Question

1In the example problem, 2.4 X 10^6 was rewritten as 24 X 10^5. Explain why those expressions are equivalent.

Answer 1

`2.4* 10^6=24* 10^5`

Reason :

When in a decimal number the decimal shifted right the exponent of 10 is decreased by the number of shifting while if it is shifted left the exponent of 10 is increased by the number of shifting,

Why ?

`2.4* 10^6 =(24)/(10)* 10^6=24* 10^(-1)* 10^6=24* 10^(-1+6)=24* 10^5`

( By using
`a^m = (1)/(a^(-m))` and
`a^m.a^n=a^(m+n)` )

Answer 2

See explanation

Explanation:

Note that

`10^6=1,000,000\\ \\10^5=100,000`

Then

`2.4* 10^6=2.4* 1,000,000=2,400,000\\ \\24* 10^5=24* 100,000=2,400,000`

As you can see, the results are the same, so

`2.4* 10^6=24* 10^5`

This means that two given expressions are equivalent.