Answer:
See below. You can set your calcluator to SCI mode and work these problems on your calculator in the normal way. (You may have to read the manual to understand how numbers are entered in scientific notation.)
Step-by-step explanation:
The key for all of these is to pay attention to the rules of exponents. Exponents of same-base factors in the numerator add; those in the denominator subtract. Everything else is regular multiplication and division.
For addition and subtraction by hand (your calculator doesn't care), all the numbers need to be adjusted so their multipliers are the same power of 10. It is often convenient to use the highest power. (Sometimes not. See 1f.)
1a. (1.2×10⁵) + (5.35×10⁶) = (0.12 + 5.35)×10⁶ = 5.47×10⁶
If you have trouble seeing that 1.2×10⁵ = 0.12×10⁶, you can rewrite it in a couple of steps.
... 1.2×10⁵ × (10⁶/10⁶)
... = 1.2 × (10⁵/10⁶) × 10⁶ . . . . rearrange the factors
... = 1.2 × 1/10 × 10⁶ . . . . . . . . simplify the factor involving 10⁵
... = 0.12 × 10⁶
1b. 6.91×10⁻² + 2.4×10⁻³ = (6.91 +0.24)×10⁻² = 7.15×10⁻²
1c. 9.70×10⁶ + 8.3×10⁵ = (9.70 +0.83)×10⁶ = 10.53×10⁶ = 1.053×10⁷
1d. 3.67×10² - 1.6×10¹ = (3.67 -0.16)×10² = 3.51×10²
1e. 8.41×10⁻⁵ - 7.9×10⁻⁶ = (8.41 -0.79)×10⁻⁵ = 7.62×10⁻⁵
1f. 1.33×10⁵ - 4.9×10⁴ = (13.3 -4.9)×10⁴ = 8.4×10⁴ (note that we chose the lower power of 10 here for the common factor because we could see the result would be less than 1 if we did it the other way. This avoided rescaling the number after the subtraction, as we had to do in 1c.)
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The attachment shows problem 1c worked on my calculator.
