Convert Decimal to Fraction: Transforming 0.007 to Simplified Form

Q: How do I know which power of 10 to use in the denominator?

Count the decimal places after the decimal point. For 0.007, there are 3 places, so use $ 10^3 = 1000 $ as your denominator.

Q: Why can't I just put 7 over 10?

Because $ \frac{7}{10} = 0.7 $, not 0.007! The position of the digit matters. The 7 is in the thousandths place, so you need 1000 in the denominator.

Q: Do I need to simplify this fraction?

Check if 7 and 1000 have any common factors. Since 7 is prime and doesn't divide 1000, $ \frac{7}{1000} $ is already in simplest form!

Q: How can I double-check my answer?

Divide the numerator by the denominator: $ 7 ÷ 1000 = 0.007 $. If this matches your original decimal, you're correct!

Decimal Conversion with Three-Place Decimals

Convert 0.007 into a fraction.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to simple fraction

00:03 Move the decimal point right until the number is whole

00:06 In a decimal fraction, the denominator must be a multiple of 10

00:10 We moved the decimal point 3 places right

00:13 Therefore we'll add three zeros to the denominator

00:19 Place the digits in the numerator

00:24 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 0.007 into a fraction.

Step-by-step solution

To solve this problem of converting the decimal 0.007 into a fraction, follow these steps:

Step 1: Recognize the number of decimal places in 0.007, which is three.
Step 2: Write 0.007 as a fraction. Place 7 (the number without the decimal) over 1 followed by three zeros, giving us a denominator of 1000. This is because there are three digits after the decimal point.

The fraction form is $\frac{7}{1000}$ .

Thus, 0.007 converted into a fraction is $\frac{7}{1000}$ .

Final Answer

$\frac{7}{1000}$

Key Points to Remember

Essential concepts to master this topic

Rule: Count decimal places to determine the denominator power
Technique: Place 7 over 1000 since 0.007 has three decimal places
Check: Verify that $\frac{7}{1000} = 0.007$ by dividing ✓

Common Mistakes

Avoid these frequent errors

Using wrong denominator based on decimal places
Don't count decimal places incorrectly and use 100 instead of 1000 = $\frac{7}{100} = 0.07$ which is wrong! This gives a decimal ten times larger than the original. Always use 10 raised to the power equal to the number of decimal places.

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

How do I know which power of 10 to use in the denominator?

Count the decimal places after the decimal point. For 0.007, there are 3 places, so use $10^3 = 1000$ as your denominator.

Why can't I just put 7 over 10?

Because $\frac{7}{10} = 0.7$ , not 0.007! The position of the digit matters. The 7 is in the thousandths place, so you need 1000 in the denominator.

Do I need to simplify this fraction?

Check if 7 and 1000 have any common factors. Since 7 is prime and doesn't divide 1000, $\frac{7}{1000}$ is already in simplest form!

How can I double-check my answer?

Divide the numerator by the denominator: $7 ÷ 1000 = 0.007$ . If this matches your original decimal, you're correct!

What if the decimal has trailing zeros like 0.0070?

Trailing zeros after the decimal don't change the value, so 0.0070 = 0.007. However, if asked to convert 0.0070 exactly, you'd get $\frac{70}{10000} = \frac{7}{1000}$ after simplifying.

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