Convert Mixed Number to Decimal: Solving 6 7/700

Q: Why should I simplify the fraction before converting to decimal?

Simplifying makes the conversion much easier! $ \frac{7}{700} $ looks complicated, but when simplified to $ \frac{1}{100} $, you instantly recognize it as one hundredth or 0.01.

Q: How do I know what number to divide by when simplifying?

Find the Greatest Common Divisor (GCD) of the numerator and denominator. For 7 and 700, the GCD is 7 because both numbers are divisible by 7.

Q: How do I convert 1/100 to a decimal?

Think of money! One penny is $ \frac{1}{100} $ of a dollar, which equals $0.01. So $ \frac{1}{100} = 0.01 $.

Q: Why is the answer 6.01 and not 6.1?

Because $ \frac{1}{100} = 0.01 $ (one hundredth), not $ \frac{1}{10} = 0.1 $ (one tenth). The zero in the tenths place is important for showing the correct place value!

Q: Can I check my answer another way?

Yes! Convert 6.01 back to a mixed number: $ 6.01 = 6\frac{1}{100} $. Then check if $ \frac{1}{100} = \frac{7}{700} $ by cross-multiplying: $ 1 × 700 = 7 × 100 $ ✓

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to decimal fraction

00:03 Break down the number into whole number and fraction

00:06 We want the denominator to be some multiple of 10 and 10

00:12 Reduce the fraction, make sure to divide both numerator and denominator

00:26 Convert from fraction to decimal fraction

00:34 Add

00:43 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$6\frac{7}{700}=$

2

Step-by-step solution

Let's solve the problem by converting $\frac{7}{700}$ into a decimal:

Step 1: Simplify $\frac{7}{700}$ :
Notice that the fraction can be simplified by dividing the numerator and the denominator by 7:
$\frac{7 \div 7}{700 \div 7} = \frac{1}{100}$ .

Step 2: Convert $\frac{1}{100}$ to a decimal:
Think of 1 penny, which is $\frac{1}{100}$ of a dollar, this is equal to $0.01$ .

Step 3: Add the whole number part to the decimal part derived:
The whole number part is $6$ , thus we express the mixed number $6\frac{1}{100}$ as the decimal
$6.01$ .

Therefore, the correct decimal representation of $6\frac{7}{700}$ is $6.01$ , which matches choice 2.

3

Final Answer

$6.01$

Key Points to Remember

Essential concepts to master this topic

Rule: Simplify the fraction part before converting to decimal
Technique: Divide numerator and denominator by GCD: $\frac{7}{700} = \frac{1}{100}$
Check: Verify decimal makes sense: $6\frac{1}{100} = 6.01$ ✓

Common Mistakes

Avoid these frequent errors

Converting 7/700 directly to decimal without simplifying
Don't divide 7 ÷ 700 directly using long division = 0.01 but with unnecessary work! This makes the calculation harder and increases chance of errors. Always simplify fractions first by finding the GCD (7) to get $\frac{1}{100} = 0.01$ .

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 should I simplify the fraction before converting to decimal?

+

Simplifying makes the conversion much easier! $\frac{7}{700}$ looks complicated, but when simplified to $\frac{1}{100}$ , you instantly recognize it as one hundredth or 0.01.

How do I know what number to divide by when simplifying?

+

Find the Greatest Common Divisor (GCD) of the numerator and denominator. For 7 and 700, the GCD is 7 because both numbers are divisible by 7.

What if I can't see the GCD right away?

+

Try dividing by small prime numbers like 2, 3, 5, 7, etc. For $\frac{7}{700}$ , notice that 7 divides into both numbers: $7 ÷ 7 = 1$ and $700 ÷ 7 = 100$ .

How do I convert 1/100 to a decimal?

+

Think of money! One penny is $\frac{1}{100}$ of a dollar, which equals 0.01. So $\( \frac{1}{100} = 0.01$ .

Why is the answer 6.01 and not 6.1?

+

Because $\frac{1}{100} = 0.01$ (one hundredth), not $\frac{1}{10} = 0.1$ (one tenth). The zero in the tenths place is important for showing the correct place value!

Can I check my answer another way?

+

Yes! Convert 6.01 back to a mixed number: $6.01 = 6\frac{1}{100}$ . Then check if $\frac{1}{100} = \frac{7}{700}$ by cross-multiplying: $1 × 700 = 7 × 100$ ✓

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Convert Mixed Number to Decimal: Solving 6 7/700

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