Rounding & Estimation

4 minQuiz at the end

Why Round Numbers?

Exact numbers aren't always necessary. Rounding makes numbers easier to work with and helps check whether answers are reasonable.

Rounding Rules

  1. Identify the target place (e.g., tens, hundreds, 1 decimal place)
  2. Look at the digit immediately to its right
  3. If it's 5 or more β†’ round up; if it's 4 or less β†’ round down (keep the same)

Rounding to the Nearest …

Nearest hundred: 3,748 β†’ look at tens digit (4 < 5) β†’ round down β†’ 3,700 Nearest ten: 3,748 β†’ look at ones digit (8 β‰₯ 5) β†’ round up β†’ 3,750

Rounding Decimals

1 decimal place (1 d.p.): 6.285 β†’ look at the second decimal (8 β‰₯ 5) β†’ round up β†’ 6.3

2 decimal places (2 d.p.): 6.285 β†’ look at third decimal (5 β‰₯ 5) β†’ round up β†’ 6.29

Significant Figures

Significant figures (s.f.) start from the first non-zero digit:

  • 3,748 to 2 s.f. β†’ 3,700
  • 0.00452 to 2 s.f. β†’ 0.0045 (first s.f. is 4, second is 5)

Estimation

Use rounding to estimate answers before calculating:

  • 48.7 Γ— 3.1 β‰ˆ 50 Γ— 3 = 150 (quick check that 151.97 is reasonable βœ“)

Estimation catches large errors in calculations.