Converting Decimal Fractions to Simple Fractions and Mixed Numbers: Comparison to simple fractions

To solve this problem, we'll follow these steps:

• Step 1: Convert the decimal $0.7$ into a fraction for easy comparison.
• Step 2: Compare the fractions $\frac{7}{100}$ and $\frac{7}{10}$ using cross-multiplication.

Now, let's work through each step:
Step 1: Convert $0.7$ to a fraction. Since $0.7 = \frac{7}{10}$, we convert it to this fraction.
Step 2: Compare $\frac{7}{100}$ and $\frac{7}{10}$ using cross-multiplication.
Calculate $7 \times 10 = 70$ and $7 \times 100 = 700$.

Since $70 < 700$, it follows that $\frac{7}{100} < \frac{7}{10}$.

Therefore, the solution to the problem is $<$.

To compare $\frac{1}{4}$ and $0.4$, we first convert $\frac{1}{4}$ to a decimal:

Step 1: Convert $\frac{1}{4}$ to a decimal.

$\frac{1}{4}$ is the same as dividing 1 by 4. Performing this division, we get:

$\frac{1}{4} = 0.25$

Step 2: Compare the decimals.

Now, we compare $0.25$ with $0.4$:

$0.25 < 0.4$

Therefore, the appropriate sign to use is <.

The comparison between $\frac{1}{4}$ and $0.4$ is $\frac{1}{4} < 0.4$.

Therefore, the correct choice is: $<$.

To compare $\frac{1}{2}$ with 0.25, we will first convert the fraction to a decimal.

Step 1: Convert $\frac{1}{2}$ to a decimal:

To do this, divide 1 by 2:

$1 \div 2 = 0.5$

Thus, $\frac{1}{2}$ is equivalent to 0.5 when expressed as a decimal.

Step 2: Compare the decimal values:

Now, we clearly see that 0.5 (from $\frac{1}{2}$) is greater than 0.25.

Therefore, the appropriate sign for the expression $\frac{1}{2} ? 0.25$ is $\gt$.

To solve this problem, we'll first convert the fraction $\frac{1}{5}$ to a decimal to directly compare it with $0.5$.

• Step 1: Convert $\frac{1}{5}$ to a decimal.
• Step 2: Compare the results.

Let's work through these steps:
Step 1: Conversion of $\frac{1}{5}$. This can be done by performing the division $1 \div 5 = 0.2$.
Now, we have two decimals to compare: $0.2$ and $0.5$.

Step 2: Compare $0.2$ and $0.5$.
Since $0.2$ is less than $0.5$, $\frac{1}{5}$ is less than $0.5$.

Therefore, the correct sign to use is $"<"$.

The inequality can be represented as $\frac{1}{5} < 0.5$.

To solve this problem, we'll follow these steps:

• Step 1: Convert the fraction $\frac{16}{10}$ into a decimal.
• Step 2: Compare the resulting decimal with $1.6$.
• Step 3: Determine the correct relational sign based on the comparison.

Let's work through each step:
Step 1: Convert the fraction $\frac{16}{10}$ to a decimal by performing division $16 \div 10$. Doing this gives us $1.6$.
Step 2: Compare the decimal $1.6$ with $1.6$.
Step 3: Since both are equal, the correct relational sign to use is $=$.

Therefore, the solution to the problem is $=$.

We begin by converting $\frac{230}{100}$ into a decimal form. To do this, we divide 230 by 100:

$\frac{230}{100} = 230 \div 100 = 2.3$

Now, we compare this result to the given decimal 2.3.

Since $2.3 = 2.3$, the appropriate sign to use between $\frac{230}{100}$ and 2.3 is $"="$.

Therefore, the solution to the problem is $\mathbf{=}$.

Let's proceed with solving the problem step by step:

• Step 1: Convert the decimal $0.7$ into a fraction.

  The number $0.7$ can be expressed as a fraction by recognizing it as $\frac{7}{10}$, since the digit $7$ is in the tenths place.

• Step 2: Compare the two fractions, $\frac{7}{100}$ and $\frac{7}{10}$.

  Both fractions have the same numerator of $7$. When comparing fractions with the same numerator, the fraction with the smaller denominator is the larger fraction. Thus, $\frac{7}{10}$ is greater than $\frac{7}{100}$.

• Step 3: Determine the appropriate sign.

  Since $\frac{7}{10}$ is greater than $\frac{7}{100}$, we have: $\frac{7}{100} < 0.7$.

The appropriate sign is therefore $<$.

Therefore, the solution to the problem is that $\frac{7}{100} < 0.7$.

To compare the given values, we first convert the fraction $\frac{25}{10}$ into a decimal form:

Step 1: Simplify $\frac{25}{10}$.

Divide 25 by 10:

$\frac{25}{10} = 2.5$.

Step 2: Compare 2.5 and 0.25.

The decimal $2.5$ is clearly greater than $0.25$.

Thus, the correct comparison sign between the values is greater than.

Therefore, we write:

$\frac{25}{10} > 0.25$.

Thus, the correct choice is >.

To solve this problem, we'll compare the fraction $\frac{2}{20}$ to the decimal $0.01$ by converting both to the same form.

Step 1: Simplify the fraction $\frac{2}{20}$.

$\frac{2}{20}$ simplifies to $\frac{1}{10}$ by dividing both the numerator and the denominator by 2.

Step 2: Convert the simplified fraction $\frac{1}{10}$ to a decimal.

Divide 1 by 10: $\frac{1}{10} = 0.1$.

Step 3: Compare the decimal form of the fraction with $0.01$.

We have $0.1$ and $0.01$. Clearly, $0.1 > 0.01$ since $0.1$ is ten times larger than $0.01$.

Therefore, the correct comparison sign for $\frac{2}{20} ? 0.01$ is $\gt$.

To solve this problem, we'll follow these steps:

• Step 1: Convert the fraction $\frac{3}{50}$ to a decimal.
• Step 2: Compare the decimal value of $\frac{3}{50}$ to $0.06$.
• Step 3: Determine the correct comparison sign.

Now, let's work through each step:

Step 1: Convert $\frac{3}{50}$ to a decimal. This is done by dividing 3 by 50:

$\frac{3}{50} = 0.06$

Step 2: Compare the decimal value $0.06$ to $0.06$.

Since both decimal values are the same, the two expressions are equal.

Step 3: Therefore, the comparison sign that satisfies the condition is $=$.

Thus, the correct answer to the problem is =.

To solve this problem, we'll follow these steps:

• Step 1: Convert $2\frac{7}{100}$ to a decimal.
• Step 2: Compare the resultant decimal with $2.7$.

Now, let's work through each step:

Step 1: Convert the mixed number $2\frac{7}{100}$ into a decimal.

The whole number part is $2$, and the fractional part $\frac{7}{100}$ as a decimal is $0.07$. Therefore, the mixed number:

$2\frac{7}{100} = 2 + 0.07 = 2.07$

Step 2: Compare $2.07$ to $2.7$.

Since $2.07$ is less than $2.7$, we conclude that:

$2\frac{7}{100} < 2.7$

Therefore, the appropriate sign to choose is $<$.