5300 divided by 10 to the third power
The Correct answer and Explanation is :
The correct answer is: 5.3
To solve ( \frac{5300}{10^3} ):
- First, understand that ( 10^3 ) means ( 10 \times 10 \times 10 = 1000 ).
- Then, divide 5300 by 1000:
[
\frac{5300}{1000} = 5.3
]
So, the result is 5.3.
Explanation:
In mathematics, exponents represent repeated multiplication. In this case, ( 10^3 ) means multiplying 10 by itself three times, which equals 1000. The term “to the third power” signifies that the base (10) is multiplied by itself three times, so ( 10^3 = 1000 ).
When dividing a number by a power of 10, you are essentially shifting the decimal point to the left. If you divide by ( 10^1 ), the decimal moves one place to the left; if you divide by ( 10^2 ), it moves two places to the left, and so on. Since ( 10^3 = 1000 ), dividing by 1000 shifts the decimal three places to the left.
In the case of 5300, we treat it as ( 5300.0 ). By dividing by 1000, the decimal moves three places:
[
5300.0 \div 1000 = 5.3
]
This concept is widely used in various fields, including science and engineering, to simplify large numbers by expressing them as powers of 10. For instance, in scientific notation, large or small numbers are written as multiples of powers of 10 to make calculations easier and more manageable.
This approach makes division simpler, especially when dealing with very large or very small numbers, and helps in expressing results concisely.