GCSE Maths Practice: place-value-and-rounding

Concept Overview

Rounding decimals to the nearest tenth is one of the most common forms of estimation in GCSE Maths. It helps us simplify long decimals into values that are easier to read and compare. The tenths place is the first digit after the decimal point. To decide whether to round this digit up or keep it the same, we check the hundredths digit — the next digit to the right.

In this question, the number is 8.375. The tenths digit is 3 and the hundredths digit is 7. Because 7 is greater than or equal to 5, we round the tenths digit up by one, giving 8.4. If the hundredths digit had been 4 or less, we would keep it the same and write 8.3 instead. This simple rule makes rounding consistent for all decimals.

Step-by-Step Method

1. Locate the tenths digit: The first digit after the decimal (3 in 8.375).
2. Look one place to the right: The hundredths digit (7) decides the rounding direction.
3. Apply the rule: 7 ≥ 5 → round up → 3 becomes 4.
4. Drop the rest: Remove digits after the tenths place. Final result = 8.4.

Worked Examples

Example 1: Round 5.86 to the nearest tenth.

• Tenths = 8; hundredths = 6.
• 6 ≥ 5 → increase tenths → 5.9.

Example 2: Round 7.32 to the nearest tenth.

• Tenths = 3; hundredths = 2.
• 2 < 5 → keep tenths → 7.3.

Example 3: Round 4.95 to the nearest tenth.

• Tenths = 9; hundredths = 5.
• Round up: 9 → 10 → carry 1 to the whole number. Result = 5.0.

Common Mistakes

• Looking at the wrong digit: Some learners check the thousandths digit instead of the hundredths digit.
• Writing 8.35: This shows rounding to the hundredth, not the tenth.
• Forgetting to carry when rounding from 9: For example, 4.95 → 5.0, not 4.10.
• Dropping trailing zeros: Writing 5 instead of 5.0 loses the place value meaning.

Real-Life Applications

Rounding to the nearest tenth is used every day in measurement, science, and finance. Here are some examples:

• Temperature: Weather forecasts often round 8.375°C to 8.4°C for easier reading.
• Cooking and recipes: 8.375 grams might be rounded to 8.4 grams for convenience.
• Sports timing: A runner’s time of 8.375 seconds might be displayed as 8.4 seconds.
• Finance: When working with money in pounds, £8.375 would round to £8.38 when rounded to the nearest penny, but £8.4 when rounded to the nearest tenth of a pound.

These examples show that rounding is not just a school skill — it’s a key tool for clear communication in daily life.

Visualising Rounding

Imagine a number line between 8.3 and 8.4. The midpoint is 8.35. Since 8.375 is past the midpoint, it’s closer to 8.4. This visual method helps you understand why the answer is 8.4, not 8.3.

FAQ

Q1: What does rounding mean?
A: Rounding means finding a nearby number that is simpler to work with, while still being close to the original value.

Q2: Why is 8.375 closer to 8.4 than 8.3?
A: Because it is past the halfway point (8.35), so it’s nearer to 8.4.

Q3: Why is 8.35 considered the midpoint?
A: The halfway value between 8.3 and 8.4 is 8.35 — that’s why anything from 8.35 and above rounds up.

Study Tip

Always underline the digit you’re rounding to and circle the next digit. Then apply the simple rule: 0–4 → stay; 5–9 → round up. If you find decimals confusing, write them on a number line — it’s a powerful way to see which rounded value is closer.