To express [tex]\( \frac{16}{3} \)[/tex] as a decimal correct to 4 decimal places, follow these steps:
1. Set up the division:
- We need to divide 16 by 3.
2. Perform the division:
- 3 goes into 16 a total of 5 times, because [tex]\( 3 \times 5 = 15 \)[/tex].
- Subtract 15 from 16, which gives us a remainder of 1.
3. Continue with decimal:
- Add a decimal point and a zero to the remainder of 1, making it 10.
- 3 goes into 10 a total of 3 times, because [tex]\( 3 \times 3 = 9 \)[/tex].
- Subtract 9 from 10, which gives a remainder of 1.
4. Repeat the process:
- Bring down another 0, making the new dividend 10.
- Again, 3 goes into 10 three times (since [tex]\( 3 \times 3 = 9 \)[/tex]), and the remainder is 1.
5. Continue until the desired precision is achieved:
- Keep repeating this process, bringing down 0 each time. The pattern will continue as:
- 3 into 10 is 3, remainder 1.
6. Stop after getting 4 decimal places:
- After repeating the division process four times with the decimal portion stabilized, we get [tex]\( 5.3333 \)[/tex].
So, the value of [tex]\( \frac{16}{3} \)[/tex] expressed as a decimal correct to 4 decimal places is:
[tex]\[ \frac{16}{3} = 5.3333 \][/tex]
This is the result of the division, rounded appropriately as needed.
