Converting Decimal Fractions to Simple Fractions and Mixed Numbers: Simple conversion to denominator 10, 100, 1000

To convert 0.0008 into a fraction, follow these steps:

Step 1: Identify the number of decimal places in 0.0008. The number 0.0008 is equal to 8 thousandths.

Step 2: Write 0.0008 as a fraction. Since there are four decimal places in 0.0008, you can express it as:

$0.0008 = \frac{8}{10000}$

Step 3: Simplify the fraction if applicable. In this case, the fraction $\frac{8}{10000}$ is already in its simplest form, as there are no common factors between 8 and 10000 apart from 1.

Therefore, the fraction representation of the decimal 0.0008 is $\frac{8}{10000}$.

To convert the decimal 0.15 into a fraction, we will follow these steps:

• Step 1: Identify the decimal places
  The number 0.15 has two decimal places.

• Step 2: Express the decimal as a fraction with a denominator of a power of 10
  Since there are two decimal places, we write 0.15 as $\frac{15}{100}$.

• Step 3: Compare with given choices
  Among the provided choices, $\frac{15}{100}$ matches the initial conversion of the decimal without simplification.

Therefore, the solution to the problem in the context of the choices provided is $\frac{15}{100}$.

To convert the decimal 0.27 into a fraction, follow these steps:

• Step 1: Identify the number of decimal places in 0.27. There are two decimal places.
• Step 2: Use a denominator of 100, since 10 to the power of 2 (the number of decimal places) is 100.
• Step 3: Write the number without the decimal point as the numerator: 27.
• Step 4: Write the fraction: $\frac{27}{100}$.
• Step 5: Check if the fraction can be simplified. In this case, 27 and 100 have no common factors other than 1, so the fraction $\frac{27}{100}$ is already in its simplest form.

Therefore, the decimal 0.27 as a fraction is $\frac{27}{100}$.

To convert the decimal 0.505 into a fraction, follow these steps:

• Step 1: Recognize that the decimal 0.505 can be expressed as $\frac{505}{1000}$. This is because there are three digits after the decimal point, so we use 1000 as the denominator.
• Step 2: Check if the fraction can be simplified. The greatest common divisor (GCD) of 505 and 1000 is 5. Therefore, we divide both the numerator and the denominator by their GCD to simplify the fraction.
• Step 3: Simplifying $\frac{505}{1000}$, we divide both the numerator and the denominator by 5:
  $\frac{505 \div 5}{1000 \div 5} = \frac{101}{200}$
• Step 4: The fraction $\frac{101}{200}$ is in its simplest form, as 101 is a prime number, and no further simplification is possible.

Therefore, the decimal 0.505 is equal to the fraction $\frac{505}{1000}$, which simplifies to $\frac{101}{200}$.

Given the multiple-choice options, the correct answer based on the problem's form is:

$\frac{505}{1000}$

To convert the decimal 0.800 into a fraction, follow these steps:

• Step 1: Recognize the placement of the decimal. Since 0.800 has three decimal places, consider it as $\frac{800}{1000}$.
• Step 2: Simplify the fraction $\frac{800}{1000}$. The greatest common divisor (GCD) of 800 and 1000 is 200. Divide both numerator and denominator by 200 to simplify:

$\frac{800}{1000} = \frac{800 \div 200}{1000 \div 200} = \frac{4}{5}$.

The fraction $\frac{4}{5}$ is the simplest form of $\frac{800}{1000}$.

Since 0.800 can be understood in terms of place value, the equivalent fraction is $\frac{8}{10}$ as well:

• Step 3: Simplify the alternative fraction $\frac{8}{10}$:

$\frac{8}{10} = \frac{8 \div 2}{10 \div 2} = \frac{4}{5}$.

Both fractions reduce to the same simplest form: $\frac{4}{5}$.

Looking at the provided choices, Choices 1 ($\frac{8}{10}$) and 2 ($\frac{800}{1000}$) are both correct representations of the same value as they simplify to the fraction $\frac{4}{5}$.

Thus, according to the choices, the correct answer is: Answers (a) and (b) are correct.

To convert the decimal 0.93 into a fraction, observe the following steps:

• Step 1: Recognize that 0.93 is in the hundredths place. Thus, it can be directly expressed as $\frac{93}{100}$. The number 93 is the numerator, and 100 is the denominator, reflecting the decimal's position.
• Step 2: Consider simplifying the fraction. Since 93 and 100 have no common factors other than 1, $\frac{93}{100}$ is already in its simplest form.
• Step 3: Check if the fraction matches the multiple-choice options provided. In this case, $\frac{93}{100}$ is the correct choice.

