Write the following numbers in scientific notation.
Problem 1 :
0.00006
Problem 2 :
5400000
Problem 3 :
71 x 10^{2}
Problem 4 :
33 x 10^{-3}
Problem 5 :
0.63 x 10^{-3}
Problem 6 :
0.000216
Problem 7 :
0.0000009
Problem 8 :
804 x 10^{2}
Problem 9 :
4.8
Problem 10 :
0.99 x 10
1. Answer :
0.00006
Here, decimal point comes first at 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 5.
So, the decimal point has to be moved 5 digits to the right and exponent of 10 should be -5 (negative integer)
Hence, the scientific notation of 0.00006 is
6.0 x 10^{-5}
2. Answer :
5400000
Here, we don't find decimal point in 5400000. So we have to assume that there is decimal point at the end .
Then,
5400000 ----> 5400000.
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 first non zero digit and the decimal point is 6.
So, the decimal point has to be moved 6 digits to the left and exponent of 10 should be 6 (positive integer)
= 5400000.
= 5.400000 x 10^{6}
= 5.4 x 10^{6}
3. Answer :
71 x 10^{2}
Here, we don't find decimal point in 71x 10^{2}. So we have to assume that there is decimal point at the end of 71
Then,
71 x 10^{2} ----> 71. x 10^{2}
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 first non zero digit and the decimal point is 1.
So, the decimal point has to be moved 1 digit to the left and exponent of 10 should be 1 (positive integer)
= 71. x 10^{2}
= 7.1 x 10^{1} x 10^{2}
= 7.1 x 10^{1+}^{2}
= 7.1 x 10^{3}
4. Answer :
33 x 10^{-3}
Here, we don't find decimal point in 33 x 10^{-3} So we have to assume that there is decimal point at the end of 33
Then,
33 x 10^{-3} ----> 33. x 10^{-3 }
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 first non zero digit and the decimal point is 1.
So, the decimal point has to be moved 1 digit to the left and exponent of 10 should be 1 (positive integer)
= 33. x 10^{-3}
= 3.3 x 10^{1} x 10^{-3}
= 3.3 x 10^{1-3}
= 3.3 x 10^{-2}
5. Answer :
0.63 x 10^{-3}
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 1.
So, the decimal point has to be moved 1 digit to the right and exponent of 10 should be -1 (negative integer)
= 0.63 x 10^{-3}
= 6.3 x 10^{-1} x 10^{-3}
= 6.3 x 10^{-1-3}
= 6.3 x 10^{-4}
6. Answer :
0.000216
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 4.
So, the decimal point has to be moved 4 digits to the right and exponent of 10 should be -4 (negative integer)
= 0.000216
= 2.16 x 10^{-4}
7. Answer :
0.0000009
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 7.
So, the decimal point has to be moved 7 digits to the right and exponent of 10 should be -7 (negative integer)
= 0.0000009
= 9 x 10^{-7}
8. Answer :
804 x 10^{2}
Here, we don't find decimal point in 804 x 10^{2}. So we have to assume that there is decimal point at the end .
Then,
804 x 10^{2} ----> 804. x 10^{2}
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 first non zero digit and the decimal point is 2.
So, the decimal point has to be moved 2 digits to the left and exponent of 10 should be 2 (positive integer)
= 804. x 10^{2}
= 8.04 x 10^{2} x 10^{2}
= 8.04 x 10^{2+2}
= 8.04 x 10^{4}
9. Answer :
4.8
Here, the given number is almost in scientific notation.
Because there is only one non zero digit before the decimal point.
We don't have to move the decimal point either to the left or right.
Then, exponent of 10 should be zero.
= 4.8
= 4.8 x 10^{0}
10. Answer :
0.99 x 10
Here, decimal point comes first and non zero digit comes next.
We have to move the decimal to the right.
Number of digits from the decimal point up to the first non zero digit is 1.
So, the decimal point has to be moved 1 digit to the right and exponent of 10 should be -1 (negative integer)
= 0.99 x 10^{1}
= 9.9 x 10^{-1} x 10^{1}
= 9.9 x 10^{-1+}^{1}
= 9.9 x 10^{0}
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