Question

scientific notation
another important calculator skill is using the scientific notation button. most calculators have a key labeled exp, ee, or \\(\times 10^x\\). this button means \times ten to the __.\ it saves time and prevents mistakes when working with very large or very small numbers.

for example:
\\(4.5 \times 10^6\\) should be entered as 4.5 exp 6
\\(3.2 \times 10^{-4}\\) should be entered as 3.2 exp -4

depending on where a number written in scientific notation appears in an equation, it is often best to place that quantity inside parentheses. this helps ensure that the \\(\times 10^x\\) part applies only to that number and not to any other part of the calculation.

checking your answers
before trusting any calculator answer, pause and ask yourself: \does this answer make sense?\ a calculator is helpful, but your brain should always stay in charge.

when solving for variables in a mathematical equation, you should be able to plug your answers back in to check your work!

practice

1. \\(9 + 3 \times 3\\)
2. \\((5 + 3) \times 8\\)
3. \\((62.93 \times 0.6917) + (64.93 \times 0.3083)\\)
4. \\(1.48 / (0.08206 \times 350)\\)
5. \\((40.08 \times 1) + (19.00 \times 2)\\)
6. \\(3 \times 10^8 \div 1.14 \times 10^{14}\\)
7. \\(100 \times 4.18 \times (25.6 - 22.0)\\)
8. \\((2.0 \times 2.5) \div 1.75\\)
9. \\((6.02 \times 10^{23}) \times 2.8\\)
10. \\((39.10 \times 2) + 32.06\\)

Explanation:

Evaluate basic arithmetic expressions

For questions 1, 2, and 5, we apply standard order of operations (PEMDAS).

• Question 1: \(9 + 3 \times 3 = 9 + 9 = 18\).
• Question 2: \((5 + 3) \times 8 = 8 \times 8 = 64\).
• Question 5: \((40.08 \times 1) + (19.00 \times 2) = 40.08 + 38.00 = 78.08\).

Evaluate decimal and fraction expressions

For questions 3, 4, 7, and 8, we perform multi-step decimal arithmetic.

• Question 3: \((62.93 \times 0.6917) + (64.93 \times 0.3083) \approx 43.5287 + 20.0179 = 63.5466 \approx 63.55\).
• Question 4: \(1.48 / (0.08206 \times 350) = 1.48 / 28.721 \approx 0.05153\).
• Question 7: \(100 \times 4.18 \times (25.6 - 22.0) = 418 \times 3.6 = 1504.8\).
• Question 8: \((2.0 \times 2.5) / 1.75 = 5.0 / 1.75 \approx 2.857\).

Evaluate scientific notation expressions

For questions 6, 9, and 10, we compute values involving powers of ten.

• Question 6: \((3 \times 10^8) / (1.14 \times 10^{14}) = (3 / 1.14) \times 10^{-6} \approx 2.63 \times 10^{-6}\).
• Question 9: \((6.02 \times 10^{23}) \times 2.8 \approx 1.6856 \times 10^{24} \approx 1.7 \times 10^{24}\).
• Question 10: \((39.10 \times 2) + 32.06 = 78.20 + 32.06 = 110.26\).

Answer:

No.	Problem	Answer
2	\((5 + 3) \times 8\)	\(64\)
3	\((62.93 \times 0.6917) + (64.93 \times 0.3083)\)	\(63.55\)
4	\(1.48 / (0.08206 \times 350)\)	\(0.0515\)
5	\((40.08 \times 1) + (19.00 \times 2)\)	\(78.08\)
6	\(3 \times 10^8 \div 1.14 \times 10^{14}\)	\(2.63 \times 10^{-6}\)
7	\(100 \times 4.18 \times (25.6 - 22.0)\)	\(1504.8\)
8	\((2.0 \times 2.5) \div 1.75\)	\(2.86\)
9	\((6.02 \times 10^{23}) \times 2.8\)	\(1.7 \times 10^{24}\)
10	\((39.10 \times 2) + 32.06\)	\(110.26\)