Therefore, the decimal 0.93 is equivalent to the fraction $\frac{93}{100}$.

To convert the fraction $\frac{105}{1000}$ to a decimal, note that the denominator, 1000, is $10^3$, which means we need to move the decimal point three places to the left in the numerator.

Let's break it down:

• Start with the numerator, 105, which can be viewed as 105.0 for clarity.
• Since the denominator is 1000, move the decimal three places to the left: $105.0 \rightarrow 10.5 \rightarrow 1.05 \rightarrow 0.105$

This places the decimal correctly according to the denominator's power of ten.

Therefore, the decimal representation of $\frac{105}{1000}$ is 0.105.

To convert the fraction $\frac{346}{1000}$ into a decimal, follow these steps:

• Recognize that the denominator is 1000, which tells us the decimal will have three places after the decimal point.
• Place the number 346 over 1000 directly into decimal form, which involves moving the decimal point three places to the left.

In this case:

$\frac{346}{1000}$ in decimal form is $0.346$.

Therefore, the solution to the problem is $0.346$.

To convert the fraction $\frac{4}{100}$ into a decimal, we follow these steps:

• Step 1: Identify that we need to divide 4 by 100. In mathematical terms, this is written as $4 \div 100$.
• Step 2: Perform the division. When dividing 4 by 100, we can move the decimal point in 4 two places to the left because there are two zeros in 100.
• Step 3: Moving the decimal point in 4 (which is 4.0) two places to the left, we shift from 4.0 to 0.04.

Therefore, the decimal representation of $\frac{4}{100}$ is $0.04$.
Upon reviewing the provided choices, we see that option 3, $0.04$, corresponds exactly to our calculated result.

To convert the fraction $\frac{5}{1000}$ into a decimal, consider the following steps:

• Step 1: Recognize that the denominator 1000 represents thousandths. We need to express 5 in terms of thousandths.
• Step 2: Convert the fraction to a decimal by aligning with the place value: $\frac{5}{1000}$ is equivalent to 5 thousandths.
• Step 3: The decimal form therefore has the digit 5 in the thousandths place, which results in the number 0.005.

Since the denominator is 1000, equivalent to three decimal places, the number 5 as part of thousandths results in $0.005$.

Therefore, the solution to the problem is $\frac{5}{1000} = 0.005$. This corresponds to choice 2.

To convert the fraction $\frac{67}{1000}$ into a decimal, we recognize that the denominator 1000 implies that this fraction can be expressed in the thousandths place of a decimal.

• Step 1: Identify that the fraction $\frac{67}{1000}$ needs to be expressed with three decimal places.
• Step 2: Understand that each place value after the decimal corresponds to tenths, hundredths, and thousandths, respectively. Since we have 67 thousandths, the decimal will have three digits after the decimal point.
• Step 3: Place 67 into the decimal system by placing it three places to the right of the decimal point:

We write it as $0.067$. Here, "0.0" represents there are no tenths or hundredths, and "67" fills the thousandths place.

Therefore, the decimal equivalent of $\frac{67}{1000}$ is $\mathbf{0.067}$.

To convert the fraction $\frac{93}{100}$ into a decimal, follow these steps:

• Step 1: Recognize that the fraction's denominator is 100, which is $10^2$.
• Step 2: Convert the fraction to a decimal by moving the decimal point two places to the left in the numerator 93 (one place for each zero in 100).
• Step 3: The decimal conversion of $\frac{93}{100}$ is $0.93$.

The resulting decimal is $0.93$, which aligns with choice 2.

To solve the problem of converting the decimal 0.0157 into a fraction, follow these steps:

• Step 1: Identify the Decimal Places
  The decimal number 0.0157 has four decimal places.
• Step 2: Convert to a Fraction
  A decimal with four decimal places can be expressed as a fraction over 10,000. Therefore, 0.0157 is $\frac{157}{10000}$. This arises because 0.0157 is $\frac{157}{10000}$ when directly considering its placement over 10000 as a power of ten.
• Step 3: Simplification (if applicable)
  In this case, $\frac{157}{10000}$ is already in its simplest form since 157 and 10000 have no common factors other than 1.

Therefore, the fractional representation of the decimal 0.0157 is $\frac{157}{10000}$.

