Convert 0.0157 to a Fraction: Step-by-Step Decimal Transformation

Q: How can I check my answer without a calculator?

Think about place value: $ \frac{157}{10000} $ means 157 parts out of 10,000, which is definitely less than $ \frac{1}{10} $ = 0.1, so 0.0157 makes sense!

Q: Do I always put the decimal digits as the numerator?

Yes! Remove the decimal point and use those digits as your numerator. The denominator is determined by counting decimal places: 0.0157 becomes $ \frac{157}{10000} $.

Decimal Conversion with Four-Place Decimals

Convert 0.0157 into a fraction.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's start by converting the decimal into a simple fraction.

00:09 Move the decimal point to the right until you get a whole number.

00:13 Remember, in a decimal fraction, the denominator is always a multiple of ten.

00:19 Here, move the point four times to the right.

00:22 So, we'll add four zeros to the denominator to match.

00:31 Place the number you just made in the numerator.

00:39 And that's how we find the fraction. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert 0.0157 into a fraction.

Step-by-step solution

To solve the problem of converting the decimal 0.0157 into a fraction, follow these steps:

Step 1: Identify the Decimal Places
The decimal number 0.0157 has four decimal places.
Step 2: Convert to a Fraction
A decimal with four decimal places can be expressed as a fraction over 10,000. Therefore, 0.0157 is $\frac{157}{10000}$ . This arises because 0.0157 is $\frac{157}{10000}$ when directly considering its placement over 10000 as a power of ten.
Step 3: Simplification (if applicable)
In this case, $\frac{157}{10000}$ is already in its simplest form since 157 and 10000 have no common factors other than 1.

Therefore, the fractional representation of the decimal 0.0157 is $\frac{157}{10000}$ .

Final Answer

$\frac{157}{10000}$

Key Points to Remember

Essential concepts to master this topic

Rule: Count decimal places to find denominator power of 10
Technique: Four decimal places means denominator is 10,000
Check: Divide numerator by denominator: 157 ÷ 10,000 = 0.0157 ✓

Common Mistakes

Avoid these frequent errors

Using wrong power of 10 as denominator
Don't count decimal places incorrectly and use 1000 instead of 10,000 = wrong fraction! This happens when you miscount the zeros after the decimal point. Always count each decimal place carefully: 0.0157 has four places, so use 10,000.

Practice Quiz

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What part of the whole does the shaded (blue) area represent?

FAQ

Everything you need to know about this question

How do I know which power of 10 to use?

Count the number of digits after the decimal point. Each digit position represents a power of 10: 1 place = 10, 2 places = 100, 3 places = 1,000, 4 places = 10,000.

Why is 0.0157 not simplified to a smaller fraction?

To simplify, we need common factors between 157 and 10,000. Since 157 is prime and doesn't divide into 10,000, $\frac{157}{10000}$ is already in lowest terms.

What if I wrote 157/1000 instead?

That would give you 0.157, not 0.0157! The extra zero after the decimal point is crucial - it changes the place value completely.

How can I check my answer without a calculator?

Think about place value: $\frac{157}{10000}$ means 157 parts out of 10,000, which is definitely less than $\frac{1}{10}$ = 0.1, so 0.0157 makes sense!

Do I always put the decimal digits as the numerator?

Yes! Remove the decimal point and use those digits as your numerator. The denominator is determined by counting decimal places: 0.0157 becomes $\frac{157}{10000}$ .

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