Write very large and very small numbers in standard form, convert back, and multiply numbers written that way.
What you practise
Converting to and from standard form
Positive and negative powers of 10
Multiplying in standard form
Ends with products that need adjusting to keep the number in front between 1 and 10. Practice moves up a level when a round goes well and down when it does not.
Sample questions
Each sample comes with the method and the reason every wrong option is wrong. Real practice rounds are ten questions at your level.
Sample question, level 2 of 5
Write 0.00097 in standard form.
9.7 × 10⁻³
9.7 × 10⁻⁴
0.97 × 10⁻⁵
9.7 × 10⁻⁵
9.7 × 10⁴
Show the answer and method
Answer: B, 9.7 × 10⁻⁴
The method: Move the decimal point right 4 places to get 9.7. Moving right makes the power negative: 0.00097 = 9.7 × 10⁻⁴.
Why the other options are wrong:
A, 9.7 × 10⁻³: The power is one too small in size. Count the places the decimal point moves.
C, 0.97 × 10⁻⁵: The number in front must be at least 1 and less than 10.
D, 9.7 × 10⁻⁵: The power is one too big in size. Count the places the decimal point moves.
E, 9.7 × 10⁴: A number smaller than 1 has a negative power of 10.
Sample question, level 4 of 5
Work out (2.5 × 10⁶) × (3 × 10³). Give your answer in standard form.
7.5 × 10¹⁸
5.5 × 10⁹
7.5 × 10⁸
7.5 × 10⁹
7.5 × 10¹⁰
Show the answer and method
Answer: D, 7.5 × 10⁹
The method: Multiply the numbers: 2.5 × 3 = 7.5. Add the powers: 6 + 3 = 9. So the answer is 7.5 × 10⁹.
Why the other options are wrong:
A, 7.5 × 10¹⁸: The powers were multiplied. When multiplying powers of 10, add the powers.
B, 5.5 × 10⁹: The numbers in front were added instead of multiplied.
