Write each of the following decimals in the form $$ \frac{\mathrm{a}}{\mathrm{b}} $$, where a and b are integers and $$ \mathrm{b}
eq 0 $$. a) 17.14 b) 0.006 c) -5.29 d) 0.443 a) $$ 17.14=\square $$ (Simplify your answer.) b) $$ 0.006=\square $$ (Simplify your answer.) c) $$ -5.29=\square $$ (Simplify your answer.) d) $$ 0.443=\square $$ (Simplify your answer.)

Question

Write each of the following decimals in the form $$ \frac{\mathrm{a}}{\mathrm{b}} $$, where a and b are integers and $$ \mathrm{b} 
eq 0 $$. a) 17.14 b) 0.006 c) -5.29 d) 0.443 a) $$ 17.14=\square $$ (Simplify your answer.) b) $$ 0.006=\square $$ (Simplify your answer.) c) $$ -5.29=\square $$ (Simplify your answer.) d) $$ 0.443=\square $$ (Simplify your answer.)

UpStudy AI · Accepted Answer

**a) Converting $$17.14$$ to a fraction**

1. Write the decimal as a fraction over 100:
   $$
   17.14 = \frac{1714}{100}
   $$
2. Simplify by dividing numerator and denominator by 2:
   $$
   \frac{1714 \div 2}{100 \div 2} = \frac{857}{50}
   $$
   
Thus,  
$$
17.14 = \frac{857}{50}
$$

**b) Converting $$0.006$$ to a fraction**

1. Write the decimal as a fraction over 1000:
   $$
   0.006 = \frac{6}{1000}
   $$
2. Simplify by dividing numerator and denominator by 2:
   $$
   \frac{6 \div 2}{1000 \div 2} = \frac{3}{500}
   $$
   
Thus,  
$$
0.006 = \frac{3}{500}
$$

**c) Converting $$-5.29$$ to a fraction**

1. Write the decimal as a fraction over 100:
   $$
   -5.29 = -\frac{529}{100}
   $$
2. Since 529 and 100 have no common factors other than 1 (529 is $$23^2$$ and 100 is $$2^2 \cdot 5^2$$), the fraction is already in simplest form.
   
Thus,  
$$
-5.29 = -\frac{529}{100}
$$

**d) Converting $$0.443$$ to a fraction**

1. Write the decimal as a fraction over 1000:
   $$
   0.443 = \frac{443}{1000}
   $$
2. Since 443 and 1000 have no common factors (443 is a prime number or has no factors that cancel with $$2^3 \cdot 5^3$$), the fraction is in simplest form.
   
Thus,  
$$
0.443 = \frac{443}{1000}
$$
a) $$17.14 = \frac{857}{50}$$ b) $$0.006 = \frac{3}{500}$$ c) $$-5.29 = -\frac{529}{100}$$ d) $$0.443 = \frac{443}{1000}$$

Write each of the following decimals in the form , where a and b are integers and .
a) 17.14
b) 0.006
c) -5.29
d) 0.443
a) (Simplify your answer.)
b) (Simplify your answer.)
c) (Simplify your answer.)
d) (Simplify your answer.)

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Write each of the following decimals in the form , where a and b are integers and . a) 17.14 b) 0.006 c) -5.29 d) 0.443 a) (Simplify your answer.) b) (Simplify your answer.) c) (Simplify your answer.) d) (Simplify your answer.)