Problems 1-5 : Write the given number in scientific notation.
Problem 1 :
205852
Problem 2 :
3449098.96
Problem 3 :
0.00008035
Problem 4 :
23.5007
Problem 5 :
0.003
Problems 5-10 : Write the given number in standard form.
Problem 6 :
5.236 x 10^{5}
Problem 7 :
6.415 x 10^{-6}
Problem 8 :
1.72 x 10^{9}
Problem 9 :
0.00023 x 10^{7}
Problem 10 :
0.036 x 10^{-3}
1. Answer :
205852
Here, we don't find decimal point in 205852. So we have to assume that there is decimal point at the end .
Then,
205852 ---------> 205852.
Here, non zero digit comes first and decimal point comes next.
We have to move the decimal point to the left.
Number of digits between the 1^{st} non zero digit and the decimal point is five.
So, the decimal point has to be moved 5 digits to the left and exponent of 10 should be 5 (positive integer).
Therefore, the scientific notation of 205852 is
2.05852 x 10^{5}
2. Answer :
3449098.96
Here, non zero digit comes first and decimal point comes next.
We have to move the decimal point to the left.
Number of digits between the 1^{st} non zero digit and the decimal point is six.
So, the decimal point has to be moved 6 digits to the left and exponent of 10 should be 6 (positive integer)
Therefore, the scientific notation of 3449098.96 is
3.44909896 x 10^{6}
3. Answer :
0.00008035
Here, decimal point comes first and non zero digit comes next.
We have to move the decimal point to the right.
Number of digits from the decimal point up to the first non zero digit is five.
So, the decimal point has to be moved 5 digits to the right and exponent of 10 should be -5 (negative integer)
Therefore, the scientific notation of 0.00008035 is
8.035 x 10^{-5}
4. Answer :
23.5007
Here, non zero digit comes first and decimal point comes next.
We have to move the decimal point to the left.
Number of digits between the 1^{st} non zero digit and the decimal point is one.
So, the decimal point has to be moved 1 digit to the left and exponent of 10 should be 1 (positive integer)
Therefore, the scientific notation of 23.5007 is
2.35007 x 10^{1}
5. Answer :
0.003
Here, decimal point comes first and non zero digit comes next.
We have to move the decimal point to the right.
Number of digits from the decimal point up to the first non zero digit is three.
So, the decimal point has to be moved 3 digits to the right and exponent of 10 should be -3 (negative integer)
Therefore, the scientific notation of 0.003 is
3.0 x 10^{-3}
6. Answer :
5.236 x 10^{5}
Here, the exponent of 10 is positive 5. So we have to move the decimal point five digits to the right.
In 5.236, we have only three digits after the decimal point.
So, we have to add two zeros to move the decimal point five digits to the right.
Therefore, the standard form of 5.236 x 10^{5} is
523600
7. Answer :
6.415 x 10^{-6}
Here, the exponent of 10 is negative 6. So we have to move the decimal point six digits to the left.
In 6.415, we have only 1 digit before the decimal point.
So, we have to add five zeros to move the decimal point six digits to the left.
Therefore, the standard form of 6.415 x 10^{-6} is
0.000006415
8. Answer :
1.72 x 10^{9}
Here, the exponent of 10 is positive 9. So we have to move the decimal point nine digits to the right.
In 1.72, we have only two digits after the decimal point.
So, we have to add seven zeros to move the decimal point nine digits to the right.
Therefore, the standard form of 1.72 x 10^{9} is
1720000000
9. Answer :
0.00023 x 10^{7}
Here, the exponent of 10 is positive 7. So we have to move the decimal point seven digits to the right.
In 0.00023, we have only five digits after the decimal point.
So, we have to add two zeros to move the decimal point seven digits to the right.
Therefore, the standard form of 0.00023 x 10^{7} is
2300
10. Answer :
0.036 x 10^{-3}
Here, the exponent of 10 is negative 3. So we have to move the decimal point three digits to the left.
In 0.036, we don't have any non zero digit before the decimal point.
So, we have to add three zeros to move the decimal point three digits to the left.
Therefore the standard form of 0.036 x 10^{-3} is
0.000036
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