Accuracy, bounds, measures and money

Q: How do you round a number to a specific number of decimal places (dp)?

Count the specified number of digits after the decimal point, then look at the next digit: if it is 5 or more, round the last digit up; if it is 4 or less, leave it the same.

Q: What are significant figures (sf) and how do you identify the first one?

Significant figures indicate the precision of a value; the first significant figure is always the first non-zero digit in the number when reading from left to right.

Q: What is the "Half-Unit" rule for finding upper and lower bounds?

Identify the degree of accuracy (the unit), divide it by 2, then add this value to the measurement for the Upper Bound and subtract it for the Lower Bound.

Q: How do you find the Upper Bound of a division calculation ($ A / B $)?

To find the maximum possible result of a division, divide the Upper Bound of the numerator by the Lower Bound of the denominator: $ \frac{\text{UB}_A}{\text{LB}_B} $.

Q: What are the standard metric conversions for length and mass?

Length: $ 10 \text{ mm} = 1 \text{ cm} $, $ 100 \text{ cm} = 1 \text{ m} $, $ 1000 \text{ m} = 1 \text{ km} $. Mass: $ 1000 \text{ g} = 1 \text{ kg} $, $ 1000 \text{ kg} = 1 \text{ tonne} $.

Q: What is the formula for average speed, and how should time be formatted?

$ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} $; time must be converted into a decimal format (e.g., 30 mins = 0.5 hours).

Q: How do you convert between two currencies using an exchange rate?

To convert from the base unit (usually 1) to the other currency, multiply by the rate. To convert back to the base unit, divide by the rate.

Mathematics (Specification B) · Pearson Edexcel IGCSE · 5 min read · Updated: 7 Sept 2026

Welcome to Accuracy, Bounds, Measures and Money!

In this chapter, we explore how we deal with numbers in the real world. Whether you are measuring the length of a football pitch, converting your pocket money for a holiday, or figuring out the maximum weight a bridge can hold, you need to understand accuracy and measures. Don't worry if these terms sound technical—we will break them down step-by-step!

Note: This chapter focuses on the "Number" part of your syllabus. For more on fractions or standard form, check out the other chapters in this section.

1. Accuracy: Rounding Numbers

In maths, we don't always need every single digit of a number. Rounding helps make numbers easier to work with. There are two main ways the Edexcel Specification B exam will ask you to round:

Decimal Places (dp)

This tells you how many digits to keep after the decimal point.

Example: Round $ 5.672 $ to $ 2 $ decimal places.
Look at the 3rd decimal digit ($ 2 $). Since it is less than $ 5 $, we keep the second digit as it is.
Answer: $ 5.67 $.

Significant Figures (sf)

Significant figures start from the first non-zero digit.

Example 1: $ 4038 $ to $ 2 $ sf is $ 4000 $.
Example 2: $ 0.00567 $ to $ 2 $ sf is $ 0.0057 $ (The zeros at the start don't count!).

Quick Tip: If the next digit is $ 5 $ or more, round UP. If it is $ 4 $ or less, keep it the SAME. A simple rhyme to remember: "Five or more, let it soar; four or less, let it rest!"

Key Takeaway: Always read the question carefully to see if it asks for decimal places or significant figures!

2. Upper and Lower Bounds

When a number is rounded, we lose a bit of the original value. Bounds tell us the range of values the original number could have been.

The "Half-Unit" Rule

To find the bounds, look at the degree of accuracy and divide it by 2. Then add it for the Upper Bound and subtract it for the Lower Bound.

Example: A bag of flour weighs $ 5 $ kg to the nearest kg.

The "unit" is $ 1 $ kg.
Half the unit is $ 0.5 $ kg.
Lower Bound (LB): $ 5 - 0.5 = 4.5 $ kg.
Upper Bound (UB): $ 5 + 0.5 = 5.5 $ kg.

We can write this as an error interval: $ 4.5 \le \text{weight} < 5.5 $.

Bounds in Calculations

Sometimes you need to find the maximum or minimum result of a calculation:

To get the maximum (Upper Bound) of $ A + B $: Use $ \text{UB}_A + \text{UB}_B $.
To get the maximum (Upper Bound) of $ \frac{A}{B} $: Use $ \frac{\text{UB}_A}{\text{LB}_B} $ (Big number divided by a small number).

