Which one is valid below? Is '5.42 X 10^5' equal to 542000. X 10^1 or 542000. X 10^0

[Indranil]

'5.42 X 10^5' this is the number in scientific notation. I rewrite the number below in two forms. Please tell me which one is correct
1. 542000. X 10^1
2. 542000. X 10^0

 

[HallsofIvy]

\(\displaystyle 10^5= 100000\) (the exponent if 5 so there are 5 zeros).
\(\displaystyle 5.42\times 10^5= 5.42\times 100000\).

Move the decimal point in 5.42 to the right five places. Moving it two places gives 542 so three more places is 542000. That is the same as \(\displaystyle 542000\times 1= 542000\times 10^0\).

 

[Indranil]

\(\displaystyle 10^5= 100000\) (the exponent if 5 so there are 5 zeros).
\(\displaystyle 5.42\times 10^5= 5.42\times 100000\).

Move the decimal point in 5.42 to the right five places. Moving it two places gives 542 so three more places is 542000. That is the same as \(\displaystyle 542000\times 1= 542000\times 10^0\).

Thanks a lot