Converting Fraction to Decimal: Solve 8/5 Step by Step

Q: Why do I divide 8 by 5 and not 5 by 8?

In a fraction like $ \frac{8}{5} $, the numerator (top number) is divided by the denominator (bottom number). Think of it as "8 divided into 5 equal parts" or "8 ÷ 5".

Q: What if the division doesn't end nicely?

Some fractions create repeating decimals! For example, $ \frac{1}{3} = 0.333... $ Keep dividing until you see the pattern, then use a bar over the repeating digits.

Q: Can I always multiply to get a denominator of 100?

Not always! Only when the denominator divides evenly into 100. Since 5 × 20 = 100, we can use this method for $ \frac{8}{5} $, but it won't work for fractions like $ \frac{1}{3} $.

Q: How do I know which method is easier?

Try direct division first! If the denominator is 2, 4, 5, 8, 10, 20, 25, or 50, the decimal will be short and easy. For other denominators, you might get repeating decimals.

Q: What does 1.6 actually mean?

1.6 means 1 whole and 6 tenths. You can think of it as 1 + 0.6, or as $ 1\frac{3}{5} $ in mixed number form, since 0.6 = $ \frac{6}{10} = \frac{3}{5} $.

Fraction to Decimal with Direct Division

Convert to decimal fraction $\frac{}{}\frac{8}{5}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's begin by converting it to a decimal fraction.

00:07 We need it in a form where we multiply both by 10.

00:12 So, we'll expand the fraction by multiplying the top and bottom.

00:16 Again, convert it to a decimal fraction.

00:20 Make sure the top number is a whole number.

00:24 When the bottom number is 10, move the decimal one spot left.

00:29 And that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert to decimal fraction $\frac{}{}\frac{8}{5}$

Step-by-step solution

To solve this problem, we'll focus on converting the fraction $\frac{8}{5}$ into a decimal. Let's follow these steps:

Step 1: Direct division of the numerator by the denominator.
Step 2: Alternative approach - adjusting the fraction to a denominator of 100.
Step 3: Verification through comparison of methods.

Now, let's work through each step:

Step 1: Divide 8 by 5. Performing this division,

$\frac{8}{5} = 8 \div 5 = 1.6$ .

Step 2: Alternatively, adjust to a denominator of 100. Multiply both the numerator and the denominator by 20:

$\frac{8}{5} = \frac{8 \times 20}{5 \times 20} = \frac{160}{100}$ .

Converting $\frac{160}{100}$ to a decimal gives us 1.6.

Through both methods, we verify that the decimal representation of $\frac{8}{5}$ is 1.6.

Thus, the solution to the problem is 1.6.

Final Answer

1.6

Key Points to Remember

Essential concepts to master this topic

Rule: Divide numerator by denominator to convert fraction to decimal
Technique: Use long division: 8 ÷ 5 = 1.6
Check: Verify by converting to hundredths: 8/5 = 160/100 = 1.6 ✓

Common Mistakes

Avoid these frequent errors

Dividing denominator by numerator instead
Don't divide 5 by 8 = 0.625! This flips the fraction and gives the reciprocal instead of the correct decimal. Always divide the top number (numerator) by the bottom number (denominator).

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 do I divide 8 by 5 and not 5 by 8?

In a fraction like $\frac{8}{5}$ , the numerator (top number) is divided by the denominator (bottom number). Think of it as "8 divided into 5 equal parts" or "8 ÷ 5".

What if the division doesn't end nicely?

Some fractions create repeating decimals! For example, $\frac{1}{3} = 0.333...$ Keep dividing until you see the pattern, then use a bar over the repeating digits.

Can I always multiply to get a denominator of 100?

Not always! Only when the denominator divides evenly into 100. Since 5 × 20 = 100, we can use this method for $\frac{8}{5}$ , but it won't work for fractions like $\frac{1}{3}$ .

How do I know which method is easier?

Try direct division first! If the denominator is 2, 4, 5, 8, 10, 20, 25, or 50, the decimal will be short and easy. For other denominators, you might get repeating decimals.

What does 1.6 actually mean?

1.6 means 1 whole and 6 tenths. You can think of it as 1 + 0.6, or as $1\frac{3}{5}$ in mixed number form, since 0.6 = $\frac{6}{10} = \frac{3}{5}$ .

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