Find the Numerical Equivalent of 1/40: Fraction Conversion

Q: Why multiply by 25/25 instead of other numbers?

We need the denominator to be a power of 10 (like 10, 100, 1000) to convert easily to decimals. Since 40 × 25 = 1000, multiplying by $ \frac{25}{25} $ gives us $ \frac{25}{1000} $.

Q: How do I know which way to move the decimal point?

Remember: dividing by powers of 10 moves the decimal left, multiplying moves it right. Since $ \frac{25}{1000} $ means 25 ÷ 1000, move 3 places left: 25.0 → 0.025

Q: Can I just divide 1 by 40 directly?

Yes! You can use long division: 1 ÷ 40 = 0.025. Both methods work, but the fraction conversion method helps you understand why the decimal looks the way it does.

Q: What if my fraction doesn't convert to a nice decimal?

Some fractions like $ \frac{1}{3} $ give repeating decimals (0.333...). That's normal! Not all fractions have exact decimal equivalents, but $ \frac{1}{40} $ does because 40 only has factors of 2 and 5.

Q: Why does the answer have trailing zeros?

The zeros in 0.025 are significant - they show the exact place value! Without them, 0.25 would be a completely different number (ten times bigger than the correct answer).

Fraction to Decimal with Place Value

Which number is equal to $\frac{1}{40}$ ?

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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 Convert the fraction to a fraction with denominator of 1000

00:06 Make sure to multiply both numerator and denominator

00:17 When the denominator equals 1000, the numerator is the decimal number

00:24 When dividing by 1000, the decimal point moves 3 places to the left

00:39 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Which number is equal to $\frac{1}{40}$ ?

Step-by-step solution

Let's multiply the numerator and denominator by a number that will help us make the denominator 1000:

$\frac{1\times25}{40\times25}=\frac{25}{1000}$

Next, we will rewrite the simple fraction as a decimal fraction:

$25.0$

Since we're dividing by 10, the decimal point will move three places to the left, giving us:

$.0250$

Finally we'll add the 0 before the decimal point to get:

$0.0250=0.025$

Final Answer

0.025

Key Points to Remember

Essential concepts to master this topic

Rule: Convert fractions to decimals by making denominators powers of 10
Technique: Multiply $\frac{1}{40}$ by $\frac{25}{25}$ to get $\frac{25}{1000}$
Check: Verify 0.025 × 40 = 1 to confirm the conversion ✓

Common Mistakes

Avoid these frequent errors

Moving decimal point wrong direction or wrong number of places
Don't move the decimal right when dividing by 1000 = 25.0 instead of 0.025! When dividing by powers of 10, the decimal moves LEFT. Always move left when dividing by 10, 100, 1000, etc.

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 multiply by 25/25 instead of other numbers?

We need the denominator to be a power of 10 (like 10, 100, 1000) to convert easily to decimals. Since 40 × 25 = 1000, multiplying by $\frac{25}{25}$ gives us $\frac{25}{1000}$ .

How do I know which way to move the decimal point?

Remember: dividing by powers of 10 moves the decimal left, multiplying moves it right. Since $\frac{25}{1000}$ means 25 ÷ 1000, move 3 places left: 25.0 → 0.025

Can I just divide 1 by 40 directly?

Yes! You can use long division: 1 ÷ 40 = 0.025. Both methods work, but the fraction conversion method helps you understand why the decimal looks the way it does.

What if my fraction doesn't convert to a nice decimal?

Some fractions like $\frac{1}{3}$ give repeating decimals (0.333...). That's normal! Not all fractions have exact decimal equivalents, but $\frac{1}{40}$ does because 40 only has factors of 2 and 5.

Why does the answer have trailing zeros?

The zeros in 0.025 are significant - they show the exact place value! Without them, 0.25 would be a completely different number (ten times bigger than the correct answer).

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