Convert Fraction to Decimal: Solving 5/100 Step by Step

Fraction to Decimal with Powers of Ten

Write the following fraction as a decimal:

5100= \frac{5}{100}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's convert this into a decimal fraction.
00:09 First, consider the numerator as a whole number.
00:13 Next, move the decimal point based on the denominator.
00:17 If the denominator is one hundred, shift the point two places to the left.
00:24 And that's how we find the solution. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Write the following fraction as a decimal:

5100= \frac{5}{100}=

2

Step-by-step solution

Let's write the simple fraction as a decimal fraction

5.0 5.0

Since the fraction divides by 100, we'll move the decimal point once to the left and get:

.050 .050

We'll add the zero before the decimal point and get:

0.050=0.05 0.050=0.05

3

Final Answer

0.05

Key Points to Remember

Essential concepts to master this topic
  • Rule: Divide numerator by denominator to convert fractions to decimals
  • Technique: For denominators like 100, move decimal point left: 5÷100=0.05 5 \div 100 = 0.05
  • Check: Multiply decimal by denominator: 0.05×100=5 0.05 \times 100 = 5

Common Mistakes

Avoid these frequent errors
  • Moving decimal point the wrong direction
    Don't move the decimal point right when dividing by 100 = gives 50.0 instead of 0.05! This makes the answer 1000 times too big. Always move the decimal point LEFT when dividing by powers of 10.

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 dividing by 100 move the decimal point left?

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When you divide by 100, you're making the number smaller. Moving the decimal point two places left divides by 100 because each place represents a power of 10.

How many places do I move the decimal for different denominators?

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Count the zeros! For 10 (1 zero), move 1 place left. For 100 (2 zeros), move 2 places left. For 1000 (3 zeros), move 3 places left.

What if my fraction doesn't have a power of 10 denominator?

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Use long division instead! Divide the numerator by the denominator step by step, or use a calculator for more complex fractions.

Do I need to simplify the fraction first?

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Not necessary for conversion! 5100 \frac{5}{100} gives the same decimal as 120 \frac{1}{20} , but powers of 10 are easier to work with directly.

Why is my answer 0.05 and not just .05?

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Always include the leading zero before the decimal point! Writing 0.05 is clearer and prevents confusion. It shows the decimal is less than 1.

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