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

Answer:

$2.4\times 10^6=24\times 10^5$

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 ?

$2.4\times 10^6 =\frac{24}{10}\times 10^6=24\times 10^{-1}\times 10^6=24\times 10^{-1+6}=24\times 10^5$

( By using $a^m = \frac{1}{a^{-m}}$ and $a^m.a^n=a^{m+n}$ )

Answer 2

Answer:

See explanation

Step-by-step explanation:

Note that

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

Then

$2.4\times 10^6=2.4\times 1,000,000=2,400,000\\ \\24\times 10^5=24\times 100,000=2,400,000$

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

$2.4\times 10^6=24\times 10^5$

This means that two given expressions are equivalent.