Answer:
2) 27.54 × 0.74
3) 9.91 × 8.74
Step-by-step explanation:
You want to know which estimates will be low when the factors of the product are rounded to tenths.
Effect of rounding
When a number has a hundredths digit that is 4 or less, rounding to tenths will result in a number with a value less than the unrounded number (the hundredths are simply dropped).
When a number has a hundredths digit that is 5 or more, the tenths digit will be increased by 1, resulting in a number that is more than the unrounded number.
Effect on product
When both positive factors of a product are reduced, it should come as no surprise that the product will be reduced. This is the case for products (2) and (3).
The product is underestimated by rounding to tenths for ...
- 2) 27.54 × 0.74
- 3) 9.91 × 8.74
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Additional comment
The calculator output shown in the attachment confirms this result. However, it also shows that product (1) is underestimated by rounding.
This is a consequence of 39.45 being rounded by the calculator down to 39.4, rather than up to 39.5. This is an instance of "round to even" (the tenths digit being even when rounded to 39.4). The purpose of this rounding rule, sometimes used in financial calculations, is to avoid the systematic upward bias introduced by always rounding half up to one.
The rounding rule described in the answer above is the usual one taught in school: half is always rounded up to 1.
In effect, the answer here depends on the rounding rule you are expected to use.
When one factor is rounded up, and the other is rounded down, whether the estimate is too large or too small will depend on the amount of error introduced by the rounding, and the size of the other number. An estimate of the effect can be had by adding the percentage errors introduced in each number by rounding.
Consider 18.14×2.28. The rounded product is 18.1×2.3 = 41.63. The error in each number introduced by rounding is -4/1814 ≈ -0.22%, and 2/228 ≈ +0.88%. This means the rounded product will be about 0.88-0.22 = 0.66% too high. (It is actually about 0.655% too high.)
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