GCSE Maths Practice: place-value-and-rounding

Question 10 of 10

This foundation-level question checks your understanding of place value. The number 642.13 has the digit 4 in the tens position, so its place value represents 4 groups of ten.

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\( \begin{array}{l}\text{What is the place value of the digit }4\text{ in }642.13\text{?}\end{array} \)

Choose one option:

Exam tip: Write each number in a place value table to avoid confusion. Remember that the tens place means multiplying by 10, the hundreds place means multiplying by 100, and so on. This simple trick helps prevent small errors in tests.

Try more: 237, 5,416, 0.54.

Concept Overview

Every digit in a number has a specific place value, which tells us how much it is worth depending on its position. As you move to the left in a number, the value of each place increases by ten times; as you move to the right, it decreases by ten times. This rule works for both whole numbers and decimals.

In the number 642.13:

  • The 6 is in the hundreds place → 6 × 100 = 600
  • The 4 is in the tens place → 4 × 10 = 40
  • The 2 is in the ones place → 2 × 1 = 2
  • The 1 is in the tenths place → 1 × 0.1 = 0.1
  • The 3 is in the hundredths place → 3 × 0.01 = 0.03

This means that 642.13 is the same as 600 + 40 + 2 + 0.1 + 0.03. Understanding this breakdown helps you see how every digit contributes to the total number.

Step-by-Step Method

  1. Locate the digit: Find the position of the 4 in 642.13.
  2. Identify the place: The 4 is in the tens place.
  3. Find its place value: Multiply 4 by 10 → 4 × 10 = 40.
  4. Write the final answer: The value of the digit 4 in this number is 40.

Worked Examples

Example 1. Find the place value of 7 in 572.

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

Example 2. Find the place value of 9 in 4,928.

  • 9 is in the hundreds place → value = 9 × 100 = 900.

Example 3. Find the place value of 3 in 0.36.

  • 3 is in the tenths place → value = 3 × 0.1 = 0.3.

Example 4. Find the place value of 5 in 5,047.

  • 5 is in the thousands place → value = 5 × 1000 = 5000.

Common Mistakes

  • Confusing the digit with its value: The digit 4 and its value 40 are not the same thing.
  • Ignoring the decimal part: Even if a number has decimals, the digits before the decimal point still follow the same place value pattern.
  • Mixing up the order: Remember, moving left multiplies by 10 each time (ones → tens → hundreds), and moving right divides by 10 each time (tenths → hundredths → thousandths).

Real-Life Applications

Understanding place value is essential in everyday life:

  • Money: £642.13 means 6 hundreds (£600), 4 tens (£40), 2 ones (£2), plus small decimals (13p).
  • Measurement: 642.13 metres can be broken down into 600 + 40 + 2 + 0.13 for more precise readings.
  • Population and statistics: Knowing place value helps you read large numbers such as 642,130 correctly (hundred-thousands, tens of thousands, etc.).

FAQ

Q1: What does “tens place” mean?
A: It means each digit in that place is worth 10 times the value of the ones place.

Q2: What happens if the digit is to the right of the decimal point?
A: Then the place values represent fractions — tenths, hundredths, thousandths, and so on.

Q3: How does place value help in rounding?
A: Rounding depends on understanding which digit affects the one you’re rounding to — that comes directly from place value knowledge.

Study Tip

Draw a place value chart with columns labelled Thousands | Hundreds | Tens | Ones | . | Tenths | Hundredths. Write the number 642.13 in it, and you’ll see that 4 sits neatly in the “Tens” column — making its value 40. Using visual aids like this can make place value much easier to remember in exams.