Question

8 nso.3.5 identify equivalent forms of positive rational numbers including (l3):

• terminating fraction → decimal
• decimal → percent
• percent → decimal

write the given value(s) as a fraction decimal & percent.
3/4
0.625
45%
write the given value(s) as a fraction decimal & percent.
7/20
0.375
12%
9 nso.3.5 rewrite positive rational numbers in different but equivalent forms including (l4):

• percent → fraction
• fraction → percent

write the given value(s) as a fraction decimal & percent.
7/25
0.55
33%
write the given value(s) as a fraction decimal & percent.
3/50
0.875
45%

Explanation:

For $\boldsymbol{\frac{3}{4}}$:

Step1: Fraction to Decimal

Divide numerator by denominator: $3 \div 4 = 0.75$

Step2: Decimal to Percent

Multiply decimal by 100: $0.75 \times 100 = 75\%$

Step3: Summary

Fraction: $\frac{3}{4}$, Decimal: $0.75$, Percent: $75\%$

For $\boldsymbol{0.625}$:

Step1: Decimal to Fraction

$0.625 = \frac{625}{1000} = \frac{5}{8}$ (simplify by dividing numerator/denominator by 125)

Step2: Decimal to Percent

$0.625 \times 100 = 62.5\%$

Step3: Summary

Fraction: $\frac{5}{8}$, Decimal: $0.625$, Percent: $62.5\%$

For $\boldsymbol{45\%}$:

Step1: Percent to Decimal

Divide by 100: $45 \div 100 = 0.45$

Step2: Decimal to Fraction

$0.45 = \frac{45}{100} = \frac{9}{20}$ (simplify by dividing numerator/denominator by 5)

Step3: Summary

Fraction: $\frac{9}{20}$, Decimal: $0.45$, Percent: $45\%$

For $\boldsymbol{\frac{7}{20}}$:

Step1: Fraction to Decimal

$7 \div 20 = 0.35$

Step2: Decimal to Percent

$0.35 \times 100 = 35\%$

Step3: Summary

Fraction: $\frac{7}{20}$, Decimal: $0.35$, Percent: $35\%$

For $\boldsymbol{0.375}$:

Step1: Decimal to Fraction

$0.375 = \frac{375}{1000} = \frac{3}{8}$ (divide by 125)

Step2: Decimal to Percent

$0.375 \times 100 = 37.5\%$

Step3: Summary

Fraction: $\frac{3}{8}$, Decimal: $0.375$, Percent: $37.5\%$

For $\boldsymbol{12\%}$:

Step1: Percent to Decimal

$12 \div 100 = 0.12$

Step2: Decimal to Fraction

$0.12 = \frac{12}{100} = \frac{3}{25}$ (divide by 4)

Step3: Summary

Fraction: $\frac{3}{25}$, Decimal: $0.12$, Percent: $12\%$

For $\boldsymbol{\frac{7}{25}}$ (Problem 9, Left):

Step1: Fraction to Decimal

$7 \div 25 = 0.28$

Step2: Decimal to Percent

$0.28 \times 100 = 28\%$

Step3: Summary

Fraction: $\frac{7}{25}$, Decimal: $0.28$, Percent: $28\%$

For $\boldsymbol{0.55}$ (Problem 9, Left):

Step1: Decimal to Fraction

$0.55 = \frac{55}{100} = \frac{11}{20}$ (divide by 5)

Step2: Decimal to Percent

$0.55 \times 100 = 55\%$

Step3: Summary

Fraction: $\frac{11}{20}$, Decimal: $0.55$, Percent: $55\%$

For $\boldsymbol{33\%}$ (Problem 9, Left):

Step1: Percent to Decimal

$33 \div 100 = 0.33$

Step2: Decimal to Fraction

$0.33 = \frac{33}{100}$ (cannot simplify further)

Step3: Summary

Fraction: $\frac{33}{100}$, Decimal: $0.33$, Percent: $33\%$

For $\boldsymbol{\frac{3}{50}}$ (Problem 9, Right):

Step1: Fraction to Decimal

$3 \div 50 = 0.06$

Step2: Decimal to Percent

$0.06 \times 100 = 6\%$

Step3: Summary

Fraction: $\frac{3}{50}$, Decimal: $0.06$, Percent: $6\%$

For $\boldsymbol{0.875}$ (Problem 9, Right):

Step1: Decimal to Fraction

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

Step2: Decimal to Percent

$0.875 \times 100 = 87.5\%$

Step3: Summary

Fraction: $\frac{7}{8}$, Decimal: $0.875$, Percent: $87.5\%$

For $\boldsymbol{45\%}$ (Problem 9, Right - repeat):

Step1: Percent to Decimal

$45 \div 100 = 0.45$

Step2: Decimal to Fraction

$0.45 = \frac{9}{20}$ (as before)

Step3: Summary

Fraction: $\frac{9}{20}$, Decimal: $0.45$, Percent: $45\%$

Answer:

(Answers are structured per each value as fraction, decimal, percent:

• $\frac{3}{4}$: $\frac{3}{4}$, $0.75$, $75\%$
• $0.625$: $\frac{5}{8}$, $0.625$, $62.5\%$
• $45\%$: $\frac{9}{20}$, $0.45$, $45\%$
• $\frac{7}{20}$: $\frac{7}{20}$, $0.35$, $35\%$
• $0.375$: $\frac{3}{8}$, $0.375$, $37.5\%$
• $12\%$: $\frac{3}{25}$, $0.12$, $12\%$
• $\frac{7}{25}$: $\frac{7}{25}$, $0.28$, $28\%$
• $0.55$: $\frac{11}{20}$, $0.55$, $55\%$
• $33\%$: $\frac{33}{100}$, $0.33$, $33\%$
• $\frac{3}{50}$: $\frac{3}{50}$, $0.06$, $6\%$
• $0.875$: $\frac{7}{8}$, $0.875$, $87.5\%$
• $45\%$ (repeat): $\frac{9}{20}$, $0.45$, $45\%$)