Place Value & Related Calculations — GCSE Maths Tutorial, Worked Examples & Practice

Revise Place Value & Related Calculations (digit values, multiplying/dividing by 10, 100, 1000 and using given calculations) within Number — Foundation Arithmetic, aligned to Edexcel, AQA & OCR GCSE (9–1) and International GCSE Maths. The interactive practice tool at the top of this page includes 30 self-marking practice questions across 3 structured skill steps, with instant diagnostic feedback and full worked solutions.

Step 1 of 310 interactive practice questions

Place Value, Words & Ordering Integers

Finding digit values, writing numbers in figures and using digit cards

Key Method & Revision Notes

Every digit in a number has a place value depending on which column it sits in:
Key Exam Tips:
• Read large integers in groups of three from the right: $\underbrace{4}_{\text{millions}},\underbrace{072}_{\text{thousands}},\underbrace{519}_{\text{units}}$.
• For the largest number from digit cards, arrange digits in descending order ($9 \to 0$).
• For an even number, the last (units) digit must be $0, 2, 4, 6,$ or $8$.

Worked Example

Question:

(a) Write down the value of the digit $8$ in $683{,}412$.

(b) Write two million, seventy thousand and fifty in figures.

Step-by-Step Solution:

(a) The $8$ is in the ten-thousands column $\rightarrow \mathbf{80{,}000}$.

(b) $2{,}000{,}000 + 70{,}000 + 50 = \mathbf{2{,}070{,}050}$.

(a) 80,000 • (b) 2,070,050

Ready to test this skill? Use the interactive tool at the top of the page to practise 10 self-marking exam-style questions (30 questions loaded in this topic module).

Step 2 of 310 interactive practice questions

Multiplying & Dividing by 10, 100 and 1000

Sliding digits left and right across the decimal point

Key Method & Revision Notes

The decimal point never moves — instead, the digits slide left or right across the columns:
Multiplying (Digits Move LEFT)
• $\times 10 \rightarrow 1$ place left
• $\times 100 \rightarrow 2$ places left
• $\times 1000 \rightarrow 3$ places left
Example: $3.07 \times 100 = 307$
Dividing (Digits Move RIGHT)
• $\div 10 \rightarrow 1$ place right

Worked Example

Question:

Work out: (a) $5.09 \times 1000$ (b) $34 \div 1000$

Step-by-Step Solution:

(a) Move digits $3$ places left: $5.09 \times 1000 = \mathbf{5090}$.

(b) Move digits $3$ places right: $34 \div 1000 = \mathbf{0.034}$.

(a) 5090 • (b) 0.034

Ready to test this skill? Use the interactive tool at the top of the page to practise 10 self-marking exam-style questions (30 questions loaded in this topic module).

Step 3 of 310 interactive practice questions

Related Calculations

Using a given product to deduce decimal multiplications and divisions

Key Method & Revision Notes

GCSE Non-Calculator papers regularly give you one worked calculation (such as $34 \times 57 = 1938$) and ask you to deduce related answers without multiplying everything out again:
Given $$34 \times 57 = 1938$$1. Multiplication: Track how each factor was scaled.
• $3.4 \times 5.7 = (34 \div 10) \times (57 \div 10) = 1938 \div 100 = \mathbf{19.38}$
• $340 \times 0.57 = (34 \times 10) \times (57 \div 100) = 1938 \div 10 = \mathbf{193.8}$
2. Division (Inverse): Start from $1938 \div 57 = 34$.
• $1938 \div 5.7$: dividing by a number $10\times$ smaller makes the answer $10\times$ bigger $\rightarrow \mathbf{340}$!

Worked Example

Question:

Given that $29 \times 46 = 1334$, write down the value of:

(a) $2.9 \times 4.6$ (b) $1334 \div 0.46$

Step-by-Step Solution:

(a) Both factors are divided by $10$, so divide $1334$ by $10 \times 10 = 100$: $\mathbf{13.34}$.

(b) Since $1334 \div 46 = 29$, dividing by $0.46$ ($100\times$ smaller) makes the answer $100\times$ larger: $\mathbf{2900}$.

(a) 13.34 • (b) 2900

Ready to test this skill? Use the interactive tool at the top of the page to practise 10 self-marking exam-style questions (30 questions loaded in this topic module).

Place Value & Related Calculations — GCSE Maths Tutorial, Worked Examples & Practice

Place Value, Words & Ordering Integers

Key Method & Revision Notes

Worked Example

Multiplying & Dividing by 10, 100 and 1000

Key Method & Revision Notes

Worked Example

Related Calculations

Key Method & Revision Notes

Worked Example

Related GCSE Maths Topics (Foundation Arithmetic)