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