Tumelo used his calculator to work out the value of 3,12 × 4,36.

Question

He wrote down the answer as 136,032
A) what simple check could Tumelo have used, without using his calculator, to show that his answer is incorrect?

Answer 1

To check if Tumelo's answer of 136.032 for the multiplication of 3.12 and 4.36 is reasonable, he could use an estimation technique based on rounding the numbers he is multiplying.

1. Rounding the Numbers:

   • Round 3.12 to 3 (or slightly higher) for simplicity.
   • Round 4.36 to 4 (or slightly higher).

2. Estimating the Product:

   • Now multiply the rounded values: \[ 3 \times 4 = 12 \]

3. Check the Placement of the Decimal:

   • The original multiplication involves two decimal numbers: 3.12 has 2 decimal places and 4.36 also has 2 decimal places, so the product should have a total of 4 decimal places.
   • This means Tumelo's final answer should be a number between 1.2 and 12, so a possible correct answer would be 13.6032 (if he had done the multiplication correctly).

Given Tumelo's result (136.032), it is too large (an order of magnitude greater than 12), which suggests he made an error in his calculation. This simple check of estimating and placing the decimal can quickly confirm that his answer is incorrect.