Write your final answer with the correct number of significant figures in proper scientific notation (one non-zero number to the left of the decimal point).

a. 917.2 + 45.63 = ___________

b. 3.423 x 10^-4 - 6.42 x 10^-3 =_________

<h2>Answer:</h2>

(a) 9.6 x 10²

(b) -6.1 x 10⁻³

<h2>Step-by-step explanation:</h2>

(a) 917.2 + 45.63

First add the two numbers as follows (ensure that the decimal numbers are well aligned);

9 1 7 . 2

+ 4 5 . 6 3

9 6 2 . 8 3

To write the result in a proper scientific notation (one non-zero number to the left of the decimal point),

i. Express the number is standard form

962.83 = 9.6283 x 10²

Note that;

From the result in (i)

9.6283 = mantissa

10 = base

² = power or exponent.

ii. Express the mantissa of the number in 1 decimal place.

9.6 x 10²

Therefore, the result in the proper scientific notation is 9.6 x 10².

(b) 3.423 x 10⁻⁴ - 6.42 x 10⁻³

Find the difference between the two numbers as follows;

i. Re-write the numbers so that they both have the same exponents:

0.3423 x 10⁻³ - 6.42 x 10⁻³

ii. Factor out 10⁻³

10⁻³(0.3423 - 6.42)

iii. Solve the bracket

10⁻³(-6.0777)

iv. Rewrite the result in (iii)

-6.0777 x 10⁻³

To write the result in a proper scientific notation (one non-zero number to the left of the decimal point),

i. Express the number is standard form

-6.0777 x 10⁻³ [already in standard form]

Note that;

From the result in (i)

-6.0777 = mantissa

10 = base

⁻³ = power or exponent.

ii. Express the mantissa of the number in 1 decimal place.

-6.1 x 10⁻³

Therefore, the result in the proper scientific notation is -6.1 x 10⁻³.

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Step-by-step explanation:

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