Question

decimals and fractions
write each decimal as a fraction or mixed number in simplest form

1. 0.6 =
2. 10.9
3. 0.084

Explanation:

1. Converting \(0.6\) to a fraction

Step 1: Identify the place value

The decimal \(0.6\) is in the tenths place, so we can write it as \(\frac{6}{10}\).

Step 2: Simplify the fraction

To simplify \(\frac{6}{10}\), we find the greatest common divisor (GCD) of 6 and 10, which is 2. Then we divide both the numerator and the denominator by 2: \(\frac{6\div2}{10\div2}=\frac{3}{5}\).

2. Converting \(10.9\) to a mixed number

Step 1: Separate the whole number and the decimal part

The whole number is 10, and the decimal part is \(0.9\).

Step 2: Convert the decimal part to a fraction

\(0.9\) is in the tenths place, so it can be written as \(\frac{9}{10}\).

Step 3: Combine the whole number and the fraction

So, \(10.9 = 10\frac{9}{10}\).

3. Converting \(0.084\) to a fraction (assuming the third decimal is \(0.084\))

Step 1: Identify the place value

The decimal \(0.084\) is in the thousandths place, so we can write it as \(\frac{84}{1000}\).

Step 2: Simplify the fraction

First, find the GCD of 84 and 1000. The GCD of 84 and 1000 is 4. Then divide both the numerator and the denominator by 4: \(\frac{84\div4}{1000\div4}=\frac{21}{250}\).

Answer:

s:

1. \(\boldsymbol{\frac{3}{5}}\)
2. \(\boldsymbol{10\frac{9}{10}}\)
3. \(\boldsymbol{\frac{21}{250}}\) (assuming the third decimal is \(0.084\))