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Questions and Answers
0.5 等於什麼分數？
要計算 25% 的 120 是多少？
比較小數 0.45 和 0.34 哪個大？
50% 等於什麼小數？
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要找到 30 是 120 的什麼百分數？
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小數和百分數在日常生活中的應用是什麼？
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要將小數 0.25 轉換為百分數？
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小數 0.75 等於什麼分數？
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Study Notes
Decimals
- A decimal is a way of expressing a fraction using a point and digits.
- Decimals can be converted to fractions and vice versa.
- Examples:
- 0.5 = 1/2
- 0.25 = 1/4
- Decimals can be added and subtracted like whole numbers, but with the point aligned.
- Decimals can be multiplied and divided, but the rules are slightly different:
- Multiply the numbers as whole numbers, then place the point in the product.
- Divide the numbers as whole numbers, then place the point in the quotient.
Comparing Decimals
- Decimals can be compared by looking at the digits in each place value.
- Example:
- 0.45 is greater than 0.34 because 5 is greater than 4.
- Decimals can also be compared by converting them to fractions and comparing the fractions.
Percentages
- A percentage is a way of expressing a value as a fraction of 100.
- Percentages can be converted to decimals by dividing by 100.
- Examples:
- 25% = 25/100 = 0.25
- 50% = 50/100 = 0.5
- Percentages can be converted to fractions by dividing by 100 and simplifying.
- Examples:
- 25% = 1/4
- 50% = 1/2
Calculating Percentages
- To find a percentage of a number, multiply the number by the percentage as a decimal.
- Example:
- 25% of 120 = 120 x 0.25 = 30
- To find what percentage one number is of another, divide the first number by the second and multiply by 100.
- Example:
- 30 is what percentage of 120? = (30 ÷ 120) x 100 = 25%
Real-World Applications
- Decimals and percentages are used in everyday life, such as:
- Measuring lengths and weights
- Calculating discounts and sales tax
- Understanding sports statistics and grades
- Comparing prices and values
小數
- 小數是一種使用點和数字表示分數的方法。
- 小數可以轉換為分數，反之亦然。
- 例子：
- 0.5 = 1/2
- 0.25 = 1/4
- 小數可以像整數一樣進行加減，但需要對齊小數點。
- 小數也可以進行乘除，但需要遵循特殊規則：
- 乘法：先將數字 treat as 整數進行乘法，然後將小數點放在乘積上。
- 除法：先將數字 treat as 整數進行除法，然後將小數點放在商上。
比較小數
- 小數可以通過比較每個位值的数字來進行比較。
- 例子：
- 0.45 大於 0.34，因為 5 大於 4。
- 小數也可以通過轉換為分數然后進行比較。
百分數
- 百分數是一種將值表示為 100 的分數的方法。
- 百分數可以通過除以 100 轉換為小數。
- 例子：
- 25% = 25/100 = 0.25
- 50% = 50/100 = 0.5
- 百分數也可以通過除以 100 並簡化轉換為分數。
- 例子：
- 25% = 1/4
- 50% = 1/2
計算百分數
- 若要找到某個數字的百分數，但需要將數字乘以百分數的小數形式。
- 例子：
- 120 的 25% = 120 x 0.25 = 30
- 若要找到某個數字是另一個數字的百分數，需要將第一個數字除以第二個數字乘以 100。
- 例子：
- 30 是 120 的百分數？= (30 ÷ 120) x 100 = 25%
實際應用
- 小數和百分數在日常生活中有著廣泛的應用，例如：
- 測量長度和重量
- 計算折扣和增值稅
- 理解體育統計和成績
- 比較價格和值
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