Question

Explain how to find 27% of 16 using multiplication by a decimal. Then explain how to use estimation to check your answer.

Answer 1

To find 27% of 16 using multiplication by a decimal, follow these steps:

1. **Convert the Percentage to a Decimal**: To convert a percentage to a decimal, divide by 100. So, 27% becomes:
\[
27\% = \frac{27}{100} = 0.27
\]

2. **Multiply by the Decimal**: Now, multiply the decimal by the number you want to find the percentage of (in this case, 16):
\[
0.27 \times 16
\]

3. **Perform the Multiplication**: Calculate the above expression:
\[
0.27 \times 16 = 4.32
\]

So, 27% of 16 is 4.32.

### Estimation to Check the Answer

To estimate and check your answer, round the percentage and the number to simpler values. Here’s how this can be done:

1. **Round the Percentage**: Round 27% to a nearby easy-to-work-with number, such as 30%. This makes calculations easier.

2. **Calculate 30% of 16**: To find 30%, you can multiply by the decimal equivalent:
\[
30\% = 0.30
\]
\[
0.30 \times 16 = 4.8
\]

3. **Compare to the Original Calculation**: Knowing that 27% is slightly less than 30%, our estimate of 4.8 provides a way to check the result. Since 4.32 is less than 4.8, this fits our expectation, confirming that the calculated answer (4.32) is reasonable.

In conclusion, 27% of 16 is indeed 4.32, and estimating with 30% gives us a useful reference to validate our method and result.