IT
07_(4)_Decimal_Numbers

# A 5 10 4 4 10 2 5 4 10 42 20 10 6 2 10 7 b 6 10 3 8

• Notes
• 26

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a. (5 ⋅ 10 4 ) ⋅ (4 ⋅ 10 2 ) = (5 ⋅ 4) ⋅ 10 4+2 = 20 ⋅ 10 6 = 2 ⋅ 10 7 b. (6 ⋅ 10 3 ) ⋅ (8 ⋅ 10 –1 ) = (6 ⋅ 8) ⋅ 10 3+(–1) = 48 ⋅ 10 2 = 4.8 ⋅ 10 3 c. (5 ⋅ 10 –6 ) ⋅ (2.4 ⋅ 10 –4 ) = (5 ⋅ 2.4) ⋅ 10 (–6)+(–4) = 12 ⋅ 10 –10 = 1.2 ⋅ 10 –9 d. (9.2 ⋅ 10 –7 ) ⋅ (4 ⋅ 10 3 ) = (9.2 ⋅ 4) ⋅ 10 –7+3 = 36.8 ⋅ 10 –4 = 3.68 ⋅ 10 –3 e. (6.9 ⋅ 10 9 ) ÷ (3.45 ⋅ 10 7 ) = (6.9 ÷ 3.45) ⋅ 10 9 – 7 = 2 ⋅ 10 2 f. (4.7 ⋅ 10 –2 ) ÷ (5.7 ⋅ 10 –6 ) = (4.7 ÷ 5.7) ⋅ 10 –2 – (–6) = 0.825 ⋅ 10 4 = 8.25 ⋅ 10 3 g. (5.12 ⋅ 10 –7 ) ÷ (3.2 ⋅ 10 –3 ) = (5.12 ÷ 3.2) ⋅ 10 –7 – (–3) = 1.6 ⋅ 10 –4 h. (7.364 ⋅ 10 5 ) ÷ (7 ⋅ 10 3 ) = (7.364 ÷ 7) ⋅ 10 5 – 3 = 1.52 ⋅ 10 2 Perform the operations. a. (2 ⋅ 10 5 ) + (3 ⋅ 10 4 ) b. (6 ⋅ 10 –4 ) + (8 ⋅ 10 –3 ) c. (7 ⋅ 10 –5 ) + (8.4 ⋅ 10 –2 ) Perform the operations. Write the result in scientific notation. a. (1.5 ⋅ 10 3 ) ⋅ (4 ⋅ 10 5 ) b. (1.2 ⋅ 10 –3 ) ⋅ (1.1 ⋅ 10 4 ) c. (1.8 ⋅ 10 4 ) ⋅ [(6 ⋅ 10 –1 ) ⋅ (1.4 ⋅ 10 –2 )] d. [(2.3 ⋅ 10 5 ) ⋅ (1.1 ⋅ 10 –1 )] ⋅ (10 –3 ⋅ 2.5 ⋅ 10 8 ) d. (3.3 ⋅ 10 9 ) – (1.28 ⋅ 10 8 ) e. (3.09 ⋅ 10 –8 ) – (1.5 ⋅ 10 –6 ) f. (1.5 ⋅ 10 –5 ) + (2.3 ⋅ 10 –3 ) – (5 ⋅ 10 –5 ) – (2.6 ⋅ 10 –4 ) e. 10 10 4 (1.5 10 4 ) h. (4.5 10 2 ) f. 10 10 1 (7.5 10 5 ) i. (2.5 10 7 ) (1.2 10 6 ) g. (5 10 2 ) (3.09 10 –3 ) j. (10.3 10 –4 ) 5 5

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248 Pre-Algebra 1
1. Write the numbers in scientific notation. a. 28 b. 265.3 c. 38.045 d. 299 000 e. 71 000 000 f. 1.07 g. 0.0002 h. 0.000101 i. 0.0000629 j. 15 ⋅ 10 4 k. 9.9 ⋅ 10 2 l. 0.05 ⋅ 10 –7 m. 525 ⋅ 10 –6 n. 75 000 ⋅ 10 10 4. Perform the operations. Write the result in scientific notation. a. (3 ⋅ 10 3 ) ⋅ (2 ⋅ 10 2 ) b. (5 ⋅ 10 –2 ) ⋅ (20 ⋅ 10 –3 ) c. (–15 ⋅ 10 –3 ) ⋅ (4.4 ⋅ 10 4 )

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