Suppose we know that , can you immediately write down the product of ?

Understand the Question We are given the product of two whole numbers: . To find the product of , we can convert the decimals into fractions or count the total number of decimal places. Since has decimal places and has decimal place, the product will have decimal places. Step 1 · Convert Decimals to Fractions Given Expressing the decimals as fractions Step 2 · Multiply and Place the Decimal Point Multiplying the fractions Answer > Common Mistakes Incorrect Decimal Count: Adding only the decimal places of one number instead of both (the product must have decimal places from the right). Decimal Shift Direction: Moving the decimal point to the right instead of shifting 3 places to the left when dividing by .

Another Peek Beyond the Point | IT

Question 8

Suppose we know that $596 \times 248 = 147808$ , can you immediately write down the product of $5.96 \times 24.8$ ?

Solution

Understand the Question

We are given the product of two whole numbers: $596 \times 248 = 147808$ .
To find the product of $5.96 \times 24.8$ , we can convert the decimals into fractions or count the total number of decimal places.
Since $5.96$ has $2$ decimal places and $24.8$ has $1$ decimal place, the product will have $2 + 1 = 3$ decimal places.

Step 1 · Convert Decimals to Fractions

Given $596 \times 248 = 147808$

Expressing the decimals as fractions $5.96 = \dfrac{596}{100}$

$24.8 = \dfrac{248}{10}$

Step 2 · Multiply and Place the Decimal Point

Multiplying the fractions

\begin{aligned} 5.96 \times 24.8 &= \dfrac{596}{100} \times \dfrac{248}{10} \\[0.6em] &= \dfrac{596 \times 248}{100 \times 10} \\[0.6em] &= \dfrac{147808}{1000} \\[0.6em] &= 147.808 \end{aligned}

Answer

$147.808$

Common Mistakes

Incorrect Decimal Count: Adding only the decimal places of one number instead of both (the product must have $2 + 1 = 3$ decimal places from the right).
Decimal Shift Direction: Moving the decimal point to the right instead of shifting 3 places to the left when dividing by $1000$ .

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Suppose we know that $596 \times 248 = 147808$ , can you immediately write down the product of $5.96 \times 24.8$ ?

Context: Observe the number of digits after the decimal point in the multiplier, the multiplicand and the product. Also note the number of zeroes in the denominator.

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