Standard form long multiplication and division for physics. Watch

Grog
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I am studying Physics and have understood how to write out standard form sums.

Here are a few examples from my practical questions with the answers.

1)

2.3 x 10² x 67021
2.3 x 10² x 6.7021 x 10⁴
2.3 x 6.7021 x 10 x 10⁴
2.3 x 6.7021 x 10 ²+⁴
2.3 x 6.7021 x 10⁶

I understand all of the above. I understand moving the decimal negative and positive. I understand all this. It is that final sum. How can I work that out without the use of a calculator? The calculator answer is 1541483. I know the real answer is as show below to which tells me that I have to round it up from 1541483 - 15415. But I'm not suppose to use a calculator. How do I work the sum,

2.3 x 6.7021

and get this answer.

15.415 x 10⁶
1.5415 x 10⁷

I understand that I have to convert it to standard form, hence you move the decimal a place to the left and add a 1 to the 6 to get 7 above the 10.

It seems like a silly question but other methods I have tried or read do not add up correctly. I got the answer from the calculator and the practical work I am doing.

One answer I received was that I had to write the sum

2 x 6.7021 = 13.4042

and then

0.3 x 6.7021 = 2.01063

What I don't understand in that first answer is the decimal comes after 13 while in the next sum the decimal comes in between 2 and 0.

Why is that?

I then know I have to add the numbers together which answers my question.


Here are some other other questions and answers. I will refrain from writing the whole sum as I understand that.

2)

2.998 x 3.2 x 10¹³

= 9.5936 x 10¹³

3)

2.4 x 1.2 x 10 -¹

= 2.88 x 10 -¹

4)

5.673 / 3.562 x 1

= 1.581 x 1

5)

3.5 / 7316 x 10⁶

= 0.4874 x 10⁶

4.874 x 10⁵

How do I do the final sum without a calculator? Thank you for your time.

I realize that is requires long division and multiplication. Something simple and I have just forgotten how to do it I guess.
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