The circle graph above gives the distribution of salad dressing chosen by customers at a restaurant. If approximately 200 customers order salad each day at the restaurant, which of the following is closest to the difference per day between the number who choose Italian dressing and the number who choose Vinaigrette dressing?

I can’t determine the difference without the graph — please provide the percentages or angle measures for the Italian and Vinaigrette slices (or upload the circle graph). Explanation / How to compute once you give the data If you are given percentages: let $p_I$ and $p_V$ be the fractions (as decimals) choosing Italian and Vinaigrette. Then $$\text{difference}=200\cdot|p_I-p_V|.$$ Example: if Italian is $30\%$ and Vinaigrette is $18\%$, then difference $=200\cdot(0.30-0.18)=24$ customers. If you are given central angles (degrees): let $d_I$ and $d_V$ be the slice angles. Convert to fractions via $p=\dfrac{d}{360}$, so $$\text{difference}=200\cdot\left|\dfrac{d_I-d_V}{360}\right|.$$ Example: if $d_I=108^\circ$ and $d_V=65^\circ$, difference $=200\cdot\frac{43}{360}\approx23.9\approx24$ customers. Send the slice percents or angles (or the image) and I’ll compute the closest daily difference.

The correct answer is: sesenta Explanation Sesenta is the Spanish cardinal number for 60. Pronunciation: /seˈsenta/ (roughly "seh-SEHN-tah"). Example: "Tengo sesenta años." = "I am sixty years old."

The correct answer is: $\frac{3}{8}$ Explanation 0.375 is a terminating decimal with three decimal places, so write it as a fraction over 1000 and reduce to lowest terms. Steps: First step: $$0.375=\frac{375}{1000}$$ Second step: Divide numerator and denominator by their greatest common divisor (125): $$\frac{375\div125}{1000\div125}=\frac{3}{8}$$ Final step: $$\frac{3}{8}=0.375$$ Therefore, $0.375=\frac{3}{8}$.

The correct answer is: $67.6280452\text{ fl oz}$ Explanation You convert liters to US fluid ounces using the factor $1\text{ L}=33.8140226\text{ fl oz}$. Steps: Conversion factor: $$1\text{ L}=33.8140226\text{ fl oz}$$ Multiply by 2 liters: $$2\text{ L}\times33.8140226\frac{\text{fl oz}}{\text{L}}=67.6280452\text{ fl oz}$$ Rounded (typical): $$\approx67.63\text{ fl oz}$$ Therefore, 2 liters ≈ $67.63\text{ fl oz}$. Note: This is for US fluid ounces. If you meant imperial (UK) fluid ounces, 2 L ≈ $70.40\text{ fl oz (imp)}$.

Dawn and Emily each had the same length of ribbon. Both girls used their ribbons to make identical bows. Dawn made 12 bows and had 128 cm of ribbon left. Emily made 9 bows and had 176 cm of ribbon left. How many bows could Emily make with the ribbon she had left?

The correct answer is:$11$ Explanation Let each bow use $x$ cm of ribbon and let the total ribbon length be $L$. Steps: Dawn: $L = 12x + 128$. Emily: $L = 9x + 176$. Equate and solve: $$12x + 128 = 9x + 176$$ $$3x = 48$$ $$x = 16$$ Emily's leftover $176\text{ cm}$ can make $$\frac{176}{16} = 11$$ bows. Therefore, Emily could make 11 more bows with the ribbon she had left.

Home /
solutions /
Math /
0.33333333333 as a fraction

Question

0.33333333333 as a fraction

Q: 0.33333333333 as a fraction

The correct answer is: $\frac{1}{3}$ Explanation If the decimal represents the repeating decimal $0.\overline{3}$ (an infinite string of 3s), it equals exactly $\frac{1}{3}$. If you mean the finite truncation $0.33333333333$ (eleven 3s), that is the rational number $\frac{33333333333}{100000000000}$, which is an approximation of $\frac{1}{3}$. Steps For the repeating decimal: Let $x=0.\overline{3}$ Then $10x=3.\overline{3}$ Subtract: $9x=3$ So $x=\frac{3}{9}=\frac{1}{3}$ For the finite 11-digit decimal: $0.33333333333=\dfrac{33333333333}{100000000000}$ (already in lowest terms) Therefore, normally $0.33333333333$ is taken to represent $0.\overline{3}$, whose exact fraction is $\frac{1}{3}$.

NewBlackStudio Ai Solution

100% (3 rated)

Answer

The correct answer is: $\frac{1}{3}$

Explanation

If the decimal represents the repeating decimal $0.\overline{3}$ (an infinite string of 3s), it equals exactly $\frac{1}{3}$.
If you mean the finite truncation $0.33333333333$ (eleven 3s), that is the rational number $\frac{33333333333}{100000000000}$, which is an approximation of $\frac{1}{3}$.

Steps