Question

1. write a fraction that is between the following decimal pairs:

a)0.4 < < 0.6 b)0.777 < < 0.7778
c)1.34 < < 1.36 d)3.24 < < 3.26

Explanation:

Part (a)

Step 1: Analyze the decimal range

We need a fraction between \(0.4\) and \(0.6\). Let's convert \(0.4=\frac{4}{10}\) and \(0.6 = \frac{6}{10}\). A number between them can be \(0.5=\frac{5}{10}=\frac{1}{2}\) or \(\frac{50}{100}\) (as shown in the original work, but we can also use \(\frac{1}{2}\) or \(\frac{5}{10}\)).

Step 2: Verify

\(0.4 = 0.4\), \(\frac{1}{2}=0.5\), and \(0.6 = 0.6\). Since \(0.4<0.5<0.6\), the fraction \(\frac{1}{2}\) (or \(\frac{5}{10}\), \(\frac{50}{100}\)) works.

Part (b)

Step 1: Analyze the decimal range

We need a fraction between \(0.777\) and \(0.7778\). Let's find a decimal in between, say \(0.7775\). Convert \(0.7775\) to a fraction. \(0.7775=\frac{7775}{10000}=\frac{311}{400}\) (simplify by dividing numerator and denominator by 25: \(\frac{7775\div25}{10000\div25}=\frac{311}{400}\)).

Step 2: Verify

\(0.777<0.7775<0.7778\) (since \(0.7775 - 0.777=0.0005\) and \(0.7778 - 0.7775 = 0.0003\)), so \(\frac{311}{400}\) (or \(0.7775=\frac{7775}{10000}\)) is a valid fraction.

Part (c)

Step 1: Analyze the decimal range

We need a fraction between \(1.34\) and \(1.36\). \(1.35\) is in between. Convert \(1.35\) to a fraction. \(1.35 = 1+\frac{35}{100}=1+\frac{7}{20}=\frac{20 + 7}{20}=\frac{27}{20}\) or \(1\frac{35}{100}=1\frac{7}{20}\).

Step 2: Verify

\(1.34<1.35<1.36\), so \(1\frac{7}{20}\) (or \(1\frac{35}{100}\)) is a valid fraction.

Part (d)

Step 1: Analyze the decimal range

We need a fraction between \(3.24\) and \(3.26\). \(3.25\) is in between. Convert \(3.25\) to a fraction. \(3.25=3+\frac{25}{100}=3+\frac{1}{4}=3\frac{1}{4}=\frac{13}{4}\).

Step 2: Verify

\(3.24<3.25<3.26\), so \(3\frac{1}{4}\) (or \(3\frac{25}{100}\)) is a valid fraction.

Answer:

s:
a) \(\boldsymbol{\frac{1}{2}}\) (or \(\frac{5}{10}\), \(\frac{50}{100}\))
b) \(\boldsymbol{\frac{311}{400}}\) (or \(\frac{7775}{10000}\))
c) \(\boldsymbol{1\frac{7}{20}}\) (or \(1\frac{35}{100}\))
d) \(\boldsymbol{3\frac{1}{4}}\) (or \(3\frac{25}{100}\))