OCR GCSE Maths: Decimal Calculations and Place Value

OCR GCSE Maths: Decimal Calculations and Place Value

Understanding Decimal Place Value

Decimals represent parts of a whole number. Each digit in a decimal has a specific place value, determined by its position relative to the decimal point.

Example:

  3  .  2  4  5
  ^  ^  ^  ^  ^
  Hundreds  Tens  Units  Tenths  Hundredths

• Units: The digit to the left of the decimal point represents the whole number.
• Tenths: The first digit to the right of the decimal point represents tenths (1/10).
• Hundredths: The second digit to the right of the decimal point represents hundredths (1/100).
• Thousandths: The third digit to the right of the decimal point represents thousandths (1/1000), and so on.

Converting Fractions to Decimals

To convert a fraction to a decimal, divide the numerator by the denominator.

Example:

1/4 = 1 ÷ 4 = 0.25

Adding and Subtracting Decimals

1. Align the decimal points: Write the numbers vertically, ensuring the decimal points are in the same column.
2. Fill in any gaps with zeros: Add zeros to the right of the decimal point in shorter numbers to ensure the same number of digits after the decimal point.
3. Add or subtract as usual: Perform the operation as you would with whole numbers.
4. Carry the decimal point down: Ensure the decimal point in the answer is aligned with the others.

Example:

  2.35
+ 1.7
-------
  4.05

Multiplying Decimals

1. Ignore the decimal points: Multiply the numbers as you would with whole numbers.
2. Count the total decimal places: Count the total number of decimal places in both numbers.
3. Place the decimal point: Count from the rightmost digit in your answer and place the decimal point so that you have the same number of decimal places as in step 2.

Example:

  2.5  (1 decimal place)
x 1.3  (1 decimal place)
-------
  75
+250
-------
  3.25 (2 decimal places)

Dividing Decimals

1. Move the decimal point in the divisor to the right: Make the divisor a whole number.
2. Move the decimal point in the dividend the same number of places: This must be done to the right.
3. Divide as usual: Now you are dividing a decimal by a whole number.

Example:

   0.5 ÷ 0.25  =  5 ÷ 2.5  =  2

Working with Negative Decimals

• Adding: When adding a negative decimal, it is the same as subtracting the positive version of that decimal.
• Subtracting: When subtracting a negative decimal, it is the same as adding the positive version of that decimal.
• Multiplying and dividing: Follow the same rules as for positive decimals, paying attention to the rules of signs for multiplication and division.

Example:

  -2.5 + 3.2 =  0.7
  -2.5 - (-3.2) = -2.5 + 3.2 = 0.7

Applying Decimals in Context

Decimals are used in various contexts, including:

• Financial calculations: Dealing with money, prices, interest rates.
• Measurements: Length, weight, volume, temperature.
• Data analysis: Representing percentages, averages, and statistics.

Example:

• Financial: Calculate the total cost of 2.5 kg of apples at £1.80 per kg.
• Measurement: Convert 1.5 meters to centimeters.
• Data analysis: Determine the average temperature from a set of decimal readings.

Practice Makes Perfect

Practice these concepts regularly to solidify your understanding and become confident in working with decimals. Use practice problems, online resources, or textbooks to enhance your skills.