These are five questions and five answers:
a. State the speed in m/sec using scientific notation
i) Find the place value of the digit with the highest place value (the digit most to the left) in the number 300,000,000: hundred millions.
ii) Determine the number of zeros corresponding to that place value: 9
ii) Write the digit with the highest place value, mulitplied by the power of ten with exponent equal to the number of zeros corresponding to the place of such digit less 1 (9 - 1 = 8): 3 × 10⁸
iii) Complete with the units: 3 × 10⁸ m/s ← answer
b. State the speed in km/sec using scientific notation
i) State the conversion factor: 1 km = 1000 m = 10³ m
⇒ 1 = 1 km / 10³ m
ii) Multiply by the conversion factor:
3 × 10⁸ m/s × 1 km / (10³ m)
iii) Simplify (cancel the units that are common in the numerator and denominator)
3 × (10⁸ / 10³) km/s = 3 × 10⁵ km/s ← answer
c. State the number of seconds in one year using scientific notation
i) Find the place value of the digit with the highest place value (the digit most to the left) in the number 32,000,000: ten millions.
ii) Determine the number of zeros corresponding to that place value: 8
ii) Write the digit with the highest place value, as integer, add the other significant figures as decimals, mulitplied by the power of ten with exponent equal to the number of zeros corresponding to the place of the digit with highest place value less 1 (8 - 1 = 7): 3.2 × 10⁷
iii) Complete with the units: 3.2 × 10⁷ s ← answer
d. Calculate the distance in meters of one light year
i) distance formula: distance = speed × time
ii) Replace with the numbers in scientific notation:
distance = 3 × 10⁸ m/s × 3.2 × 10⁷ s
iii) Simplify (due the operations and cancel the units that are common in the numerator and denominator)
3 × 10⁸ m/s × 3.2 × 10⁷ s = 9.6 × 10 ¹⁵ m ← answer
e. State this distance in centimeters
i) State the conversion factor: 1m = 100 cm = 10² cm
⇒ 1 = 10² cm / 1 m
ii) Multiply by the conversion factor: 9.6 × 10 ¹⁵ m × 10² cm / 1 m
iii) Simplily: 9.6 × 10⁷ cm ← answer