Convert Fraction to Decimal: Solving 4/25 Step-by-Step

Q: Why convert 25 to 100 instead of just dividing 4 by 25?

Converting to powers of 10 makes the decimal conversion obvious! When you have $ \frac{16}{100} $, you immediately see it's 0.16. Direct division works too, but requires more careful calculation.

Q: How do I know what to multiply 25 by to get 100?

Think: what times 25 equals 100? Since 25 × 4 = 100, multiply both numerator and denominator by 4. For other denominators, find what makes them into 10, 100, or 1000.

Q: What if the denominator can't become a nice power of 10?

Some fractions like $ \frac{1}{3} $ can't convert to powers of 10 easily. In those cases, use long division to divide the numerator by the denominator directly.

Q: Can I use a calculator instead of this method?

Yes, but understanding this method helps you mentally estimate decimal values and check if calculator answers make sense. Plus, it builds your number sense!

Q: How do I remember which decimal place the digits go in?

Count the zeros in the denominator! $ \frac{16}{100} $ has 2 zeros, so 16 goes 2 places after the decimal: 0.16.

Fraction to Decimal with Power of 10 Conversion

Convert $\frac{4}{25}$ into a decimal.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to decimal fraction

00:03 We want a denominator that's a multiple of 10 and 10

00:07 Therefore we'll expand the fraction, making sure to multiply both numerator and denominator

00:15 Convert to decimal fraction

00:19 When the denominator equals 100

00:22 Place the numerator 2 digits after the decimal point

00:26 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert $\frac{4}{25}$ into a decimal.

Step-by-step solution

To convert $\frac{4}{25}$ into a decimal, we can make the denominator a power of 10. Follow these steps:

Step 1: Determine the conversion factor needed to change the denominator (25) to 100. Since $25 \times 4 = 100$ , the conversion factor is 4.
Step 2: Multiply both the numerator and the denominator of the fraction by this conversion factor.
$\frac{4 \times 4}{25 \times 4} = \frac{16}{100}$
Step 3: Convert the fraction $\frac{16}{100}$ directly into a decimal. Since 100 is the base of the decimal system, $\frac{16}{100} = 0.16$ .

Therefore, the decimal representation of $\frac{4}{25}$ is 0.16.

Final Answer

0.16

Key Points to Remember

Essential concepts to master this topic

Rule: Convert denominators to powers of 10 for easy decimal conversion
Technique: Multiply $\frac{4}{25}$ by $\frac{4}{4}$ to get $\frac{16}{100}$
Check: Verify that 16 ÷ 100 equals your decimal answer ✓

Common Mistakes

Avoid these frequent errors

Dividing numerator by denominator incorrectly
Don't calculate 4 ÷ 25 = 0.25 without proper long division! This gives the wrong decimal. Always convert to a power of 10 denominator first, or use careful long division with proper place values.

Practice Quiz

Test your knowledge with interactive questions

Write the following fraction as a decimal:

$\frac{5}{100}=$

FAQ

Everything you need to know about this question

Why convert 25 to 100 instead of just dividing 4 by 25?

Converting to powers of 10 makes the decimal conversion obvious! When you have $\frac{16}{100}$ , you immediately see it's 0.16. Direct division works too, but requires more careful calculation.

How do I know what to multiply 25 by to get 100?

Think: what times 25 equals 100? Since 25 × 4 = 100, multiply both numerator and denominator by 4. For other denominators, find what makes them into 10, 100, or 1000.

What if the denominator can't become a nice power of 10?

Some fractions like $\frac{1}{3}$ can't convert to powers of 10 easily. In those cases, use long division to divide the numerator by the denominator directly.

Can I use a calculator instead of this method?

Yes, but understanding this method helps you mentally estimate decimal values and check if calculator answers make sense. Plus, it builds your number sense!

How do I remember which decimal place the digits go in?

Count the zeros in the denominator! $\frac{16}{100}$ has 2 zeros, so 16 goes 2 places after the decimal: 0.16.

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