Common Mistake: For the Upper Bound of a division or subtraction, students often use two Upper Bounds. Remember: To make a result as small as possible in subtraction, take the largest amount away from the smallest start ($ \text{LB} - \text{UB} $).

Key Takeaway: Bounds define the "window" of possibility for a rounded measurement.

3. Weights and Measures

In your exam, you will only use Metric and SI units. You should be comfortable converting between them.

Length and Mass

Length: $ 10 \text{ mm} = 1 \text{ cm} $; $ 100 \text{ cm} = 1 \text{ m} $; $ 1000 \text{ m} = 1 \text{ km} $.
Mass: $ 1000 \text{ g} = 1 \text{ kg} $; $ 1000 \text{ kg} = 1 \text{ tonne} $.
Capacity/Volume: $ 1000 \text{ ml} = 1 \text{ litre} $; $ 1 \text{ cm}^3 = 1 \text{ ml} $.

Average Speed

Speed is a measure of how far you go in a certain amount of time. The formula is:

$ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} $

Did you know? If you are given a time like $ 1 $ hour and $ 30 $ minutes, you must convert it to a decimal before calculating speed. $ 1 \text{ hour } 30 \text{ mins} = 1.5 \text{ hours} $, not $ 1.3 $!

Key Takeaway: Always check that your units match (e.g., if distance is in km and time is in hours, speed should be in km/h).

4. Money and Currency Conversion

Money questions usually involve basic arithmetic or changing from one currency to another (like $\text{\pounds}$ to $\$$).

Currency Conversion

The exam will always give you the exchange rate.
Example: $ \text{\pounds}1 = 1.20 \text{ Euros} $.

To change from $\text{\pounds}$ to Euros: Multiply by $ 1.20 $.
To change from Euros back to $\text{\pounds}$: Divide by $ 1.20 $.

Real-world Tip: If you're stuck, look at the numbers. If $ \text{\pounds}1 $ is worth more than $ 1 $ unit of another currency, your final answer in that other currency should be a bigger number!

Key Takeaway: Multiply to go "forward" through the exchange rate, divide to go "backward".

Quick Review Box

1. Rounding: "5 or more, round up."
2. Bounds: Find half the degree of accuracy, then $ + $ and $ - $.
3. Speed: $ \text{Speed} = \frac{\text{Distance}}{\text{Time}} $.
4. Money: Always use the provided exchange rate; multiply to convert from the base unit ($ 1 $).

You've reached the end of the notes for Accuracy, Bounds, Measures and Money. Ready to try some practice questions? You've got this!

Quick check

Can you answer these now?

Open each question to check the key ideas from this chapter.

How do you round a number to a specific number of decimal places (dp)?

Count the specified number of digits after the decimal point, then look at the next digit: if it is 5 or more, round the last digit up; if it is 4 or less, leave it the same.

What are significant figures (sf) and how do you identify the first one?

Significant figures indicate the precision of a value; the first significant figure is always the first non-zero digit in the number when reading from left to right.

What is the "Half-Unit" rule for finding upper and lower bounds?

Identify the degree of accuracy (the unit), divide it by 2, then add this value to the measurement for the Upper Bound and subtract it for the Lower Bound.

How do you find the Upper Bound of a division calculation ($ A / B $)?

To find the maximum possible result of a division, divide the Upper Bound of the numerator by the Lower Bound of the denominator: $ \frac{\text{UB}_A}{\text{LB}_B} $.

What are the standard metric conversions for length and mass?

Length: $ 10 \text{ mm} = 1 \text{ cm} $, $ 100 \text{ cm} = 1 \text{ m} $, $ 1000 \text{ m} = 1 \text{ km} $. Mass: $ 1000 \text{ g} = 1 \text{ kg} $, $ 1000 \text{ kg} = 1 \text{ tonne} $.

What is the formula for average speed, and how should time be formatted?

$ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} $; time must be converted into a decimal format (e.g., 30 mins = 0.5 hours).

How do you convert between two currencies using an exchange rate?

To convert from the base unit (usually 1) to the other currency, multiply by the rate. To convert back to the base unit, divide by the rate.

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