Comparing Decimal Fractions: Is the equality correct?

To determine if the fractions are equal, compare the two decimal numbers:

$0.250$ and $0.0250$.

The placement of zeros can affect the value, but in this case:

$0.250$ is equivalent to $\frac{250}{1000}$, which simplifies to $\frac{1}{4}$.

$0.0250$ is equivalent to $\frac{250}{10000}$, which simplifies to $\frac{1}{40}$.

The fractions $\frac{1}{4}$ and $\frac{1}{40}$ are not equal, therefore:

$0.250 \neq 0.0250$

To determine if these two decimal fractions are equal, we compare the numbers directly. The first number is $0.25$, which is equivalent to the fraction $\frac{25}{100}$. The second number is $0.052$, which is equivalent to the fraction $\frac{52}{1000}$.

First, let's convert $0.25$ to thousandths to compare it directly with $0.052$:

$0.25 = \frac{25}{100} = \frac{250}{1000}$

Now, compare $\frac{250}{1000}$ and $\frac{52}{1000}$: clearly, $250 \neq 52$.

Therefore, $0.25 \neq 0.052$, making the expression false.

To determine if these two decimal fractions are equal, we compare the numbers directly. The first number is $0.45$, which is equivalent to the fraction $\frac{45}{100}$. The second number is $0.045$, which is equivalent to the fraction $\frac{45}{1000}$.

First, let's convert $0.45$ to thousandths to compare it directly with $0.045$:

$0.45 = \frac{45}{100} = \frac{450}{1000}$

Now, compare $\frac{450}{1000}$ and $\frac{45}{1000}$: clearly, $450 \neq 45$.

Therefore, $0.45 \neq 0.045$, making the expression false.

To determine if the fractions are equal, we compare the decimal numbers carefully.

In $0.505$, the digits are 0, 5, 0, and 5.

In $0.5005$, the digits are 0, 5, 0, 0, and 5.

The first fraction, $0.505$, has no digit in the thousandths place, whereas the second fraction, $0.5005$, has a zero in the thousandths place.

Therefore, $0.505 \neq 0.5005$.

To determine if the fractions are equal, examine each digit of the decimal numbers.

In the number $0.707$, the digits are 0, 7, and 7.

In the number $0.7007$, the digits are 0, 7, 0, and 7.

The first fraction, $0.707$, has no digit in the thousandths place, but the second fraction, $0.7007$, contains a zero in the thousandths place.

Thus, $0.707 \neq 0.7007$.

The question asks if the two decimal numbers $0.75$ and $0.750$ are equal. Decimal numbers can have trailing zeros which do not affect their value. Therefore, $0.75$ is indeed equal to $0.750$ because trailing zeros after the decimal point do not change the number's value. Hence, the fractions are equal.

To determine if the fractions are equal, compare the two decimal numbers:

$1.2300$ and $1.0230$.

Check the whole number and decimal parts:

Here, the whole numbers $1$ are equal, but the decimal parts are different:

$0.2300$ and $0.0230$.

$0.2300$ is equivalent to $\frac{2300}{10000} = \frac{23}{100}$.

$0.0230$ is equivalent to $\frac{230}{10000} = \frac{23}{1000}$.

$\frac{23}{100} \neq \frac{23}{1000}$.

Therefore, $1.2300 \neq 1.0230$.

The question asks if the decimal numbers $1.5$ and $1.50$ are equal. When dealing with decimals, trailing zeros are not necessary for determining equality. In the case of the given numbers, $1.5$ is exactly equal to $1.50$ because the trailing zero in $1.50$ does not alter its value. Thus, the fractions are indeed equal.