Working With Data - Decimal Places, Significant Figures And Standard Form

Your specification says you should be able to:
1. Recognise and use expressions in decimal form.
2. Use an appropriate number of significant figures.
3. Recognise and use expressions in standard form.

Decimal Places

• Decimal places show how many digits are after the decimal point.
• E.g. 4.5678 rounded to 2 decimal places is 4.57.
• In biology data tables, results should be rounded to the same number of decimal places for consistency.

How to round:

• Find the last digit to keep.
• Look at the next digit:
  
  • If 5 or more → round up.
  • If less than 5 → keep the same.

Practice:

• Round 6.378 to 1 d.p.: 6.4
• Round 0.54321 to 3 d.p.: 0.543

Significant Figures

• Show the precision of a measurement.
• Always start counting from the first non-zero digit.
• Zeros between significant digits are significant.
• Zeros at the end of a number with a decimal point are significant.
  

Examples:

• 0.00456 → This number has 3 s.f. (456)
• 12300 → This number has 3 s.f. (123)
• 2.300 → This number has 4 s.f. (2300)

Practice:

• Write 45.678 to 2 s.f. = 46
• Write 0.009876 to 3 s.f. = 0.00988
• Write 5078 to 3 s. f. = 5080

Did you get the last one correct? Let me explain why…

Step-by-step:

• First s.f. is 5
• Second s.f. is 0 (zeros between significant digits count!)
• Third s.f.is 7

Look at the next digit (8):

• 8 is 5 or more, so round the 7 up to 8.

So:

• 5078 → 3 s.f. → 5080

Standard Form

• Very useful for large or small numbers, e.g. bacteria populations.
• Format: a × 10ⁿ
  
  • a must be between 1 and 10.
  • n is the number of places you move the decimal.

Examples:

• 3500 = 3.5 × 10³
• 0.00042 = 4.2 × 10⁻⁴

Steps:

1. Move the decimal to get a number between 1 and 10.
2. Count how many places you moved - that’s the exponent.

• • Left = positive exponent.
  • Right = negative exponent.

Practice:

• Write 0.00067 in standard form: 6.7 × 10⁻⁴
• Write 98700 in standard form: 9.87 × 10⁴

Practice Questions