Use long divisions to convert 4/15 to a decimal

Answer 1

To convert the fraction $\frac{4}{15}$ to a decimal using long division, follow these steps:

1. Set up the division: You're dividing 4 by 15.

   $$4÷15$$

2. Since 4 is less than 15, you will add a decimal point and zeros to continue the division. Rewrite 4 as 4.000. Now you are calculating $40.00÷15$.

3. Perform the long division:

   • 15 goes into 40: 2 times (because $15\times 2=30$).
   • Subtract: $40-30=10$.
   • Bring down the next 0: Now you have 100.

4. Continue dividing:

   • 15 goes into 100: 6 times (because $15\times 6=90$).
   • Subtract: $100-90=10$.
   • Bring down the next 0: Now you have 100 again.

5. Repeat:

   • 15 goes into 100: 6 times (again).
   • Subtract: $100-90=10$.
   • Bring down the next 0: You will see that it will again yield 100.

6. It becomes apparent that the pattern will repeat. Each time you perform the division from $100$, you'll get 6 with a remainder of 10, leading to another 100.

So, the decimal representation of $\frac{4}{15}$ is:

$$0.2666...$$

This can also be noted as $0.2\bar{6}$, indicating that the digit 6 repeats indefinitely. Thus:

$$\frac{4}{15}=0.26666...$$