Standard form arithmetic
AQA GCSE Maths revision on Standard form arithmetic. Aligned to the AQA GCSE Mathematics 8300 specification. This bank has 16 practice questions on this topic.
Sample questions (3 of 16)
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Question 1
When adding two numbers in standard form, why must the powers of 10 be identical before performing the addition?
- A) To ensure the digits represent the same place value columns.
- B) To make the final result a smaller number.
- C) Because the index laws only apply to multiplication.
- D) To avoid the need to use a calculator.
Show answer
Answer: To ensure the digits represent the same place value columns.
In decimal arithmetic, you cannot add units to tens without adjusting; the same applies to standard form. By making the powers of 10 equal, you align the place values of the significant figures, allowing for direct addition of the coefficients. Failing to do this results in adding values of different magnitudes incorrectly.
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Question 2
A student calculates (2 x 10^3) x (4 x 10^5) and writes 8 x 10^15. What is the fundamental error in their reasoning?
- A) They multiplied the powers of 10 instead of adding them.
- B) They forgot to square the coefficients.
- C) They added the coefficients instead of multiplying them.
- D) They failed to convert the answer back into standard form.
Show answer
Answer: They multiplied the powers of 10 instead of adding them.
When multiplying terms with the same base, the index law states that you must add the exponents (a^m x a^n = a^(m+n)). The student erroneously multiplied the indices (3 x 5 = 15) instead of adding them (3 + 5 = 8).
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Question 3
If you multiply a number in standard form by 10, what happens to the exponent?
- A) It increases by 1.
- B) It doubles.
- C) It remains unchanged.
- D) It decreases by 1.
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Answer: It increases by 1.
Standard form is defined as a x 10^n. Multiplying by 10^1 adds 1 to the exponent n because 10^n x 10^1 = 10^(n+1). This is consistent with how place value works in our base-10 number system.
Want to test yourself on the remaining cards for this topic?
13 more questions on Standard form arithmetic — plus mistakes tracking and spaced repetition across the whole Maths spec.