Practise the method.
Example 1
Each of 105 identical batches uses exactly 32kg of an ingredient costing $11 per kg. A spreadsheet first rounds the kilograms per batch to 2 decimal places, then multiplies by the batch count and price. Compared with using the exact fraction throughout, by how many cents does the spreadsheet's total differ? Enter a positive number for an overestimate and a negative number for an underestimate.
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Answer: 385
- Rounded mass is 0.67kg.
- The rounded total is $773.85 and the exact total is $770.
- Rounded minus exact is 385 cents.
Example 2
Tank A contains an unknown volume of mixture that is 54 juice. Tank B contains 90L of mixture that is 61 juice. Transfer exactly 51 of A's mixture into B, then mix B thoroughly. B is now 5021 juice. How many litres were originally in A?
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Answer: 300
- If t litres were transferred, the juice in B is (54)t+15, and its total volume is t+90.
- Equate their ratio to 5021 and solve: t=60.
- A originally held 5t=300L.
Example 3
Each of 308 identical batches uses exactly 112kg of an ingredient costing $8 per kg. A spreadsheet first rounds the kilograms per batch to 2 decimal places, then multiplies by the batch count and price. Compared with using the exact fraction throughout, by how many cents does the spreadsheet's total differ? Enter a positive number for an overestimate and a negative number for an underestimate.
Show worked answer
Answer: −448
- Rounded mass is 0.18kg.
- The rounded total is $443.52 and the exact total is $448.
- Rounded minus exact is−448 cents.