How can you write $10,000,000$ using exponents?
F $10^4$
G $10^5$
H $10^6$
J $10^7$
Answer (2)
The number 10 , 000 , 000 can be expressed as a power of 10, specifically as 1 0 7 because it contains 7 zeros. Hence, the correct answer is J: 1 0 7 .
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Count the number of zeros in 10 , 000 , 000 .
Recognize that the number of zeros corresponds to the exponent when expressing the number as a power of 10.
Express 10 , 000 , 000 as 1 0 7 .
The answer is 1 0 7 .
Explanation
Understanding the Problem We are asked to express the number 10 , 000 , 000 as a power of 10 . This means we want to find an integer x such that 1 0 x = 10 , 000 , 000 .
Counting the Zeros To find the exponent x , we can count the number of zeros in 10 , 000 , 000 . Counting the zeros, we find that there are 7 zeros.
Expressing as a Power of 10 Therefore, 10 , 000 , 000 = 1 0 7 .
Identifying the Correct Option Comparing our result with the given options, we see that option J, 1 0 7 , is the correct answer.
Final Answer Thus, 10 , 000 , 000 can be written as 1 0 7 .
Examples
Exponents are used to represent very large or very small numbers in a compact form. For example, the distance to a star can be several quadrillion miles, which is more easily written in scientific notation using exponents. Similarly, the size of a virus can be a fraction of a micrometer, which is also more easily expressed using exponents. Understanding exponents helps in simplifying calculations and comprehending the scale of numbers in various scientific and engineering applications.
