Question

name
date
dec equivalent test
find the decimal equivalent of the following fractions
1/8 = _ 1/4 = _ 3/8 = _ 1/2 = _ 5/8 = _ 3/4 = _ 7/8 = ___
change these dec to fractions
.062= _ .125= _ .312= _ .187= _ .750= _ .875= _ .937= ___
change these three fractions to dec and add them up
5/16 + 3/32 +5/32 =
find the circumference of the following. use pie d = c
diameter= 5 7 2 3 3/16
4 1/8 4 5/16 7 1/32 8 5/8
3 3/32 8 ¼ 9 5/32 11 3/64

Answer:

Part 1: Decimal Equivalent of Fractions

Step 1: \( \frac{1}{8} \)

To convert a fraction to a decimal, divide the numerator by the denominator.
\( 1 \div 8 = 0.125 \)

Step 2: \( \frac{1}{4} \)

Divide 1 by 4.
\( 1 \div 4 = 0.25 \)

Step 3: \( \frac{3}{8} \)

Divide 3 by 8.
\( 3 \div 8 = 0.375 \)

Step 4: \( \frac{1}{2} \)

Divide 1 by 2.
\( 1 \div 2 = 0.5 \)

Step 5: \( \frac{5}{8} \)

Divide 5 by 8.
\( 5 \div 8 = 0.625 \)

Step 6: \( \frac{3}{4} \)

Divide 3 by 4.
\( 3 \div 4 = 0.75 \)

Step 7: \( \frac{7}{8} \)

Divide 7 by 8.
\( 7 \div 8 = 0.875 \)

Part 2: Decimal to Fractions

Step 1: \( 0.062 \)

\( 0.062 = \frac{62}{1000} = \frac{31}{500} \) (simplified by dividing numerator and denominator by 2)

Step 2: \( 0.125 \)

\( 0.125 = \frac{125}{1000} = \frac{1}{8} \) (divided by 125)

Step 3: \( 0.312 \)

\( 0.312 = \frac{312}{1000} = \frac{39}{125} \) (divided by 8)

Step 4: \( 0.187 \)

\( 0.187 = \frac{187}{1000} \) (187 and 1000 have no common factors other than 1)

Step 5: \( 0.750 \)

\( 0.750 = \frac{750}{1000} = \frac{3}{4} \) (divided by 250)

Step 6: \( 0.875 \)

\( 0.875 = \frac{875}{1000} = \frac{7}{8} \) (divided by 125)

Step 7: \( 0.937 \)

\( 0.937 = \frac{937}{1000} \) (937 and 1000 have no common factors other than 1)

Part 3: Convert Fractions to Decimals and Add

Step 1: Convert \( \frac{5}{16} \) to decimal

\( 5 \div 16 = 0.3125 \)

Step 2: Convert \( \frac{3}{32} \) to decimal

\( 3 \div 32 = 0.09375 \)

Step 3: Convert \( \frac{5}{32} \) to decimal

\( 5 \div 32 = 0.15625 \)

Step 4: Add the decimals

\( 0.3125 + 0.09375 + 0.15625 = 0.3125 + (0.09375 + 0.15625) = 0.3125 + 0.25 = 0.5625 \)

Part 4: Circumference (Using \( C = \pi D \))

Step 1: Diameter = 5

\( C = \pi \times 5 \approx 3.1416 \times 5 = 15.708 \)

Step 2: Diameter = 7

\( C = \pi \times 7 \approx 3.1416 \times 7 = 21.9912 \)

Step 3: Diameter = 2

\( C = \pi \times 2 \approx 3.1416 \times 2 = 6.2832 \)

Step 4: Diameter = \( 3\frac{3}{16} \) (convert to improper fraction: \( \frac{51}{16} \))

\( C = \pi \times \frac{51}{16} \approx 3.1416 \times 3.1875 = 10.017 \)

Step 5: Diameter = \( 4\frac{1}{8} \) (convert to improper fraction: \( \frac{33}{8} \))

\( C = \pi \times \frac{33}{8} \approx 3.1416 \times 4.125 = 12.964 \)

Step 6: Diameter = \( 4\frac{5}{16} \) (convert to improper fraction: \( \frac{69}{16} \))

\( C = \pi \times \frac{69}{16} \approx 3.1416 \times 4.3125 = 13.559 \)

Step 7: Diameter = \( 7\frac{1}{32} \) (convert to improper fraction: \( \frac{225}{32} \))

\( C = \pi \times \frac{225}{32} \approx 3.1416 \times 7.03125 = 22.089 \)

Step 8: Diameter = \( 8\frac{5}{8} \) (convert to improper fraction: \( \frac{69}{8} \))

\( C = \pi \times \frac{69}{8} \approx 3.1416 \times 8.625 = 27.006 \)

Step 9: Diameter = \( 3\frac{3}{32} \) (convert to improper fraction: \( \frac{99}{32} \))

\( C = \pi \times \frac{99}{32} \approx 3.1416 \times 3.09375 = 9.719 \)

Step 10: Diameter = \( 8\frac{1}{4} \) (convert to improper fraction: \( \frac{33}{4} \))

\( C = \pi \times \frac{33}{4} \approx 3.1416 \times 8.25 = 25.918 \)

Step 11: Diameter = \( 9\frac{5}{32} \) (convert to improper fraction: \( \frac{293}{32} \))

\( C = \pi \times \frac{293}{32} \approx 3.1416 \times 9.15625 = 28.765 \)

Step 12: Diameter = \( 11\frac{3}{64} \) (convert to improper fraction: \( \frac{707}{64} \))

\( C = \pi \times \frac{707}{64} \approx 3.1416 \times 11.046875 = 34.707 \)

Final Answers (Selected Parts for Clarity)

• Decimal Equivalent of \( \frac{1}{8} \): \( 0.125 \)
• Decimal to Fraction for \( 0.125 \): \( \frac{1}{8} \)
• Sum of \( \frac{5}{16} + \frac{3}{32} + \frac{5}{32} \) (as decimals): \( 0.5625 \)
• Circumference for Diameter = 5: \( \approx 15.71 \) (rounded to two decimal places)