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Anettt [7]
3 years ago
8

Find S15 for the geometric series 72 + 12 + 2 + 1/3 +…

Mathematics
1 answer:
Gemiola [76]3 years ago
5 0
S1 = 72
S2 = 12 = 72*(1/6)
S3 = 2 = 72*(1/6)^2
.
.
.
S15 = 72*(1/6)^14 = 9.18*10^(-10)
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Karen is making a set of costumes for the school play using a piece of cloth. She reduces the length of the cloth she intends to
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Perform each of the following computations using the measured quantities below.
mylen [45]
<h2>Question </h2>

Perform each of the following computations using the measured quantities below.

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

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

   9  1   7 . 2

+   <u>   4  5 . 6  3</u>

   <u>9  6 2  . 8  3</u>

<u></u>

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

i. Express the number is standard form

962.83 = 9.6283 x 10²

<em>Note that;</em>

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 <em>9.6 x 10²</em>.

(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

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

i. Express the number is standard form

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

<em>Note that;</em>

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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2 years ago
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