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3 years ago

Write a decimal that represents 8×100+4×1+5×1√100+3×1√1000 help please

Mathematics

2 answers:

Alborosie3 years ago

5 0

The rules for converting fractions with denominators 10, 100, 1000, etc. into decimal fraction:

(i) Count the number of zeroes coming after 1 in the denominator.

(ii) Count an equal number of places in the numerator starting from the unit digit then place the decimal point to the left of the digit reached.

Let us consider some of the following examples;

1. Convert 819/100 to decimal.

Given, 819/100 This explanation will help you

Jobisdone [24]3 years ago

5 0

Yea what they said , there answer is right

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Find the sum of a finite geometric series. The Smiths spent $2,000 on clothes in a particular year. If they increase the amount

boyakko [2]

$\bf \stackrel{\textit{first year}}{2000}~~,~~\stackrel{\textit{second year}}{2000+\stackrel{\textit{10\% of 2000}}{\frac{2000}{10}}}\implies 2200$

now, if we take 2000 to be the 100%, what is 2200? well, 2200 is just 100% + 10%, namely 110%, and if we change that percent format to a decimal, we simply divide it by 100, thus $\bf 110\%\implies \cfrac{110}{100}\implies 1.1$ .

so, 1.1 is the decimal number we multiply a term to get the next term, namely 1.1 is the common ratio.

$\bf \qquad \qquad \textit{sum of a finite geometric sequence}\\\\S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases}n=n^{th}\ term\\a_1=\textit{first term's value}\\r=\textit{common ratio}\\----------\\a_1=2000\\r=1.1\\n=4\end{cases}\\\\\\S_4=2000\left[ \cfrac{1-(1.1)^4}{1-1.1} \right]\implies S_4=2000\left(\cfrac{-0.4641}{-0.1} \right)\\\\\\S_4=2000(4.641)\implies S_4=9282$

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3 years ago