Problem

Express each of the following numbers in exponent…

02:06

Problem 44 Easy Difficulty

Express each of the following numbers in scientific notation with correct significant figures:
(a) 711.0
(b) 0.239
(c) 90743
(d) 134.2
(e) 0.05499
(f) 10000.0
(g) 0.000000738592

Answer

a) $7.110 \times 10^{2}$
b) $2.39 \times 10^{-1}$
c) $9.0743 \times 10^{4}$
d) $1.342 \times 10^{2}$
e) $5.499 \times 10^{-2}$
f) $1.00000 \times 10^{4}$
g) $7.38592 \times 10^{-7}$

Mari G.

November 30, 2020

Bisrat B.

May 7, 2021

0.239

Ryan C.

May 12, 2021

PERFORM THE FOLLOWING CALCULATIONS AND REPORT EACH ANSWERS WITH THE CORRECT NUMBER OF SIGNIFICANT FIGUR

Top Chemistry 101 Educators

Allea C.

University of Maryland - University College

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Video Transcript

Okay. What we're gonna do is we want to convert each of these numbers into scientific notation. So one thing we have to remember is in proper scientific notation you're only allowed one numerical value, not zero. So it's going to be a numerical value between one and nine to the left of the decimal point. But you can have as many numbers including a zero to the right of the decimal point And then it's going to be times 10 raised to some exponent. Okay. And so remember though when we rewrite a numerical value into scientific notation we need to keep the integrity of that numerical value by keeping the correct significant digits. So as we walk through converting these into scientific notation we talk about significant digits as well. So for a there are four significant digits here. Remember a zero, a trailing zero Um is significant with a decimal point. So seven is so any number is significant. Any numerical number between one through nine is significant and a zero can be significant significant if there is a decimal point and it trails the other numbers or is in between two other Non zero numbers. So this has four significant visit digits. And so when I convert it I have to move the decimal place to the left. one, two values. So I would have seven 0.110. And now I've got to keep that zero because he was significant here. So I need four significant here since I was started with four times 10. Now I your exponent is how many places you moved it to the left and if you're moving it to the left it's going to be positive. If you move it to the right it's going to be negative. So we had to move it 12 values to the left. So it's going to be a positive too. Okay, so in our next one we have only three significant digits because a leading zero, no matter what whether there's a decimal point or not, a decimal point, a leading zero is never significant. So I only have three significant digits and so now I need to move the decimal place over to the right one time to get a non zero value. So that would be 2.3 nine I think it's a nine or it could be a four um times 10 to the negative one because I had to move it over to the right one time. Okay, so here I have five significant digits um and so I don't see a decimal point. So it's going to be implied to be at the very end. So that means I would move it one 234 to the left. And so this would be 9.07 43 Times 10 to the 4th. Because I had to move it four places to the left. Okay, so same thing here, this has four significant digits And I have to move the decimal place over 1, 2 places to the left. So this would be 1.34, two times 10 to the second. Okay so here I only have four significant digits because remember our leading zeros do not count. And so I would have to move the decimal place over one To to the right. So my exponents going to be a -2. So this would be 5.4 9, 9 times 10 to the negative two. Okay so here all of these are trailing zeros. So they are significant. So I have 12345 123456 significant digits. And so and I have to move the decimal place over one 234 places to the left. And so this would be times 10 to the fourth. And now I got it since these are significant I have to keep them significant. So I had 123450es. And there I have it remember leading zeros never count. So I only have 123456 significant digits. And I have to move the decimal place over one 23 for 56 and seven places to the right. So that's going to be times 10 To the -7. And there I have it

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