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Why is estimating not as helpful when multiplying very small numbers such as 0.007 and 0.053?

a) Estimation is not useful for small numbers
b) Small errors in estimation can significantly impact the result
c) Estimation is only effective for large numbers
d) Exact multiplication is always faster than estimation

User BlackGlory
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1 Answer

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Final answer:

Estimating is not as helpful when multiplying very small numbers like 0.007 and 0.053 due to the significant impact of small errors in estimation.

Step-by-step explanation:

When multiplying very small numbers, such as 0.007 and 0.053, estimating is not as helpful for several reasons. Firstly, small errors in estimation can significantly impact the result. Since these numbers are very close to zero, even a small error in estimation can change the result drastically. For example, if you estimate 0.007 as 0.01 and 0.053 as 0.05, the product will be 0.0005, which is significantly different from the exact product of 0.000371.

Secondly, estimating is generally more effective for large numbers, where the impact of small errors is relatively small. When multiplying large numbers, the estimation can still provide a reasonably accurate approximation. However, with very small numbers, any error in estimation becomes more significant.

Therefore, the correct answer is b) Small errors in estimation can significantly impact the result as it accurately describes why estimating is not as helpful when multiplying very small numbers.

User Rolling Stone
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