Scientific Notation
Write 3.456 x 104 in Standard Form.
34,560
How many meters are in 3 kilometers?
3,000 m
How many significant figures are in 4,582?
4. All nonzero digits are significant.
A student walks 40 m east, then 30 m west. Find the distance traveled and the displacement.
Distance = 40 + 30 = 70 m. Displacement = 40 − 30 = 10 m east.
A car travels 150 km in 3 hours. What is its average speed?
Speed = 150 ÷ 3 = 50 km/h
Write 0.00072 in Scientific Notation
7.2 x 10-4
Convert 450 centimeters to meters.
4.5 m
How many significant figures are in 0.0072?
2. The leading zeros only hold the decimal place, so only the 7 and 2 count.
A runner completes one full lap of a 400 m track and ends where she started. Find the distance and the displacement.
Distance = 400 m. Displacement = 0 m, because she ended at the starting point.
A swimmer swims 200 m in 80 seconds. What is her average speed?
Speed = 200 ÷ 80 = 2.5 m/s
Write 3.08 x 10-5 in Standard Form
0.0000308
A bottle holds 2,500 milliliters. How many liters is that?
2.5 L
How many significant figures are in 3,050?
3. The zero between 3 and 5 is significant, but the trailing zero with no decimal point is not.
A cyclist rides 8 km east, then 3 km west, then 6 km east. Find the distance and the displacement.
Distance = 8 + 3 + 6 = 17 km. Displacement = 8 − 3 + 6 = 11 km east.
A student walks 40 m east, then 10 m west, in a total of 25 seconds. Find his average speed and his average velocity.
Answer: Distance = 40 + 10 = 50 m, so speed = 50 ÷ 25 = 2 m/s. Displacement = 40 − 10 = 30 m east, so velocity = 30 ÷ 25 = 1.2 m/s east.
Write 45,600,000 in Scientific Notation
4.56 x 107
Convert 6 kilograms to grams, then to milligrams.
6,000g, which is 6,000,000mg
How many significant figures are in 0.04200?
4. The leading zeros don't count, but the 4, 2, and both trailing zeros do, because the trailing zeros come after a decimal point.
A delivery driver goes 7 km north, then 4 km south, then 2 km north, then 5 km south. Find the distance and the displacement.
Distance = 7 + 4 + 2 + 5 = 18 km. Net north = 7 + 2 = 9 km and net south = 4 + 5 = 9 km, so displacement = 0 km. The driver ends at the starting point.
A cyclist travels at an average speed of 6 m/s for 2 minutes. How far does she travel?
Time = 2 × 60 = 120 s. Distance = speed × time = 6 × 120 = 720 m.
A student writes 63 × 10⁻⁴ and says it is in scientific notation. Explain what is wrong, then give the correct scientific notation and the standard form.
Correct scientific notation is 6.3 × 10⁻³, and standard form is 0.0063.
Convert 0.35 kilometers to centimeters. Give your answer in standard form and in scientific notation.
35,000 cm, which is 3.5 × 10⁴ cm
How many significant figures are in 6.0200 × 10⁴, and why does the 10⁴ not affect the count?
5. The digits 6, 0, 2, 0, 0 are all significant: the zero between nonzero digits counts, and the trailing zeros count because they follow a decimal point. The 10⁴ only sets the size of the number and is not a measured digit.
A student walks 9 m east, 8 m north, 3 m west, then 2 m south. Find the distance and the magnitude of the displacement. Round displacement to the nearest tenth.
Distance = 9 + 8 + 3 + 2 = 22 m. Net east = 9 − 3 = 6 m, and net north = 8 − 2 = 6 m. Displacement = √(6² + 6²) = √72 ≈ 8.5 m (northeast, at 45° north of east).
A runner goes 300 m east in 60 seconds, then turns around and runs 300 m west back to the start in 90 seconds. Find his average speed and average velocity for the whole trip.
Total distance = 600 m and total time = 150 s, so speed = 600 ÷ 150 = 4 m/s. Displacement = 0 m, so velocity = 0 ÷ 150 = 0 m/s.