Convert 0.019 to Fraction: Step-by-Step Decimal Transformation

Q: Why does 0.019 become 19/1000 and not 019/1000?

Great question! The leading zero in 019 doesn't add value to the number. Just like 019 apples is the same as 19 apples, we can drop unnecessary zeros from the numerator.

Q: How do I remember which denominator to use?

Use this trick: count the decimal places, then write 1 followed by that many zeros. For 0.019: 3 decimal places → 1000 (1 followed by 3 zeros).

Q: What if the decimal has trailing zeros like 0.0190?

Trailing zeros after the last non-zero digit don't change the value! So 0.0190 = 0.019, and both convert to $ \frac{19}{1000} $.

Q: How do I convert this fraction back to check my work?

Divide the numerator by the denominator: 19 ÷ 1000 = 0.019. If you get back your original decimal, you did it correctly!

Decimal Conversion with Thousandths Place

Convert into fraction form:

$0.019=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to fraction

00:04 First, we'll match the digit positions with the appropriate division

00:09 We'll place the number in the numerator, and the last digit position in the denominator

00:13 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

Convert into fraction form:

$0.019=$

Step-by-step solution

Let's pay attention to where the decimal point is located in the number.

Remember:

One number after the zero represents tens

Two numbers after the zero represent hundreds

Three numbers after the zero represent thousands

And so on

In this case, there are three numbers after the zero, so the number is divided by 1000

Let's write the fraction in the following way:

$\frac{0019}{1000}$

We'll then remove the unnecessary zeros as follows:

$\frac{19}{1000}$

Final Answer

$\frac{19}{1000}$

Key Points to Remember

Essential concepts to master this topic

Decimal Places: Count digits after decimal to find denominator
Technique: 0.019 has 3 decimal places, so denominator is 1000
Check: Verify $\frac{19}{1000} = 19 ÷ 1000 = 0.019$ ✓

Common Mistakes

Avoid these frequent errors

Counting decimal places incorrectly
Don't count 0.019 as having 2 decimal places because you see "19" = $\frac{19}{100} = 0.19$ which is wrong! The zero after the decimal counts as a place. Always count every single digit after the decimal point: 0.019 has 3 places, so use 1000.

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 does 0.019 become 19/1000 and not 019/1000?

Great question! The leading zero in 019 doesn't add value to the number. Just like 019 apples is the same as 19 apples, we can drop unnecessary zeros from the numerator.

How do I remember which denominator to use?

Use this trick: count the decimal places, then write 1 followed by that many zeros. For 0.019: 3 decimal places → 1000 (1 followed by 3 zeros).

What if the decimal has trailing zeros like 0.0190?

Trailing zeros after the last non-zero digit don't change the value! So 0.0190 = 0.019, and both convert to $\frac{19}{1000}$ .

Can I simplify 19/1000 further?

Let's check! Since 19 is prime and doesn't share any common factors with 1000, $\frac{19}{1000}$ is already in its simplest form.

How do I convert this fraction back to check my work?

Divide the numerator by the denominator: 19 ÷ 1000 = 0.019. If you get back your original decimal, you did it correctly!

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