Question

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

a) \\(\frac{4}{10} < \\) \\( < \frac{5}{10} \\)
b) \\(\frac{4}{3} < \\) \\( < 1\frac{4}{9} \\)
c) \\(\frac{7}{20} < \\) \\( < \frac{2}{5} \\)
d) \\(4\frac{8}{10} < \\) \\( < 4\frac{8}{9} \\)

Explanation:

Part a)

Step1: Convert fractions to decimals

Convert $\frac{4}{10}$ to decimal: $\frac{4}{10} = 0.4$. Convert $\frac{5}{10}$ to decimal: $\frac{5}{10}=0.5$.

Step2: Find a decimal between 0.4 and 0.5

A decimal like $0.45$ (or any decimal such as $0.42, 0.43, 0.44, 0.46, 0.47, 0.48, 0.49$) lies between $0.4$ and $0.5$. Let's take $0.45$ as an example.

Part b)

Step1: Convert fractions to decimals

Convert $\frac{4}{3}$ to decimal: $\frac{4}{3}\approx1.333\cdots$. Convert $1\frac{4}{9}$ to decimal: $1+\frac{4}{9}\approx1 + 0.444\cdots=1.444\cdots$.

Step2: Find a decimal between $1.333\cdots$ and $1.444\cdots$

A decimal like $1.35$ (or $1.4, 1.38$ etc.) lies between them. Let's take $1.4$ (or more precisely, a decimal like $1.38$).

Part c)

Step1: Convert fractions to decimals

Convert $\frac{7}{20}$ to decimal: $\frac{7}{20}=0.35$. Convert $\frac{2}{5}$ to decimal: $\frac{2}{5} = 0.4$.

Step2: Find a decimal between 0.35 and 0.4

A decimal like $0.36$ (or $0.37, 0.38, 0.39$) lies between them. Let's take $0.36$.

Part d)

Step1: Convert mixed numbers to decimals

Convert $4\frac{8}{10}$ to decimal: $4+\frac{8}{10}=4.8$. Convert $4\frac{8}{9}$ to decimal: $4+\frac{8}{9}\approx4 + 0.888\cdots=4.888\cdots$.

Step2: Find a decimal between 4.8 and 4.888\cdots

A decimal like $4.85$ (or $4.82, 4.83, 4.84, 4.86, 4.87, 4.88$) lies between them. Let's take $4.85$.

Answer:

s:
a) $\boldsymbol{0.45}$ (or any decimal between 0.4 and 0.5)
b) $\boldsymbol{1.4}$ (or any decimal between approximately 1.333 and 1.444)
c) $\boldsymbol{0.36}$ (or any decimal between 0.35 and 0.4)
d) $\boldsymbol{4.85}$ (or any decimal between 4.8 and approximately 4.888)