Question

rrp.sklbldr1 mid-unit re
math 8: skillbuilder #
5.1

1. write each percent as a fraction and as

a decimal.
a) 60% b) 9.75% c) 97.5%

Explanation:

Part (a): 60%

Step 1: Convert to Fraction

To convert a percent to a fraction, we divide by 100 and simplify. So, \(60\%=\frac{60}{100}\). Simplifying this fraction by dividing numerator and denominator by their greatest common divisor (20), we get \(\frac{60\div20}{100\div20}=\frac{3}{5}\).

Step 2: Convert to Decimal

To convert a percent to a decimal, we divide by 100 (which is the same as moving the decimal point two places to the left). So, \(60\% = \frac{60}{100}=0.6\).

Part (b): 9.75%

Step 1: Convert to Fraction

\(9.75\%=\frac{9.75}{100}\). To eliminate the decimal in the numerator, multiply numerator and denominator by 100: \(\frac{9.75\times100}{100\times100}=\frac{975}{10000}\). Simplify by dividing numerator and denominator by 25: \(\frac{975\div25}{10000\div25}=\frac{39}{400}\).

Step 2: Convert to Decimal

Divide 9.75 by 100: \(9.75\%=\frac{9.75}{100} = 0.0975\).

Part (c): 97.5%

Step 1: Convert to Fraction

\(97.5\%=\frac{97.5}{100}\). Multiply numerator and denominator by 10 to eliminate the decimal: \(\frac{97.5\times10}{100\times10}=\frac{975}{1000}\). Simplify by dividing numerator and denominator by 25: \(\frac{975\div25}{1000\div25}=\frac{39}{40}\).

Step 2: Convert to Decimal

Divide 97.5 by 100: \(97.5\%=\frac{97.5}{100}=0.975\).

Answer:

s:
a) Fraction: \(\boldsymbol{\frac{3}{5}}\), Decimal: \(\boldsymbol{0.6}\)
b) Fraction: \(\boldsymbol{\frac{39}{400}}\), Decimal: \(\boldsymbol{0.0975}\)
c) Fraction: \(\boldsymbol{\frac{39}{40}}\), Decimal: \(\boldsymbol{0.975}\)