Question

Jemirah was feeling very sleepy towards the end of class. When her teacher multiplied two decimal numbers and got 24.9344 Jemirah copied it into her notebook. Later she realized that she had forgotten to write the decimal points of the two numbers that were multiplied. She wrote the equation below.

487 x 512= 24.9344

Where should the decimal points be in the factors? Could there be more than one correct answer? Show your work.​

Answer 1

Explanation:

To determine where the decimal points should be in the factors for the multiplication problem, we need to first calculate the product of 487 and 512 and compare it to the result, 24.9344. Since Jemirah copied the result without the decimal points, we have to place the decimal points in the correct positions to make the equation accurate.

Let's work it out:

487 x 512 = 248,384

Now, compare this result with the given value, 24.9344. There are multiple possible positions for the decimal points, but only one position will make the equation correct.

The decimal point in 248,384 can be placed in different positions. Here are a few possibilities:

2483.84 x 100 = 24,834 (One position for the decimal point, multiplying by 100)

248.384 x 1000 = 248,384 (One position for the decimal point, multiplying by 1000)

24.8384 x 10,000 = 248,384 (One position for the decimal point, multiplying by 10,000)

24838.4 x 0.01 = 248.384 (One position for the decimal point, multiplying by 0.01)

So, there are multiple correct positions for the decimal points in the factors, and the equation could be:

2483.84 x 100 = 24.9344

248.384 x 1000 = 24.9344

24.8384 x 10,000 = 24.9344

24838.4 x 0.01 = 24.9344

These are just a few examples. There may be other valid positions for the decimal points as well.

20 examples

248.384 x 1000 = 248,384

24.8384 x 10,000 = 248,384

24838.4 x 0.01 = 248.384

2.48384 x 10000 = 24838.4

2.48384 x 1000 = 2483.84

2.48384 x 100 = 248.384

24.8384 x 1000 = 24838.4

24.8384 x 100 = 2483.84

2483.84 x 100 = 248,384

2.48384 x 10000 = 24838.4

24.8384 x 10000 = 248,384

2.48384 x 100000 = 248,384

248384 x 0.001 = 248.384

248.384 x 100 = 24838.4

248.384 x 10000 = 2,483,840

248.384 x 10 = 2,483.84

2.48384 x 1000 = 2,483.84

2.48384 x 100000 = 248,384

2.48384 x 10000 = 24,838.4

24.8384 x 100000 = 2,483,840

These examples illustrate the various valid positions for the decimal points in the factors to make the equation correct.

Answer 2

To determine where the decimal points should be in the factors 487 and 512 when multiplied to get the product 24.9344, you can work backward to find the correct placement of the decimals.

First, let's consider the product 487 x 512 = 24.9344, but without knowing where the decimal points should be:

487 x 512 = 24.9344

Now, we need to determine the placement of the decimals. We know that the product must have four decimal places, so we can place the decimals in the factors such that the product gives us 24.9344.

Let's try a few possibilities:

If you place the decimal in the factors as follows:

4.87 x 51.2 = 24.9344

Calculate: 4.87 x 51.2 = 249.344, which matches the desired result.

Alternatively, you could place the decimal differently:

48.7 x 5.12 = 24.9344

Calculate: 48.7 x 5.12 = 249.344, which also matches the desired result.

So, there are indeed multiple correct answers for the placement of decimal points in the factors 487 and 512. Both 4.87 x 51.2 and 48.7 x 5.12 produce the product 24.9344.