Certainly! Let's convert each number from scientific notation to standard form.
(a) [tex]\( 2.34 \times 10^5 \)[/tex]
To convert [tex]\( 2.34 \times 10^5 \)[/tex], we move the decimal point 5 places to the right:
[tex]\[ 2.34 \times 10^5 = 234000.0 \][/tex]
(b) [tex]\( 4.56 \times 10^8 \)[/tex]
To convert [tex]\( 4.56 \times 10^8 \)[/tex], we move the decimal point 8 places to the right:
[tex]\[ 4.56 \times 10^8 = 455999999.99999994 \][/tex] (or approximately [tex]\( 456000000 \)[/tex])
(c) [tex]\( 3.14 \times 10^9 \)[/tex]
To convert [tex]\( 3.14 \times 10^9 \)[/tex], we move the decimal point 9 places to the right:
[tex]\[ 3.14 \times 10^9 = 3140000000.0 \][/tex]
(e) [tex]\( 6.02 \times 10^{23} \)[/tex]
To convert [tex]\( 6.02 \times 10^{23} \)[/tex], we move the decimal point 23 places to the right:
[tex]\[ 6.02 \times 10^{23} = 6.019999999999999 \times 10^{23} \][/tex] (approximately [tex]\( 6.02 \times 10^{23} \)[/tex])
(f) [tex]\( 7.9 \times 10^{-3} \)[/tex]
To convert [tex]\( 7.9 \times 10^{-3} \)[/tex], we move the decimal point 3 places to the left:
[tex]\[ 7.9 \times 10^{-3} = 0.0079 \][/tex]
(g) [tex]\( 9.87 \times 10^{-4} \)[/tex]
To convert [tex]\( 9.87 \times 10^{-4} \)[/tex], we move the decimal point 4 places to the left:
[tex]\[ 9.87 \times 10^{-4} = 0.000987 \][/tex]
(j) [tex]\( 8.62 \times 10^{-7} \)[/tex]
To convert [tex]\( 8.62 \times 10^{-7} \)[/tex], we move the decimal point 7 places to the left:
[tex]\[ 8.62 \times 10^{-7} = 8.619999999999999 \times 10^{-7} \][/tex] (approximately [tex]\( 0.000000862 \)[/tex])
(k) [tex]\( 3.45 \times 10^{-8} \)[/tex]
To convert [tex]\( 3.45 \times 10^{-8} \)[/tex], we move the decimal point 8 places to the left:
[tex]\[ 3.45 \times 10^{-8} = 3.4500000000000004 \times 10^{-8} \][/tex] (approximately [tex]\( 0.0000000345 \)[/tex])
Thus, the standard form of each number is:
(a) [tex]\( 234000.0 \)[/tex]
(b) [tex]\( 455999999.99999994 \)[/tex] or (approximately [tex]\( 456000000 \)[/tex])
(c) [tex]\( 3140000000.0 \)[/tex]
(e) [tex]\( 6.019999999999999 \times 10^{23} \)[/tex]
(f) [tex]\( 0.0079 \)[/tex]
(g) [tex]\( 0.000987 \)[/tex]
(j) [tex]\( 8.619999999999999 \times 10^{-7} \)[/tex] or (approximately [tex]\( 0.000000862 \)[/tex])
(k) [tex]\( 3.4500000000000004 \times 10^{-8} \)[/tex] or (approximately [tex]\( 0.0000000345 \)[/tex])
