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name relating percents, decimals, and fractions write each expression i…

Question

name
relating percents, decimals, and fractions
write each expression in two other ways

  1. 19%
  2. \\(\frac{23}{100}\\)
  3. 0.7
  4. 11%
  5. 2%
  6. \\(\frac{9}{100}\\)
  7. 0.13
  8. 25%

write each percent as a decimal and as a fraction in simplest form

  1. 60%
  2. 5%
  3. 16%
  4. 45%

express each shaded part as a decimal, as a percent, and as a fraction in simplest form.

  1. image of a grid
  2. image of a grid
  3. image of a grid
  4. in mrs. hughes’s class \\(\frac{3}{5}\\) of the students voted to have tacos at their end of the year party. what percentage of students voted for tacos?
  5. reasoning when dividing a number by 100, the decimal point is moved two places to the left. how does this relate to the conversion of a percent into a decimal?

Explanation:

Let's solve some of these problems step by step. We'll start with problem 11: 19%.

Problem 11: 19%
Step 1: Convert to decimal

To convert a percent to a decimal, we divide by 100 (or move the decimal point two places to the left). So, \( 19\% = \frac{19}{100} = 0.19 \).

Step 2: Convert to fraction

A percent is a ratio out of 100, so \( 19\% = \frac{19}{100} \) (and 19 and 100 have no common factors other than 1, so it's in simplest form).

Problem 12: \( \frac{23}{100} \)
Step 1: Convert to percent

To convert a fraction with denominator 100 to a percent, we write it as the numerator with a % sign. So, \( \frac{23}{100} = 23\% \).

Step 2: Convert to decimal

\( \frac{23}{100} = 23 \div 100 = 0.23 \).

Problem 13: 0.7
Step 1: Convert to percent

To convert a decimal to a percent, we multiply by 100 (or move the decimal point two places to the right). So, \( 0.7 \times 100 = 70\% \).

Step 2: Convert to fraction

0.7 is 7 tenths, so \( 0.7 = \frac{7}{10} \).

Problem 14: 11%
Step 1: Convert to decimal

\( 11\% = \frac{11}{100} = 0.11 \).

Step 2: Convert to fraction

\( 11\% = \frac{11}{100} \) (11 and 100 are coprime).

Problem 15: 2%
Step 1: Convert to decimal

\( 2\% = \frac{2}{100} = 0.02 \).

Step 2: Convert to fraction

Simplify \( \frac{2}{100} \) by dividing numerator and denominator by 2: \( \frac{2 \div 2}{100 \div 2} = \frac{1}{50} \).

Problem 16: \( \frac{9}{100} \)
Step 1: Convert to percent

\( \frac{9}{100} = 9\% \).

Step 2: Convert to decimal

\( \frac{9}{100} = 9 \div 100 = 0.09 \).

Problem 17: 0.13
Step 1: Convert to percent

\( 0.13 \times 100 = 13\% \).

Step 2: Convert to fraction

0.13 is 13 hundredths, so \( 0.13 = \frac{13}{100} \).

Problem 18: 25%
Step 1: Convert to decimal

\( 25\% = \frac{25}{100} = 0.25 \).

Step 2: Convert to fraction

Simplify \( \frac{25}{100} \) by dividing numerator and denominator by 25: \( \frac{25 \div 25}{100 \div 25} = \frac{1}{4} \).

Problem 19: 60%
Step 1: Convert to decimal

\( 60\% = \frac{60}{100} = 0.6 \).

Step 2: Convert to fraction (simplest form)

Simplify \( \frac{60}{100} \) by dividing numerator and denominator by 20: \( \frac{60 \div 20}{100 \div 20} = \frac{3}{5} \).

Problem 20: 5%
Step 1: Convert to decimal

\( 5\% = \frac{5}{100} = 0.05 \).

Step 2: Convert to fraction (simplest form)

Simplify \( \frac{5}{100} \) by dividing numerator and denominator by 5: \( \frac{5 \div 5}{100 \div 5} = \frac{1}{20} \).

Problem 21: 16%
Step 1: Convert to decimal

\( 16\% = \frac{16}{100} = 0.16 \).

Step 2: Convert to fraction (simplest form)

Simplify \( \frac{16}{100} \) by dividing numerator and denominator by 4: \( \frac{16 \div 4}{100 \div 4} = \frac{4}{25} \).

Problem 22: 45%
Step 1: Convert to decimal

\( 45\% = \frac{45}{100} = 0.45 \).

Step 2: Convert to fraction (simplest form)

Simplify \( \frac{45}{100} \) by dividing numerator and denominator by 5: \( \frac{45 \div 5}{100 \div 5} = \frac{9}{20} \).

Problem 26: \( \frac{3}{5} \) to percent
Step 1: Convert fraction to decimal

Divide 3 by 5: \( 3 \div 5 = 0.6 \).

Step 2: Convert decimal to percent

Multiply by 100: \( 0.6 \times 100 = 60\% \).

Problem 27: Relating percent to decimal conversion

To convert a percent to a decimal, we know that "percent" means "per hundred" (or divided by 100). So, \( x\% = \frac{x}{100} \). Dividing a number by 100 is the same as moving the decimal point two places to the left (for example, 50%: \( 50 \div 100 = 0.5 \), which i…

Answer:

s:

  1. Decimal: \( 0.19 \), Fraction: \( \frac{19}{100} \)
  2. Percent: \( 23\% \), Decimal: \( 0.23 \)
  3. Percent: \( 70\% \), Fraction: \( \frac{7}{10} \)
  4. Decimal: \( 0.11 \), Fraction: \( \frac{11}{100} \)
  5. Decimal: \( 0.02 \), Fraction: \( \frac{1}{50} \)
  6. Percent: \( 9\% \), Decimal: \( 0.09 \)
  7. Percent: \( 13\% \), Fraction: \( \frac{13}{100} \)
  8. Decimal: \( 0.25 \), Fraction: \( \frac{1}{4} \)
  9. Decimal: \( 0.6 \), Fraction: \( \frac{3}{5} \)
  10. Decimal: \( 0.05 \), Fraction: \( \frac{1}{20} \)
  11. Decimal: \( 0.16 \), Fraction: \( \frac{4}{25} \)
  12. Decimal: \( 0.45 \), Fraction: \( \frac{9}{20} \)
  13. \( 60\% \)
  14. Converting a percent to a decimal involves dividing by 100 (moving decimal two places left), as \( x\% = \frac{x}{100} \).

(For problems 23 - 25, we would need to see the shaded grids, but typically, a grid with 100 squares: count shaded squares, divide by 100 for decimal, multiply by 100 for percent, and simplify the fraction. For example, if 23 has 50 shaded squares: decimal \( 0.5 \), percent \( 50\% \), fraction \( \frac{1}{2} \).)