Question

5. Perform the following operations. Express each
answer in scientific notation.
a. (1.54 x 10 -2 g) + (2.86 x 10-1 g)
b. (7.023 x 109 g) -(6.62 x 107g)
c. (8.99 × 10 -4 m) x (3.57 x 104 m)
2.17 x 10-3g
d.
5.002 x 104 mL

Answer 1

The result of the operations expressed in scientific notation are :

• $30.14 \times {10}^{ - 2} \: g$
• $6.9568 \times {10}^{9} \: g$
• $3.20943 \times {10}^{1} \: {m}^{2}$

A.)

$(1.54 \times {10}^{ - 2} ) + (2.86 \times {10}^{ - 1} )$

Converting each value to the same power of 10;

$(1.54 \times {10}^{ - 2} ) + (28.6 \times {10}^{ - 2} ) = (1.54 + 28.6) \times {10}^{ - 2} = 30.14 \times {10}^{ - 2} \: g$

B.)

$(7.023 \times {10}^{9} ) - (6.62 \times {10}^{7} )$

Converting each value to the same power of 10;

$(7.023 \times {10}^{9} ) - (6.62 \times {10}^{7} ) = (7.023 \times {10}^{9}) - (0.0662 \times {10}^{9}) = 6.9568 \times {10}^{9} \: g$

C.)

$(8.99 \times {10}^{ - 4} ) \times (3.57 \times {10}^{4} )$

From indices ; we add the powers when dealing with multiplication operation :

$(8.99 \times {10}^{ - 4} ) \times (3.57 \times {10}^{4}) = (8.99 \times 3.57) \times {10}^{( -4 + 4)} = 32.0943 \times {10}^{0} = 32.0943 = 3.20943 \times {10}^{1} \: {m}^{2}$

Therefore, the result of the expressions written in scientific notation are given above, except for the 4th which isn't well formatted.

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