To solve this problem, let's convert the decimal 0.3 into a fraction:

• Step 1: Identify the place value of 0.3.
  Since the decimal 0.3 has one digit after the decimal point, it is in the tenths place. This means that 0.3 is equivalent to 3 tenths, or $\frac{3}{10}$.
• Step 2: Write the fraction based on the place value:
  The decimal 0.3 is expressed as $\frac{3}{10}$, where 3 is the numerator and 10 is the denominator, reflective of the tenths place.
• Step 3: Verify the answer using multiple-choice options:
  Among the choices provided, $\frac{3}{10}$ is the correct match, which corresponds to choice 3.

Therefore, the correct fraction representation for 0.3 is $\frac{3}{10}$.

To solve this problem, let's convert the fraction $\frac{3}{10}$ into a decimal.

First, identify the given fraction: $\frac{3}{10}$.

Since the denominator is 10, a power of 10, the conversion to a decimal is straightforward. The fraction $\frac{3}{10}$ can be interpreted as dividing 3 by 10.

Perform the division: $3 \div 10 = 0.3$.

This results in the decimal number $0.3$.

Therefore, the decimal conversion of the fraction $\frac{3}{10}$ is $\mathbf{0.3}$.

To solve this problem, let us follow these steps:

• Step 1: Understand the given fraction $\frac{100}{1000}$.
• Step 2: Simplify the fraction if possible.
• Step 3: Convert the simplified fraction into a decimal.

Now, let's dive into the details:

Step 1: We are given $\frac{100}{1000}$. This fraction represents 100 divided by 1000.

Step 2: The fraction can be simplified because both the numerator (100) and denominator (1000) have a common factor of 100.
Dividing both by 100 gives:

Step 3: Convert $\frac{1}{10}$ into a decimal:

The fraction $\frac{1}{10}$ means one-tenth, which can be directly written as the decimal $0.1$.

There are also other decimal forms which retain the same value such as $0.10$ and $0.100$, which are legitimate representations with different coverage of decimal precision.

Therefore, the decimal representation of $\frac{100}{1000}$ is 0.1, and among the choices provided, the answer choice representing this is "All answers are correct".

To solve this problem of converting the decimal 0.007 into a fraction, follow these steps:

• Step 1: Recognize the number of decimal places in 0.007, which is three.
• Step 2: Write 0.007 as a fraction. Place 7 (the number without the decimal) over 1 followed by three zeros, giving us a denominator of 1000. This is because there are three digits after the decimal point.

The fraction form is $\frac{7}{1000}$.

Thus, 0.007 converted into a fraction is $\frac{7}{1000}$.

To solve this problem of converting the decimal 0.7 into a fraction, follow these clear steps:

• Step 1: Understand the place value of the decimal number 0.7. The digit 7 is in the tenths place, which means it can be expressed as a fraction over 10.
• Step 2: Write down the fraction as $\frac{7}{10}$. Here, 7 is the numerator, representing the part, and 10 is the denominator, representing the whole.
• Step 3: Check if the fraction $\frac{7}{10}$ can be simplified. Since 7 and 10 have no common divisors other than 1, the fraction is already in its simplest form.

Therefore, the decimal 0.7 is equivalent to the fraction $\frac{7}{10}$.

Comparing this result with the given choices, the correct answer is choice 2: $\frac{7}{10}$.

Thus, the solution to the problem is $\frac{7}{10}$.

To solve this problem, we'll convert the decimal 0.1 into a fraction:

• Step 1: Recognize that in the decimal 0.1, the digit "1" is in the tenths place.
• Step 2: Convert 0.1 directly into a fraction by placing 1 over 10. This is because 0.1 means 1 part out of 10, i.e., $\frac{1}{10}$.

Now, let's consider the problem:

Step 1: Observe the decimal 0.1. The "1" is in the tenths place, which means it represents one-tenth.
Step 2: Hence, as a fraction, 0.1 is $\frac{1}{10}$ since there is one digit after the decimal point, implying a denominator of 10.

Therefore, the correct answer to converting 0.1 into a fraction is $\frac{1}{10}$.

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

• Step 1: Identify the decimal number given as 0.55.
• Step 2: Express 0.55 as a fraction using its place value.
• Step 3: Verify which choice this corresponds to among the provided options.

Let's work through each step:

Step 1: We have the decimal 0.55.

Step 2: In the decimal number 0.55, the first '5' is in the tenths place, and the second '5' is in the hundredths place, so this can be expressed as:
$0.55 = \frac{55}{100}$ This places 55 over 100 to correspond with its placement in the hundredths position in decimal terminology.

Step 3: Comparing the resulting fraction $\frac{55}{100}$ with the choices provided, this matches choice number two. Therefore, choice number two is the correct answer.

Hence, the solution to the problem is $\frac{55}{100}$.