1.8x10^5 and 3x10^4 in scientific notation?

Question

1.8x10^5 and 3x10^4 in scientific notation? Confused on what the answer is, help?

Answer 1

Hello, Mackenzie

 

Scientific Notation is one of the easiest math skills you can learn.  All you have to remember is the following, the exponent , the little number on top of the ten, represents the number of times that you are going to move the decimal either to the right (if the exponent is postive) or to the left ( if the exponent is negative). Here are some examples.  And since I don't know what grade level you are in, I am going to show you only a couple of problems dealing with positive exponents since that is what your question is all about.

 

a) 4.67* 10^ 3  = 4670. Move the decimal 3 times to the right.  The 6 times one space, the 7 takes another space, you have an empty space.  Put a zero on the empty space.  So, the answer is 4,670.  Warning: The exponent does not tell you how many zeros you are going to use.

 

b) 3.234* 10^6= 3234000.  Moving the decimal to the right, the 234 take three spaces, so we are going to have three empty spaces.  Remember, we are moving to the right six spaces.  So, always put a zero for any empty spaces.  Our final answer is 3,234,000.  Again, note that the power does not indicatr the number of zeros we are going to need.

 

c) 5* 10^4= 50000.  Note, that this number, 5, has no decimal point.  So you have an imaginary decimal right after the five. So, if you move four times to the right of the decimal, you will end up with four empty spaces. And as I told you before, use zeros for the empty spaces. So, our answer is 50,000.  This is where my sixth grade students get confused.  They think that because the power is 4, you use 4 zeros.  You need 4 zeros because you have four empty spaces. Look at the next example.

 

d) 5.3 * 10^ 4= You might think, erronously, that the answer is 530000.  But, that is not the case.  Because, when you move four times to the right, the 3 will take one of those places. So, you will have only 3 empty spaces. Thus, you will need three zeros instead of four.  The correct answer, therefore, should be 53,000 instead of 530,000,

 

Now, to answer you questions

a) 1.8* 10^ 5= 180000. Or 180,000.  We need to move five times to the right. The 8 will take one space, so we are going to need four zeros.

 

b) 3* 10^4= 30000 of 30,000.  In this case we are moving four spaces to the right.  And since the three has no number to its right, we are going to have four empty spaces, which we need to fill with a zero.

 

Ok, Mackenzie, just remember that the exponent of 10 means how many times you move the decimal.  I hope this helps. Take care, and please rate my answer.

 

D.Y. Taylor