Hint
Use the stated units and precision. Move the decimal point until the leading coefficient lies in [1,10).
Worked solution
(a)
The coefficient is at least 1 and below 10; multiplying by the given power recovers N.
Answer: \(\displaystyle \frac{41}{10}\times10^{7}\)
(b)
Count the decimal places moved.
\(7\)
Answer: \(7\)
(c)
Multiply the value by \(\displaystyle 10^{2}\).
\(4100000000\)
Answer: \(4100000000\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternative methods and consequential reasoning. An unexplained result does not earn a method mark.
(a) · 2 marks
- 1 mark: Choose a correctly normalised coefficient and its compensating power of ten.
- 1 mark: Give the complete requested result, using the required units, precision and boundary inclusion.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
(b) · 2 marks
- 1 mark: Count the decimal places moved.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Check the answer against the original conditions.
(c) · 2 marks
- 1 mark: Multiply the value by \(\displaystyle 10^{2}\).
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
Total: 6 marks.