GCSE Maths Practice: place-value-and-rounding

Question 9 of 10

This question checks your understanding of place value — how the position of a digit in a number changes its actual value. Once you understand this, rounding and comparing numbers become much easier.

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\( \begin{array}{l}\text{What is the place value of the digit }3\text{ in }53.65\text{?}\end{array} \)

Choose one option:

Exam tip: To find place value, label each position using a chart or spacing: Tens | Ones | . | Tenths | Hundredths. Then multiply the digit by its place value (e.g., 3 × 1 = 3). Remember, place ≠ place value!

Try more: 248, 0.39, 4,502.

Concept Overview

Understanding place value is one of the most important foundations in mathematics. Every digit in a number has a value that depends on its position. For example, the number 53.65 has two parts: the whole-number part (53) to the left of the decimal, and the fractional part (0.65) to the right of it.

The digits in each part represent different place values:

  • The 5 in 53.65 is in the tens place → value = 5 × 10 = 50
  • The 3 is in the ones place → value = 3 × 1 = 3
  • The 6 is in the tenths place → value = 6 × 0.1 = 0.6
  • The 5 is in the hundredths place → value = 5 × 0.01 = 0.05

Each time you move one place to the left, the place value becomes ten times bigger. Each move to the right makes it ten times smaller.

Step-by-Step Method

  1. Locate the digit: In 53.65, the digit 3 is just before the decimal point.
  2. Identify its place: The position directly before the decimal is the ones place.
  3. Calculate its value: 3 × 1 = 3.
  4. Write your answer clearly: The place value of 3 is 3.

Worked Examples

Example 1. What is the place value of 7 in 478?

  • 7 is in the tens place → value = 7 × 10 = 70.

Example 2. What is the place value of 2 in 0.254?

  • 2 is in the tenths place → value = 2 × 0.1 = 0.2.

Example 3. What is the place value of 9 in 9,036?

  • 9 is in the thousands place → value = 9 × 1000 = 9000.

Example 4. What is the place value of 4 in 345.2?

  • 4 is in the tens place → value = 4 × 10 = 40.

Common Mistakes

  • Confusing the place with place value: The place tells you where the digit is (ones, tens, etc.); the place value tells you how much it’s worth.
  • Ignoring the decimal point: Always notice where the decimal separates whole numbers and fractions.
  • Mixing up tenths and hundreds: Tenths = 0.1; hundredths = 0.01 — a tenfold difference!

Real-Life Applications

Place value is used every day, even outside the classroom:

  • Money: In £53.65, 3 represents £3 and 6 represents 60p (0.6 of a pound).
  • Measurement: In 53.65 cm, the 3 means 3 cm, while digits after the decimal show parts of a centimetre.
  • Data and coding: Computers use place value in binary (base-2) and hexadecimal systems, where the same principle applies.

Without understanding place value, it’s impossible to make sense of decimals, rounding, or even multiplication and division of large numbers.

FAQ

Q1: What is the difference between a digit and a number?
A: A digit is a single symbol (0–9). A number is made up of one or more digits, each with its own place value.

Q2: How do decimals fit into place value?
A: Digits to the right of the decimal show fractions of a whole — tenths, hundredths, thousandths, etc.

Q3: Why is the decimal point important?
A: It separates whole numbers from fractional parts. Moving one place right or left changes the value by a factor of ten.

Study Tip

When analysing place value, write out a place value chart showing thousands, hundreds, tens, ones, tenths, hundredths, and thousandths. Place each digit in its correct column. This method is especially helpful when working with large or decimal numbers in exams.