Question

The distance between the sun and Saturn is 1,433,500,000,000m. The distance between Saturn and Uranus is 1,439,000,000,000m. The distance between the Sun and the Earth is 149,600,000,000m.
The distance in an ascending order is $0.1496\times {{10}^{12}}<1.4335\times {{10}^{12}} < 1.439\times {{10}^{12}}$ . If true enter 1 else 0.

Answer 1

Hint: Here, we are given numbers with very high values. So, just we will assume that distances as three different numbers and we will convert it into decimal form. Then, we will arrange those numbers in ascending order i.e. from smallest to largest number. For example: 5, 7, 11, 12, 15 are said to be arranged in ascending order.

Complete step by step solution:
We are given 3 different distances i.e. sun to Saturn, sun to Earth and Saturn to Uranus given as 1,433,500,000,000, 149,600,000,000 and 1,439,000,000,000, respectively. Now, we will convert this distance in decimal form like say for example: 10000 can be written as $0.1\times {{10}^{5}}$ so. On shifting the decimal point 5 times to the right side we get number 10000. Similarly, we can write the distance as
\[1,433,500,000,000=1.4335\times {{10}^{12}}\]
\[1,439,000,000,000=1.439\times {{10}^{12}}\]
\[1,49,600,000,000=0.1496\times {{10}^{12}}\]
So, now we will check the first digit of all 3numbers. Here 0 is small as compared to 1. So, the first number will be \[0.1496\times {{10}^{12}}\] .
Now, there are 2 numbers having digit 1 before the decimal point. So, we will check the digit after the decimal point. Also, the digit is the same in both numbers i.e. 4. Also, again we will check the second digit after the decimal point which is 3 in both numbers so, checking the third digit which is 3 and 9. So, here we know that 3 is smaller than 9. Thus, \[1.4335\times {{10}^{12}}\] will come first then at last \[1.439\times {{10}^{12}}\] .
Thus, ascending order will be $0.1496\times {{10}^{12}}<1.4335\times {{10}^{12}}<1.439\times {{10}^{12}}$ . So, we have to enter 1 as given in question.

Note: Remember in this long digit number, we can also find by all the numbers in the same power of 10 i.e. either ${{10}^{11}}$ or ${{10}^{10}}$ . But all should be in same power then only it will be easy to solve the problem otherwise if let say we have $143.35\times {{10}^{10}}$ and $14.39\times {{10}^{11}}$ then it will be difficult to identify which smaller and which will come first in order. So, make sure all numbers should have the same power to 10.