Question

Buster was given this expression and asked to determine whether the answer is greater than or less than 1. (9.763 × 108) (1.56 × 1013) How can Buster tell without fully performing the calculations?

Answer 1

"Buster can tell the answer is less than 1, because he can subtract the exponents to see that the solution will have an exponent of –5"

Answer 2

The given expression is less than 1

Explanation:

Given : Expression -
`(9.763*10^8)/(1.56*10^(13))`

By the theory of fractions i.e.

→ If the numerator is less than the denominator the fraction is called proper fraction and it is greater then 0 but less than 1.

→ If the numerator is greater than or equal to the denominator the fraction is called improper fraction and it is always greater then 1 or equal to 1.

In the given expression, the numerator
`{9.763*10^8}` is less then the denominator
`{1.56*10^(13)}`

as
`10^8<10^(13)`

which means it is a proper fraction or the fraction is greater than 0 but less than 1.

Therefore, the given expression is less than 1.