Decimals and place value (Edexcel GCSE Maths): Revision Notes
Decimals and place value
Understanding place value diagrams
Place value diagrams help you understand the position and value of digits in decimal numbers. Each column represents a different place value, from largest to smallest.
Understanding place value is essential for working with decimals accurately. The position of each digit determines its actual value in the number.
The main place values you need to know are:
- Tens (10)
- Units (1)
- Tenths (0.1)
- Hundredths (0.01)
- Thousandths (0.001)
When working with decimals, remember that adding extra zeros at the end doesn't change the value. For example, is exactly the same as - the extra zero doesn't make it bigger or smaller.
Comparing decimal numbers
To compare decimal numbers effectively, you need to work systematically from left to right, checking each decimal place in turn.
Step-by-step method for comparing decimals:
- Start with the tenths place (first digit after the decimal point)
- If the tenths digits are the same, move to the hundredths place
- If the hundredths digits are the same, move to the thousandths place
- Continue until you find a difference
Let's see this method in action when comparing and :
Worked Example: Comparing 0.76 and 0.759
- Both have in the tenths place
- has in the hundredths place, has in the hundredths place
- Since , we know that 0.76 > 0.759
Ordering decimals from smallest to largest
When putting decimal numbers in order, use the same comparison method but apply it to all numbers systematically.
Exam tip: If all numbers have the same tenths digit, focus on comparing the hundredths digits first. This saves time and reduces errors.
Example process for ordering decimals:
- Look at all the tenths digits first
- Group numbers with the same tenths digit
- Within each group, compare hundredths digits
- Continue with thousandths if needed
- Always check your answer by crossing out each number as you include it in your final order
Multiplying and dividing by powers of 10
Understanding how digits move when multiplying or dividing by , , or is crucial for decimal calculations.
Multiplying by powers of 10
Key rule: When multiplying, digits move left in the place value system.
- Multiplying by 10: Digits move 1 place to the left
- Multiplying by 100: Digits move 2 places to the left
- Multiplying by 1000: Digits move 3 places to the left
Worked Example: Multiplying by 10
Each digit moves one place left - the decimal point appears to move one place to the right.
Dividing by powers of 10
Key rule: When dividing, digits move right in the place value system.
- Dividing by 10: Digits move 1 place to the right
- Dividing by 100: Digits move 2 places to the right
- Dividing by 1000: Digits move 3 places to the right
Worked Example: Dividing by 100
Each digit moves two places right - the decimal point appears to move two places to the left.
Exam techniques and common mistakes
Writing place values: When asked for the place value of a digit, give the complete value. For example, the place value of in is hundredths, not just "hundredths position."
Ordering numbers: Start with the smallest number or the largest - choose whichever feels more natural to you. Both approaches work equally well.
Checking your work: Always verify multiplication and division by working backwards. If , then should give you .
Key concepts summary
Key Points to Remember:
- Place value diagrams help you understand decimal positions - tens, units, tenths, hundredths, thousandths
- Compare decimals by working left to right through each decimal place systematically
- Adding zeros at the end of decimals doesn't change their value ()
- Multiplying by powers of 10 moves digits left; dividing moves digits right
- Always check your answers and cross out numbers as you use them in ordering questions