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Following are the distances between: s...

Following are the distances between:
sun and saturn - `1433500000000 m`
saturn and uranus - `1439000000000` m
sun and earth - `149600000000` m
which of the three distances is the least ?

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The correct Answer is:
To determine which of the three distances is the least, we will convert each distance into exponential form and compare them. ### Step 1: Convert the distances into exponential form 1. **Distance between Sun and Saturn:** - Given: `1433500000000 m` - In scientific notation: \[ 1433500000000 = 1.4335 \times 10^{12} \text{ m} \] 2. **Distance between Saturn and Uranus:** - Given: `1439000000000 m` - In scientific notation: \[ 1439000000000 = 1.439 \times 10^{12} \text{ m} \] 3. **Distance between Sun and Earth:** - Given: `149600000000 m` - In scientific notation: \[ 149600000000 = 1.496 \times 10^{11} \text{ m} \] ### Step 2: Compare the distances Now we have the distances in scientific notation: - Sun to Saturn: \( 1.4335 \times 10^{12} \) - Saturn to Uranus: \( 1.439 \times 10^{12} \) - Sun to Earth: \( 1.496 \times 10^{11} \) ### Step 3: Analyze the powers of ten The powers of ten are: - For Sun to Saturn and Saturn to Uranus: \( 10^{12} \) - For Sun to Earth: \( 10^{11} \) Since \( 10^{12} \) is greater than \( 10^{11} \), we can conclude that both distances from the Sun to Saturn and from Saturn to Uranus are greater than the distance from the Sun to Earth. ### Step 4: Compare the decimal parts Now we need to compare the distances between Sun to Saturn and Saturn to Uranus: - \( 1.4335 \) (Sun to Saturn) - \( 1.439 \) (Saturn to Uranus) Since \( 1.4335 < 1.439 \), we conclude that: - Distance from Sun to Saturn is less than the distance from Saturn to Uranus. ### Conclusion Thus, the least distance among the three is: - **Distance between Sun and Earth: \( 1.496 \times 10^{11} \text{ m} \)**
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MTG IIT JEE FOUNDATION-EXPONENTS AND POWERS-SOLVED EXAMPLES
  1. Express each of the following numbers as a product of powers of their ...

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  2. Express each of the following as product of powers of their prime f...

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  3. Express each of the following as product of powers of their prime f...

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  4. Exprtess the following as the power of a rational number. (16)/(81)

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  5. Express the following as the power of a rational number. (-32)/(3125...

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  6. Find the product of cube of ((-3)/(5)) and fourth power of (2)/(-3).

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  7. Find the value of 'a' if [(-3)^3]^(5) =(-3)^(3a).

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  8. Find the value of p, if 5^(2p+1)div25=125.

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  9. Find the value of p in the following: ((15)/(9))^(3) div ((5)/(9))^(...

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  10. Find the value of p in the following: ((4)/(3))^(3) div ((-4)/(3))^...

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  11. Simplify : ((-1/2)^8)/((-1/2)^5)-((-1/2)^5)/((-1/2)^3)

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  12. Simplify : [(125)/(27)xx((9)/(25))^3]div((3)/(5))^2

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  13. Express 6.022xx10^3 as a whole number.

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  14. Following are the distances between: sun and saturn - 1433500000000 ...

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  15. A teacher asked the students to write 3^(5)xx6^2, but they wrote 3562....

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  16. If a=2 and b=3, then find the value of [(1)/(a^b)+(1)/(b^a)].

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  17. If 9^(3)xx 27^(2)xx 81^(2) is equal to 3^(2k), then find k.

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  18. If (52)/(x)=(169)/(144), find the value of x.

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  19. Evaluate : (625)/(11)xx(14)/(25)xx(11)/(196)

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