4 27/125 as a decimal

Steps to Solve

1. Convert the Mixed Number to an Improper Fraction

To convert the mixed number $4 \frac{27}{125}$ into an improper fraction, we can use the formula: $$ \text{Improper Fraction} = \text{Whole Number} \times \text{Denominator} + \text{Numerator} $$

In this case: $$ \text{Improper Fraction} = 4 \times 125 + 27 = 500 + 27 = 527 $$

So, the improper fraction form is: $$ \frac{527}{125} $$

2. Perform the Division to Convert to Decimal

Now we need to convert the improper fraction $\frac{527}{125}$ into decimal form by dividing the numerator by the denominator: $$ 527 \div 125 $$

This division can be carried out as follows:

• 125 goes into 527 four times (since $4 \times 125 = 500$)
• Subtract $500$ from $527$ to get the remainder: $527 - 500 = 27$.
• Now, we can append a decimal and a zero to the remainder to continue the division: $270 \div 125$

125 goes into 270 two times (since $2 \times 125 = 250$)

• Subtract $250$ from $270$: $270 - 250 = 20$.
• Append another zero to make it $200 \div 125$.

125 goes into 200 once (since $1 \times 125 = 125$)

• Subtract $125$ from $200$: $200 - 125 = 75$.
• Append another zero to make it $750 \div 125$.

125 goes into 750 six times (since $6 \times 125 = 750$)

• The division ends here, and there is no remainder.

So $527 \div 125 = 4.216$.

Now we combine the results from the division to get the complete decimal.

3. Combining the Results

From the steps of our division, we have: $$ 4 + 0.216 = 4.216 $$

Thus, the decimal representation of the mixed number $4 \frac{27}{125}$ is $4.216$.