Question

addition and subtraction with scientific notation
simplify. write each answer in scientific notation.

1. $3.1 \times 10^3 + 4.3 \times 10^3$
2. $3 \times 10^1 + 6.4 \times 10^2$
3. $2.4 \times 10^4 + 5.57 \times 10^3$
4. $5 \times 10^{-2} + 1.6 \times 10^{-3}$
5. $2.5 \times 10^1 + 6.14 \times 10^4$
6. $7 \times 10^{-1} + 6.4 \times 10^{-5}$
7. $5 \times 10^{-3} + 3.3 \times 10^{-6}$
8. $8 \times 10^{-1} + 6.9 \times 10^3$
9. $1.39 \times 10^5 - 4 \times 10^2$
10. $2.74 \times 10^{-1} - 6.53 \times 10^{-4}$
11. $8.14 \times 10^5 - 7.8 \times 10^2$
12. $6.36 \times 10^3 - 5.8 \times 10^{-1}$
13. $5.1 \times 10^{-1} + 0.38 \times 10^4$
14. $5.9 \times 10^{-2} - 0.078 \times 10^3$

Explanation:

1) Step1: Factor out $10^3$

$(3.1 + 4.3) \times 10^3$

1) Step2: Add coefficients

$7.4 \times 10^3$

2) Step1: Rewrite to same exponent

$3 \times 10^1 = 0.3 \times 10^2$

2) Step2: Factor out $10^2$

$(0.3 + 6.4) \times 10^2$

2) Step3: Add coefficients

$6.7 \times 10^2$

3) Step1: Rewrite to same exponent

$5.57 \times 10^3 = 0.557 \times 10^4$

3) Step2: Factor out $10^4$

$(2.4 + 0.557) \times 10^4$

3) Step3: Add coefficients

$2.957 \times 10^4$

4) Step1: Rewrite to same exponent

$5 \times 10^{-2} = 50 \times 10^{-3}$

4) Step2: Factor out $10^{-3}$

$(50 + 1.6) \times 10^{-3}$

4) Step3: Add coefficients, adjust notation

$51.6 \times 10^{-3} = 5.16 \times 10^{-2}$

5) Step1: Rewrite to same exponent

$2.5 \times 10^1 = 0.00025 \times 10^4$

5) Step2: Factor out $10^4$

$(0.00025 + 6.14) \times 10^4$

5) Step3: Add coefficients

$6.14025 \times 10^4$

6) Step1: Rewrite to same exponent

$6.4 \times 10^{-5} = 0.00064 \times 10^{-1}$

6) Step2: Factor out $10^{-1}$

$(7 + 0.00064) \times 10^{-1}$

6) Step3: Add coefficients

$7.00064 \times 10^{-1}$

7) Step1: Rewrite to same exponent

$3.3 \times 10^{-6} = 0.0033 \times 10^{-3}$

7) Step2: Factor out $10^{-3}$

$(5 + 0.0033) \times 10^{-3}$

7) Step3: Add coefficients

$5.0033 \times 10^{-3}$

8) Step1: Rewrite to same exponent

$8 \times 10^{-1} = 0.0008 \times 10^3$

8) Step2: Factor out $10^3$

$(0.0008 + 6.9) \times 10^3$

8) Step3: Add coefficients

$6.9008 \times 10^3$

9) Step1: Rewrite to same exponent

$4 \times 10^2 = 0.004 \times 10^5$

9) Step2: Factor out $10^5$

$(1.39 - 0.004) \times 10^5$

9) Step3: Subtract coefficients

$1.386 \times 10^5$

10) Step1: Rewrite to same exponent

$6.53 \times 10^{-4} = 0.00653 \times 10^{-1}$

10) Step2: Factor out $10^{-1}$

$(2.74 - 0.00653) \times 10^{-1}$

10) Step3: Subtract coefficients

$2.73347 \times 10^{-1}$

11) Step1: Rewrite to same exponent

$7.8 \times 10^2 = 0.0078 \times 10^5$

11) Step2: Factor out $10^5$

$(8.14 - 0.0078) \times 10^5$

11) Step3: Subtract coefficients

$8.1322 \times 10^5$

12) Step1: Rewrite to same exponent

$5.8 \times 10^{-1} = 0.00058 \times 10^3$

12) Step2: Factor out $10^3$

$(6.36 - 0.00058) \times 10^3$

12) Step3: Subtract coefficients

$6.35942 \times 10^3$

13) Step1: Rewrite to same exponent

$5.1 \times 10^{-1} = 0.000051 \times 10^4$

13) Step2: Factor out $10^4$

$(0.000051 + 0.38) \times 10^4$

13) Step3: Add coefficients

$0.380051 \times 10^4 = 3.80051 \times 10^3$

14) Step1: Rewrite to same exponent

$5.9 \times 10^{-2} = 0.00059 \times 10^3$

14) Step2: Factor out $10^3$

$(0.00059 - 0.078) \times 10^3$

14) Step3: Subtract coefficients, adjust notation

$-0.07741 \times 10^3 = -7.741 \times 10^1$

Answer:

1. $\boldsymbol{7.4 \times 10^3}$
2. $\boldsymbol{6.7 \times 10^2}$
3. $\boldsymbol{2.957 \times 10^4}$
4. $\boldsymbol{5.16 \times 10^{-2}}$
5. $\boldsymbol{6.14025 \times 10^4}$
6. $\boldsymbol{7.00064 \times 10^{-1}}$
7. $\boldsymbol{5.0033 \times 10^{-3}}$
8. $\boldsymbol{6.9008 \times 10^3}$
9. $\boldsymbol{1.386 \times 10^5}$
10. $\boldsymbol{2.73347 \times 10^{-1}}$
11. $\boldsymbol{8.1322 \times 10^5}$
12. $\boldsymbol{6.35942 \times 10^3}$
13. $\boldsymbol{3.80051 \times 10^3}$
14. $\boldsymbol{-7.741 \times 10^1}$