Lesson 4 - Dimensional Analysis
What is the perimeter in cm of a rectangular lot with a length of 5.5 m and a width of 3.25 m?
1750 cm
A hiker is standing 500 meters away from the base of a mountain. He measures the angle of elevation to the peak of the mountain as 30°. What is the height of the mountain in feet?
946.85 ft
It is a systematic mathematical method using conversion factors to convert from one unit of measurement to another.
Dimensional Analysis
A car travels 545 km in 3.5 hours. How fast is it going in meters per second?
43.25 m/s
A square has a side length of 8 cm. Inside the square, a smaller square is drawn with a side length of 4 cm, centered within the larger square. What is the area of the shaded region in square meters (the area of the larger square not covered by the smaller square)?
4.80 x 10⁻³ m²
Change 16°48’25” to decimal degrees.
16.81°
A rectangle has a length of 10 cm and a width of 6 cm. Inside the rectangle, a circle with a radius of 3 cm is inscribed. What is the area of the shaded region (the area of the rectangle not covered by the circle)?
31.73 cm²
Which of the following is NOT true regarding measurement in chemistry?
We make literary compositions.
A liquid sample has a density of 1.030 g/cm3. Calculate the mass in grams of the sample if its volume is equal to 235 cubic centimeters?
242.05 g
A standard metric ruler is divided into how many equal parts between the 0 cm and 1 cm mark?
10
What is the density in g/cm3 of 120 g of a metal if the metal raises the level of water in a graduated cylinder from 50 mL to 65 mL?
8 g/cm³
The mass of a given substance is 250 g. What is this mass in milligrams?
2.50 x 10^5 mg
The bus runs 5 km in 8 minutes. What is its speed in m/s?
10.42 m/s
What is 84°33'57" in decimal degrees?
84.57°
You measured the mass of three round metal chips. The measurements are: 5.95 g, 5.89 g, and 5.01 g. What is the total mass of the three metal chips in milligrams?
16,850 mg
Convert 4.57 x 10¹² m³ to mL.
4.57 × 10 ¹⁸ mL
How may square centimeters are there in 8.5 m²?
8.50 × 10⁴ cm²
A block of lead has dimensions of 4.50 cm by 5.20 cm by 6.00 cm. The block weighs 1.587 kg. From this information, calculate the density of lead in g/cm³
11.30 g/cm³
A surveyor is on top of a building that is 40 meters tall. From the top of the building, he observes a car on the ground at an angle of depression of 45°. What is the distance of the car from the building in cm?
4000 cm
How many divisions are found between 0 inch mark and 1 inch mark on a standard foot ruler?
16
Which of the following is a fundamental quantity?
Distance
Convert 23.45° to DMS.
23°27’00”
Convert 120 km/hr to m/s.
33.33 m/s
Convert 30°15’50” to decimal degree.
30.26°
On a standard foot ruler, how many inches are there?
12
The perimeter of a rectangular pool is 76 meters. The length of the pool is 19.50 meters. Calculate the width of the pool in centimeters.
1850 cm
Calculate the density in kg/m3 of a 15.80 g sample of which that was tested has a volume of 19.29 mL.
8.19 x 10² kg/m3
This figure is a right cylinder with radius of 2 m and a height of 10 m.
6.28 × 10⁷ m³
Consider a large rectangle with dimensions 10 cm by 15 cm. Inside this large rectangle, there is a smaller rectangle whose dimensions are 6 cm by 9 cm. What is the area of the shaded region in square meters? (The shaded region is outside the small rectangle.)
9.60 x 10⁻³ m²
Convert 156.742° to degree-minute-second (DMS) reading.
156°44'31"
Determination of dimensions, capacity ,quantity or extent of something.
Measurement
It is the ratio of the mass of an object to its volume.
Density
_________ is a physical science, one
that depends heavily on
measurement to obtain ____________
data.
Chemistry ; quantitative