Bounds Patrol

Bounds Patrol 📏

Real measurements are never perfectly exact, so we **round** them, **estimate** with them, and state the **interval** they truly lie in. Three skills patrol this topic: rounding (decimal places and significant figures), quick estimation, and error bounds. Suit up.

Decimal places and significant figures 🔢

Two ways to round: • **Decimal places (dp)** — count digits after the decimal point. 3.14159 to 2 dp = 3.14. • **Significant figures (sf)** — count from the **first non-zero** digit. Leading zeros do **not** count, so 0.00408 to 2 sf = 0.0041. In both, look at the **next** digit: 5 or more rounds up.

Round to 2 decimal places

An interactive activity.

Round to 2 significant figures

An interactive activity.

Significant figures

Round 34,700 to 2 significant figures.

• 35,000
• 34,000
• 35
• 34,700

Match each rounding to its result

Estimation 🧮

To **estimate** a calculation quickly, round every number to **1 significant figure**, then work it out: **31 × 19 ≈ 30 × 20 = 600.** The answer is not exact, but it is close and easy — perfect for checking a calculator answer is sensible. Use the ≈ ("approximately equal") sign.

Order the method

An interactive activity.

Estimate the product

An interactive activity.

Error intervals ✳️

A rounded measurement hides a range. A value rounded to the nearest unit could be up to **half a unit** either way: A length of **12 cm to the nearest cm** lies in **11.5 ≤ x < 12.5**. The **lower bound** (11.5) is **included** (≤), but the **upper bound** (12.5) is **excluded** (<) — because 12.5 would itself round up to 13.

Upper and lower bounds

A distance is 20 m measured to the nearest 10 m. Pick the TWO values that are its lower and upper bounds.

• 15 m
• 25 m
• 20 m
• 10 m

The accuracy rules

To estimate a calculation, round each number to 1 _____ figure first. A length given as 12 cm to the nearest cm has a lower bound of _____ cm. When counting significant figures, leading _____ do not count.