A megaliter is ____ times larger than a hectoliter.
Answer (2)
Divide the power of 10 representing a megaliter by the power of 10 representing a hectoliter: 1 0 2 1 0 6 .
Apply the rule of exponents: 1 0 2 1 0 6 = 1 0 6 − 2 .
Simplify the exponent: 1 0 6 − 2 = 1 0 4 .
Calculate the result: 1 0 4 = 10000 . A megaliter is 10000 times larger than a hectoliter.
Explanation
Understanding the Problem We are given a table that represents different units as powers of 10. We are asked to find how many times larger a megaliter is than a hectoliter. A megaliter is represented by 1 0 6 and a hectoliter is represented by 1 0 2 .
Setting up the Division To find how many times larger a megaliter is than a hectoliter, we need to divide the power of 10 representing a megaliter by the power of 10 representing a hectoliter. This can be written as: 1 0 2 1 0 6
Applying the Exponent Rule Using the rule of exponents, which states that a n a m = a m − n , we can simplify the expression: 1 0 2 1 0 6 = 1 0 6 − 2 = 1 0 4
Calculating the Result Now, we calculate 1 0 4 : 1 0 4 = 10 × 10 × 10 × 10 = 10000 Therefore, a megaliter is 10,000 times larger than a hectoliter.
Final Answer A megaliter is 10,000 times larger than a hectoliter.
Examples
Imagine you're comparing the water storage capacity of a large reservoir (megaliter) to that of a small community water tank (hectoliter). Knowing that a megaliter is 10,000 times larger helps you understand the scale difference. This kind of comparison is useful in many fields, such as urban planning, environmental science, and resource management, where understanding relative sizes and scales is crucial for making informed decisions and managing resources effectively. For example, if a city uses 500 hectoliters of water per day, you can quickly determine how many days a 2 megaliter reservoir would last: 500 hectoliters/day 2 megaliters = 500 hectoliters/day 20000 hectoliters = 40 days .
A megaliter is 10,000 times larger than a hectoliter. This is calculated using their representations as powers of ten, specifically 1 0 6 for a megaliter and 1 0 2 for a hectoliter. Dividing these gives us the result of 1 0 4 , which equals 10,000.
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