simplify. write each answer in scientific notation.\n1) $3.1\times10^{3}+4.3\times10^{3}$\n2)…

simplify. write each answer in scientific notation.\n1) $3.1\times10^{3}+4.3\times10^{3}$\n2) $3\times10^{1}+6.4\times10^{2}$\n3) $2.4\times10^{4}+5.57\times10^{3}$\n4) $5\times10^{-2}+1.6\times10^{-3}$\n5) $2.5\times10^{1}+6.14\times10^{4}$\n6) $7\times10^{-1}+6.4\times10^{-5}$\n7) $5\times10^{-3}+3.3\times10^{-6}$\n8) $8\times10^{-1}+6.9\times10^{3}$\n9) $1.39\times10^{5}-4\times10^{2}$\n10) $2.74\times10^{-1}-6.53\times10^{-4}$\n11) $8.14\times10^{5}-7.8\times10^{2}$\n12) $6.36\times10^{3}-5.8\times10^{-1}$\n13) $5.1\times10^{-1}+0.38\times10^{4}$\n14) $5.9\times10^{-2}-0.078\times10^{3}$
Answer
Explanation:
Step1: Make exponents the same
For (3.1\times 10^{3}+4.3\times 10^{3}), since the exponents are already the same, we can directly add the coefficients. ((3.1 + 4.3)\times10^{3})
Step2: Calculate the sum of coefficients
(3.1+4.3 = 7.4), so the result is (7.4\times 10^{3})
Answer for 1): (7.4\times 10^{3})
Step1: Make exponents the same for (3\times 10^{1}+6.4\times 10^{2})
Rewrite (3\times 10^{1}=0.3\times 10^{2})
Step2: Add the numbers
((0.3 + 6.4)\times10^{2}=6.7\times 10^{2})
Answer for 2): (6.7\times 10^{2})
Step1: Make exponents the same for (2.4\times 10^{4}+5.57\times 10^{3})
Rewrite (5.57\times 10^{3}=0.557\times 10^{4})
Step2: Add the numbers
((2.4+ 0.557)\times10^{4}=2.957\times 10^{4})
Answer for 3): (2.957\times 10^{4})
Step1: Make exponents the same for (5\times 10^{-2}+1.6\times 10^{-3})
Rewrite (1.6\times 10^{-3}=0.16\times 10^{-2})
Step2: Add the numbers
((5 + 0.16)\times10^{-2}=5.16\times 10^{-2})
Answer for 4): (5.16\times 10^{-2})
Step1: Make exponents the same for (2.5\times 10^{1}+6.14\times 10^{4})
Rewrite (2.5\times 10^{1}=0.0025\times 10^{4})
Step2: Add the numbers
((0.0025+6.14)\times 10^{4}=6.1425\times 10^{4})
Answer for 5): (6.1425\times 10^{4})
Step1: Make exponents the same for (7\times 10^{-1}+6.4\times 10^{-5})
Rewrite (6.4\times 10^{-5}=0.000064\times 10^{-1})
Step2: Add the numbers
((7+0.000064)\times 10^{-1}=7.000064\times 10^{-1})
Answer for 6): (7.000064\times 10^{-1})
Step1: Make exponents the same for (5\times 10^{-3}+3.3\times 10^{-6})
Rewrite (3.3\times 10^{-6}=0.0033\times 10^{-3})
Step2: Add the numbers
((5 + 0.0033)\times10^{-3}=5.0033\times 10^{-3})
Answer for 7): (5.0033\times 10^{-3})
Step1: Make exponents the same for (8\times 10^{-1}+6.9\times 10^{3})
Rewrite (8\times 10^{-1}=0.0008\times 10^{3})
Step2: Add the numbers
((0.0008 + 6.9)\times10^{3}=6.9008\times 10^{3})
Answer for 8): (6.9008\times 10^{3})
Step1: Make exponents the same for (1.39\times 10^{5}-4\times 10^{2})
Rewrite (4\times 10^{2}=0.004\times 10^{5})
Step2: Subtract the numbers
((1.39-0.004)\times 10^{5}=1.386\times 10^{5})
Answer for 9): (1.386\times 10^{5})
Step1: Make exponents the same for (2.74\times 10^{-1}-6.53\times 10^{-4})
Rewrite (6.53\times 10^{-4}=0.00653\times 10^{-1})
Step2: Subtract the numbers
((2.74 - 0.00653)\times10^{-1}=2.73347\times 10^{-1})
Answer for 10): (2.73347\times 10^{-1})
Step1: Make exponents the same for (8.14\times 10^{5}-7.8\times 10^{2})
Rewrite (7.8\times 10^{2}=0.0078\times 10^{5})
Step2: Subtract the numbers
((8.14-0.0078)\times 10^{5}=8.1322\times 10^{5})
Answer for 11): (8.1322\times 10^{5})
Step1: Make exponents the same for (6.36\times 10^{3}-5.8\times 10^{-1})
Rewrite (5.8\times 10^{-1}=0.00058\times 10^{3})
Step2: Subtract the numbers
((6.36 - 0.00058)\times10^{3}=6.35942\times 10^{3})
Answer for 12): (6.35942\times 10^{3})
Step1: Make exponents the same for (5.1\times 10^{-1}+0.38\times 10^{4})
Rewrite (5.1\times 10^{-1}=0.000051\times 10^{4})
Step2: Add the numbers
((0.000051 + 0.38)\times10^{4}=0.380051\times 10^{4}=3.80051\times 10^{3})
Answer for 13): (3.80051\times 10^{3})
Step1: Make exponents the same for (5.9\times 10^{-2}-0.078\times 10^{3})
Rewrite (5.9\times 10^{-2}=0.000059\times 10^{3})
Step2: Subtract the numbers
((0.000059-0.078)\times 10^{3}=- 0.077941\times 10^{3}=-77.941=-7.7941\times 10^{1})
Answer for 14): (-7.7941\times 10^{1})