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.