The order of magnitude of the radius of our solar system is 10 to the 13th power meters. the order of magnitude of the radius of the visible universe is 10 to the 13th power times as great. find the approximate radius of the visible universe. can anyone explain to me how to work out and solve this problem?
to solve this problem, you would simply add the exponent of 13 from both tens since you are multiplying the exponents together. the answer would be 10 to the 26th power.
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To find the approximate radius of the visible universe, we need to multiply the radius of our solar system by the order of magnitude of the visible universe.
Given that the order of magnitude of the radius of our solar system is 10^13 meters, we can express it as:
Radius of Solar System = 10^13 meters
Now, we are told that the order of magnitude of the radius of the visible universe is 10^13 times as great. So, to find the radius of the visible universe, we need to multiply the radius of our solar system by 10^13.
Radius of Visible Universe = Radius of Solar System × (Order of Magnitude of Visible Universe)
Radius of Visible Universe = 10^13 × 10^13 meters
To simplify this multiplication, we can add the exponents:
Radius of Visible Universe = 10^(13 + 13) meters
Radius of Visible Universe = 10^26 meters
Therefore, the approximate radius of the visible universe is 10^26 meters.
To find the approximate radius of the visible universe, we need to multiply the radius of our solar system by the order of magnitude of the visible universe. Here's how you can solve this problem step by step:
Step 1: Convert the order of magnitude values to numerical form.
The order of magnitude of the radius of our solar system is 10^13 (10 raised to the power of 13).
The order of magnitude of the radius of the visible universe is 10^13 times greater, so it would be 10^13 * 10^13.
Step 2: Multiply the numerical values.
To multiply two numbers written in scientific notation (with exponents), you add the exponents but keep the base the same. In this case, we have 10^13 * 10^13, so we add the exponents: 13 + 13 = 26.
Step 3: Write the result in scientific notation.
The result of the multiplication is 10^26. Now, we need to express this in standard scientific notation, which has a coefficient between 1 and 10. So, we can rewrite 10^26 as 1 x 10^26.
Step 4: Multiply the coefficient by the radius of our solar system.
The coefficient 1 in 1 x 10^26 represents the enlargement of the radius. So, you multiply the radius of our solar system by 1. Since any number multiplied by 1 remains the same, the radius of the visible universe would be the same as the radius of our solar system.
Therefore, the approximate radius of the visible universe is 10^13 meters.
Note: This calculation assumes we are using the same unit of measurement for both the solar system and the visible universe.