The value of 10−2 is equal to 0.01.
When encountering a negative exponent, it indicates that we are dealing with a reciprocal. Specifically, 10−2 can be rewritten as
1021.The exponent specifies how many times to multiply the base, which in this case is 10, by itself. Thus, 102 can be expressed as
10×10,resulting in 100. Consequently,
1021is equivalent to
1001,which simplifies to 0.01.
Grasping the concept of negative exponents is essential, as they frequently appear in various mathematical contexts, including scientific notation, algebra, and even practical applications such as calculating interest rates or interpreting scales on maps and models. By recognizing that a negative exponent signifies a reciprocal, you can simplify and solve many mathematical problems with greater ease. For instance, 10−3 can be expressed as
1031,which simplifies to 0.001.
In conclusion, 10−2 simplifies to 0.01 because the negative exponent indicates taking the reciprocal of the base raised to the positive exponent. This principle is a fundamental aspect of exponent rules and is instrumental in efficiently simplifying and solving mathematical expressions.
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