To determine if Yari is correct that the product \( 230 \times 104 \) has four zeroes, let's first calculate the actual product step by step.
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Multiply 230 by 100: This part is straightforward since multiplying by 100 adds two zeroes: \[ 230 \times 100 = 23000 \]
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Multiply 230 by 4: Next, we calculate \( 230 \times 4 \): \[ 230 \times 4 = 920 \]
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Now, add these two products: So now we need to add the two results from above: \[ 23000 + 920 = 23920 \]
Thus, the product \( 230 \times 104 = 23920 \).
Now, let’s analyze how many zeroes are in \( 23920 \). The number 23920 has two zeroes at the end. Therefore, Yari's claim that the product has four zeroes is incorrect.
Explanation Using Patterns with Powers of 10
When multiplying numbers, particularly by powers of 10, we can easily identify how many zeroes will be at the end of the product. If we multiply by 10, we typically add one zero, hence:
- \( n \times 10^1 \) adds 1 zero.
- \( n \times 10^2 \) adds 2 zeroes.
In our case, \( 230 \times 104 \) is not simply multiplying by powers of 10, but we can break down \( 104 \) as \( 100 + 4 \). The effective multiplication involves \( 100 \) (which contributes two zeroes) and \( 4 \) (which contributes none). Thus the total contribution to zeroes is 2 from \( 100 \) and none from \( 4 \).
In conclusion, the final product \( 23920 \) has two zeroes, not four, which confirms Yari’s assertion is incorrect.