Convert 2.87 kg to grams. Use only the metric system. STARTING AMOUNT ADD FACTOR ANSWER PERCENT 10 0.01 28.7 0.287 0.001 2.87 2870 100 0.1 1000 0.00287 kg
The Correct Answer and Explanation is:
Of course. Here is the solution to the conversion problem.
Correct Answer:
To correctly solve the problem on the screen, you would fill the boxes as follows:
- STARTING AMOUNT: In the first box, enter 2.87. In the second box, enter kg.
- CONVERSION FACTOR (the fraction):
- In the top left box, enter 1000. In the top right box, enter g.
- In the bottom left box, enter 1. In the bottom right box, enter kg.
- ANSWER: The final answer is 2870 g.
Explanation of the Conversion
The problem asks to convert 2.87 kilograms (kg) to grams (g) using the factor-label method, also known as dimensional analysis. This method uses conversion factors to change units without changing the value of the quantity.
First, you must identify the starting amount, which is given as 2.87 kg. This value is placed in the “STARTING AMOUNT” section of the interface, with 2.87 in the number field and kg in the unit field.
Next, you need the correct conversion factor that relates kilograms and grams. Within the metric system, the prefix “kilo” means 1,000. Therefore, the fundamental relationship is that 1 kilogram is equal to 1,000 grams. This relationship can be written as a fraction in two ways: (1000 g / 1 kg) or (1 kg / 1000 g).
To choose the correct fraction, you must set up the equation so that the original unit (kg) cancels out, leaving you with the desired unit (g). Since the starting amount has kilograms in the numerator (2.87 kg is the same as 2.87 kg / 1), you need to multiply it by the conversion factor that has kilograms in the denominator. This makes (1000 g / 1 kg) the correct choice.
The complete setup for the calculation is:
2.87 kg × (1000 g / 1 kg)
In this equation, the kilogram (kg) unit in the numerator cancels out with the kilogram unit in the denominator. You are left with the unit of grams. The final step is to perform the mathematical calculation: multiply 2.87 by 1000, which equals 2870.
Thus, 2.87 kilograms is equivalent to 2870 grams. ANSWER: 2870 g
Explanation of the Solution
The problem asks to convert a measurement from kilograms (kg) to grams (g) using the provided digital interface, which is set up for dimensional analysis. This method involves multiplying the starting value by a conversion factor to cancel the original unit and introduce the desired unit.
1. Identify the Starting Amount
The first step is to identify the value we are converting. The problem states, “Convert 2.87 kg”. Therefore, the starting amount is 2.87 with the unit of kilograms. In the provided interface, you would place “2.87” in the first box under “STARTING AMOUNT” and “kg” in the second box.
2. Determine the Conversion Factor
Next, we need a conversion factor that relates kilograms and grams. In the metric system, the prefix “kilo” means 1,000. This tells us that one kilogram is equal to one thousand grams. The relationship is:
1 kg = 1000 g
From this equality, we can create a fraction, or conversion factor, that is equal to one. We must arrange this fraction so that the original unit (kg) will cancel out, leaving us with the desired unit (g). Since our starting amount has “kg” in the numerator (2.87 kg is the same as 2.87 kg / 1), we need the conversion factor to have “kg” in the denominator. The correct setup is:
(1000 g / 1 kg)
In the interface, you would place “1000” and “g” in the top boxes of the fraction and “1” and “kg” in the bottom boxes.
3. Calculate the Final Answer
With the equation fully set up, we can perform the calculation. The units are treated algebraically, so the “kg” in the numerator of the starting amount cancels with the “kg” in the denominator of the conversion factor.
Equation: 2.87 kg × (1000 g / 1 kg)
The remaining calculation is a simple multiplication of the numbers:
2.87 × 1000 = 2870
The only unit left is grams (g), which is our target unit. Thus, the final answer is 2870 grams.
