Convert 159 mi/h to m/s.
Convert 4.45 103 kg/m3 to g/cm3.
please explain in detail with full steps
you can always multiply by 1 without changing anything.
1h = 3600s
That means that 1h/3600s = 3600s/1h = 1
Now you don't have to worry whether to multiply or divide -- just multiply using the version of 1 that cancels the unwanted units. For example,
159 mi/h * 1h/3600s * 1609.344m/mi = 71.079 m/s
Do any other unit conversions in like wise.
The secret to conversions is to keep the units straight. Here is a detailed explanation; it would be much easier to do in person. Let's take a simple one. Convert 15 feet to inches.
Step 1. What is the factor? Actually there are two factors; i.e., they are 12 in/1 ft OR 1 ft/12 in. Your job is to determine which factor to use and you have a 50% change of getting it right if you just guess. But there is no reason to guess and you can get it right all the time.
Step 2. Multiply 15 ft x factor = ? inches
Step 3. So let's just multiply by the two factors for the fun of it to see what we get. Don't multiply just the numbers but do the units also.
a. 15 ft x (1 ft/12 in) = 1.25 ft^2/in
b. 15 ft x (12 in/1 ft) = 180 in. (Note that the ft unit cancels and the inch unit is the only unit let. Note also that the inch unit is what we want.)
Step 4. You KNOW the answer must come out in inches because the problem is to convert to inches so you KNOW 3b must be the correct way to set up the problem. That's the secret of all of these conversions; i.e. to use the factor in such a manner (one of two choices) so as to make the units come out to what you want.
So on to 159 mi/hr to m/s. You can look in tables to obtain a factor for miles to meters but to give practice let's use factors that are more common such as 1 mile = 5,280 ft
1 ft = 12 inches
1 in - 2.54 cm
100 cm = 1 m
and for the time we can use
1 hr = 60 min
1 min = 60 sec so the set up would look like this. Remember we're just convert miles to feet to inches to cm to m and hr to min to sec. It looks like this.
159 mi/hr x (5,280 ft/mi) x (12 in/ft) x (2.54 cm/in) x (1 m/100 cm) x (1 hr/60 min) x (60 sec/1 min) = ? m/s and I get about 71.08 m/s.
The other problem is done the same way.
Post your work if you get stuck. Good luck.
To convert 159 mi/h to m/s, we can follow the following steps:
Step 1: Set up the conversion factor.
We know that 1 mile is equal to 1.60934 kilometers, and 1 kilometer is equal to 1000 meters. Additionally, 1 hour is equal to 3600 seconds. Therefore, we have the following conversion factors:
1 mi = 1.60934 km
1 km = 1000 m
1 h = 3600 s
Step 2: Use the conversion factors to cancel out the units.
We want to convert from miles per hour (mi/h) to meters per second (m/s). We can start by converting miles to kilometers, then kilometers to meters, and finally, hours to seconds.
159 mi/h * (1.60934 km / 1 mi) * (1000 m / 1 km) * (1 h / 3600 s)
Step 3: Perform the calculations.
First, we convert miles to kilometers:
159 mi * (1.60934 km / 1 mi) = 255.53906 km/h
Next, we convert kilometers to meters:
255.53906 km * (1000 m / 1 km) = 255539.06 m/h
Finally, we convert hours to seconds:
255539.06 m/h * (1 h / 3600 s) = 70.98307333 m/s
Therefore, 159 mi/h is equivalent to approximately 70.98 m/s.
Now let's convert 4.45 * 10^3 kg/m^3 to g/cm^3.
Step 1: Set up the conversion factor.
We know that 1 kilogram is equal to 1000 grams, and 1 meter is equal to 100 centimeters. Therefore, we have the following conversion factors:
1 kg = 1000 g
1 m = 100 cm
Step 2: Use the conversion factors to cancel out the units.
We want to convert from kilograms per cubic meter (kg/m^3) to grams per cubic centimeter (g/cm^3). We can start by converting kilograms to grams and meters to centimeters.
4.45 * 10^3 kg/m^3 * (1000 g / 1 kg) * (1 m / 100 cm) * (1 m / 100 cm) * (1 m / 100 cm)
Step 3: Perform the calculations.
First, we convert kilograms to grams:
4.45 * 10^3 kg * (1000 g / 1 kg) = 4.45 * 10^6 g/m^3
Next, we convert meters to centimeters:
4.45 * 10^6 g/m^3 * (1 m / 100 cm) * (1 m / 100 cm) * (1 m / 100 cm) = 4.45 g/cm^3
Therefore, 4.45 * 10^3 kg/m^3 is equivalent to 4.45 g/cm^3.