's convert this into a simple, reduced fraction.

00:07 First, place the numbers into equation form.

00:11 Now, move the decimal point to the right until the number is a whole number.

00:17 We moved it once, so our denominator will be ten.

00:21 Let's reduce this fraction as much as we can.

00:26 Break down forty-six into factors: twenty-three and two. And break ten into five and two.

00:32 Cancel out the common factors if possible.

00:36 And that's the solution to our problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Write 4.6 as a fraction.

Step-by-step solution

To write the decimal 4.6 as a fraction, follow these steps:

Step 1: Recognize that 4.6 can be written as $\frac{4.6}{1}$ .
Step 2: Multiply both the numerator and the denominator by 10 to eliminate the decimal. This gives you $\frac{46}{10}$ .
Step 3: Simplify the fraction $\frac{46}{10}$ by finding the greatest common divisor (GCD) of 46 and 10, which is 2. Divide both the numerator and the denominator by 2.
Step 4: Perform the division to simplify: $\frac{46 \div 2}{10 \div 2} = \frac{23}{5}$ .

Thus, the decimal 4.6 expressed as a fraction in its simplest form is $\frac{23}{5}$ .

Final Answer

$\frac{23}{5}$

Key Points to Remember

Essential concepts to master this topic

Rule: Express decimal as fraction over power of 10
Technique: Multiply by 10 to get $\frac{46}{10}$ , then find GCD
Check: Divide 23 by 5 to verify: 23 ÷ 5 = 4.6 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to simplify the fraction
Don't leave $\frac{46}{10}$ as your final answer = not in simplest form! This shows incomplete understanding of equivalent fractions. Always find the GCD and divide both numerator and denominator to get the simplest form.

Practice Quiz

Test your knowledge with interactive questions

Convert into fraction form:

$$ 0.38= $$

FAQ

Everything you need to know about this question

Why do I multiply by 10 and not 100?

Count the decimal places! Since 4.6 has one decimal place, multiply by 10¹ = 10. If it were 4.66, you'd multiply by 10² = 100.

How do I find the GCD of 46 and 10?

List the factors: 46: 1, 2, 23, 46 and 10: 1, 2, 5, 10. The largest number that appears in both lists is 2, so GCD = 2.

Can I convert 4.6 differently?

Yes! You can think of it as 4 and 6 tenths: $4 + \frac{6}{10} = \frac{40}{10} + \frac{6}{10} = \frac{46}{10}$ . Then simplify to $\frac{23}{5}$ .

What if the decimal doesn't simplify evenly?

Some decimals create fractions that can't be simplified further, like 0.7 = $\frac{7}{10}$ . That's perfectly fine - just make sure you've found the greatest common divisor correctly!

How can I check my answer without a calculator?

Use long division! Divide 23 by 5: 5 goes into 23 four times (20), with 3 remaining. Then 30 ÷ 5 = 6, so you get 4.6 - exactly what you started with!

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