Scientific notation helps us to represent the numbers which are very huge or very tiny in a form of multiplication of single-digit numbers and 10 raised to the power of the respective exponent.
a × 10^{b} ; 1 ≤ a < 10
Convert Between Scientific Notation and Standard Form
Problem 1 :
5.3 × 10^{6}
Solution :
Exponent is positive, so we have to move the decimal 6 digits to the right.
But we have one digit after the decimal. We should use zeroes for the rest of the places.
5300000.
So, the number 5.3 × 10^{6} in standard notation is 53,00,000.
Problem 2 :
4.7 × 10^{-5}
Solution :
= 4.7 × 10^{-5}
Exponent is negative, so we have to move the decimal 5 digits to the left.
= 0.000047
Problem 3 :
5 × 10^{4}
Solution :
= 5 × 10^{4}
Exponent is positive, so we have to move the decimal 4 digits to the right.
50000.
So, the number 5 × 10^{4} in standard notation is 50000.
Problem 4 :
4.59 × 10^{1}
Solution :
= 4.59 × 10^{1}
Exponent is positive 1, so we have to move the decimal one digit to the right.
= 45.9
So, the number 4.59 × 10^{1 }in standard notation is 45.9.
Problem 5 :
6.7 × 10^{4}
Solution :
= 6.7 × 10^{4}
We have positive 4, so move the decimal 4 digits to the right.
So, the number 6.7 × 10^{4} in standard notation is 67000.
Problem 6 :
9.6 × 10^{4}
Solution :
= 9.6 × 10^{4}
We have positive 4, so move the decimal 4 digits to the right.
= 96000
Problem 7 :
8.78 × 10^{3}
Solution :
= 8.78 × 10^{3}
Exponent is positive 3, so we have to move the decimal 3 digits to the right.
8780.
Problem 8 :
5.82 × 10^{3}
Solution :
= 5.82 × 10^{3}
We have positive exponent, we have to move the decimal to the right.
= 5820
So, the number 5.82 × 10^{3} in standard notation is 5820.
Problem 9 :
1.3 × 10^{5}
Solution :
= 1.3 × 10^{5}
We have positive exponent, so we have to move the decimal 5 digits to the right.
= 130000
Problem 10 :
4.1 × 10^{4}
Solution :
= 4.1 × 10^{4}
= 41000
So, the number 4.1 × 10^{4} in standard notation is 41000.
Problem 11 :
6.4 × 10^{2}
Solution :
= 6.4 × 10^{2}
= 640
Problem 12 :
6.91 × 10^{-2}
Solution :
= 6.91 × 10^{-2}
= 0.0691
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM