Compare Fractions and Decimals: 16/10 ? 1.6

Q: Why can't I just compare 16 and 1.6 directly?

Because $ \frac{16}{10} $ means 16 divided by 10, not just the number 16. You must perform the division first to get the actual value for comparison.

Q: What if I get a long decimal when dividing?

That's fine! Some fractions create repeating decimals or long decimals. Just calculate enough decimal places to make an accurate comparison.

Q: How do I know when two numbers are equal?

Two numbers are equal when they have exactly the same value. After converting $ \frac{16}{10} $ to 1.6, both sides show 1.6, so they're equal.

Q: Can I use this method for any fraction and decimal?

Absolutely! Converting fractions to decimals by dividing works for any fraction. This is a reliable method for all fraction-decimal comparisons.

Fraction-Decimal Comparison with Equivalent Values

Choose the appropriate sign (?):

$\frac{16}{10}?1.6$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 First, choose the correct sign for the problem.

00:10 Now, let's convert the fraction into a decimal.

00:14 Write the top number, or numerator, as a whole number.

00:18 If the bottom number, or denominator, is 10, move the decimal one place left.

00:25 Replace the fraction with the decimal.

00:29 Choose the correct sign again to complete the equation.

00:33 And that's how you solve the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Choose the appropriate sign (?):

$\frac{16}{10}?1.6$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Convert the fraction $\frac{16}{10}$ into a decimal.
Step 2: Compare the resulting decimal with $1.6$ .
Step 3: Determine the correct relational sign based on the comparison.

Let's work through each step:
Step 1: Convert the fraction $\frac{16}{10}$ to a decimal by performing division $16 \div 10$ . Doing this gives us $1.6$ .
Step 2: Compare the decimal $1.6$ with $1.6$ .
Step 3: Since both are equal, the correct relational sign to use is $=$ .

Therefore, the solution to the problem is $=$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Conversion Rule: Divide numerator by denominator to get decimal form
Technique: Calculate $\frac{16}{10} = 16 ÷ 10 = 1.6$
Check: Both values are 1.6, so they're equal: = ✓

Common Mistakes

Avoid these frequent errors

Comparing fraction and decimal without converting
Don't try to compare $\frac{16}{10}$ and 1.6 directly without converting = confusion and wrong answers! You can't properly compare different number formats. Always convert the fraction to decimal first by dividing.

Practice Quiz

Test your knowledge with interactive questions

Convert into fraction form:

$$ 0.38= $$

FAQ

Everything you need to know about this question

Why can't I just compare 16 and 1.6 directly?

Because $\frac{16}{10}$ means 16 divided by 10, not just the number 16. You must perform the division first to get the actual value for comparison.

Is there a faster way than converting to decimals?

Yes! You can convert the decimal to a fraction instead: 1.6 = $\frac{16}{10}$ . Either method works, but converting fractions to decimals is usually easier.

What if I get a long decimal when dividing?

That's fine! Some fractions create repeating decimals or long decimals. Just calculate enough decimal places to make an accurate comparison.

How do I know when two numbers are equal?

Two numbers are equal when they have exactly the same value. After converting $\frac{16}{10}$ to 1.6, both sides show 1.6, so they're equal.

Can I use this method for any fraction and decimal?

Absolutely! Converting fractions to decimals by dividing works for any fraction. This is a reliable method for all fraction-decimal comparisons.

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