Multiplying and Dividing Decimal Fractions by 10, 100, etc.: Complete the missing numbers

To solve the problem $? \times 10 = 45$, we can use the following steps:

• Step 1: Understand the equation $(? \times 10 = 45)$.
• Step 2: Rearrange the equation to solve for the unknown: $? = \frac{45}{10}$.
• Step 3: Perform the division operation: $\frac{45}{10} = 4.5$.

We divide 45 by 10 to find that the missing number is 4.5. Therefore, $4.5 \times 10 = 45$.

Thus, the missing number in the equation is $\boxed{4.5}$.

From the given choices, the correct answer is $\boxed{4.5}$, which corresponds to choice 3.

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

• Step 1: Write down the given equation $0.1 \times ? = 10$.
• Step 2: Solve the equation by isolating $'?'$ using division. We divide both sides of the equation by $0.1$.

Let's work through these steps in detail:
Step 1: We have $0.1 \times ? = 10$.
Step 2: To isolate $'?'$, divide both sides of the equation by $0.1$. This gives us $? = \frac{10}{0.1}$.
Calculating this division: $? = \frac{10}{0.1} = 100$.

Therefore, the solution to this problem is $\boxdot 100$, confirming the equivalence $0.1 \times 100 = 10$.

To solve this problem, we need to find out what number, when multiplied by $0.1$, equals $1$. This means setting up the equation $0.1 \times x = 1$.

To isolate $x$, rearrange the equation:
$x = \frac{1}{0.1}$

Next, perform the division $1 \div 0.1$. Dividing by a decimal is equivalent to multiplying by its reciprocal, thus:
$\frac{1}{0.1} = 1 \times 10 = 10$

Therefore, the solution to the equation is $x = 10$.

To solve this problem, we need to determine the value that, when multiplied with 1.56, results in 15.6. Let's proceed with a step-by-step approach:

• Step 1: Identify the task. We have the division relationship $15.6 : x = 1.56$, where $x$ is the missing number we want to find.
• Step 2: Set up an equation based on this relationship: $x = \frac{15.6}{1.56}$.
• Step 3: Perform the division. Convert 15.6 and 1.56 to eliminate decimals, facilitating easier division: - Multiply both numerator and denominator by 100 to make it an integer division: $\frac{15.6 \times 100}{1.56 \times 100} = \frac{1560}{156}$.
• Step 4: Simplify the fraction $\frac{1560}{156}$: - Divide both numbers by the greatest common divisor, which is 156: $\frac{1560 \div 156}{156 \div 156} = \frac{10}{1} = 10$.
• Step 5: Verify. Multiply 1.56 by 10 to check: $1.56 \times 10 = 15.6$, confirming our calculation.

Therefore, the solution to the problem is that the missing number is $10$.

To solve this problem, we'll use the equation $1.66 \div x = 0.166$. This can be rewritten in terms of multiplication as:

• $x = \frac{1.66}{0.166}$

Now, let's perform the division:

First, recognize that dividing by a decimal is equivalent to dividing their fractions:

• $1.66 = \frac{166}{100}$
• $0.166 = \frac{166}{1000}$

Therefore, we have:

$x = \frac{1.66}{0.166} = \frac{\frac{166}{100}}{\frac{166}{1000}}$

Dividing these fractions is equivalent to multiplying by the reciprocal:

$x = \frac{166}{100} \times \frac{1000}{166}$

Cancel out $166$ in the numerator and denominator:

$x = \frac{1000}{100} = 10$

Therefore, the missing number $x$ is $\boxed{10}$.

To find the value of '?', we'll set up the equation based on the division of numbers:

Given that $5.2 \div ? = 0.52$, we can rewrite this equation as:

$5.2 = 0.52 \times ?$

To isolate the '?', we divide both sides of the equation by 0.52:

$? = \frac{5.2}{0.52}$

Calculating this division gives us:

$? = 10$

This means when 5.2 is divided by 10, the result is 0.52, confirming that '? = 10' is correct.

Therefore, the solution to the problem is $10$.

To find the missing number that, when multiplied by 10, equals 3.3, let's follow these steps:

• Step 1: Start with the equation $x \times 10 = 3.3$.

• Step 2: To isolate $x$, divide both sides of the equation by 10:

$x = \frac{3.3}{10}$

Step 3: Perform the division. Dividing 3.3 by 10 effectively shifts the decimal point one place to the left:

$x = 0.33$

Therefore, the solution to the equation is $x = 0.33$.

This matches choice 4: $0.33$.

To solve this problem, we need to find the value of $x$ in the equation:

$\frac{x}{100} = 0.0244$

Let's follow these steps:

• Step 1: Recognize that $\frac{x}{100}$ is equivalent to dividing $x$ by 100.

• Step 2: To isolate $x$, we need to perform the inverse operation of dividing by 100, which is multiplying by 100.

• Step 3: Multiply both sides of the equation by 100.
  $\frac{x}{100} \times 100 = 0.0244 \times 100$

• Step 4: Simplify the left-hand side to just $x$, and calculate the right-hand side:
  $x = 2.44$

Thus, the value of $x$ that satisfies the equation is $x = 2.44$.

Accordingly, the correct answer is the choice '$2.44$'.

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

• Step 1: Start with the equation $\frac{x}{100} = 0.0111$.
• Step 2: Multiply both sides of the equation by 100 to isolate $x$.

Now, let's work through each step:
Step 1: We have $\frac{x}{100} = 0.0111$.
Step 2: To solve for $x$, multiply both sides by 100:
$(x = 0.0111 \times 100)$

This simplifies to:
$x = 1.11$

Therefore, the number that fits the equation is $x = 1.11$.

Looking at the choices provided, the correct answer is $1.11$.

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

• Step 1: Identify the equation given in the problem
• Step 2: Solve for the unknown variable $x$

Now, let's work through each step:
Step 1: The problem asks us to find the value of $x$ in the equation $12.33 \times x = 1233$.
Step 2: To isolate $x$, divide both sides by 12.33:

$x = \frac{1233}{12.33}$

Calculate the division:

$x \approx 100$

Therefore, the solution to the problem is $\boxed{100}$. Given the multiple-choice options, the correct answer matches choice 2: $100$.

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

• Step 1: Recognize the given expression as a division problem: $52.3 : x = 0.523$.
• Step 2: Convert it into a multiplication equation: $52.3 = 0.523 \times x$.
• Step 3: Solve for $x$. This means rearranging the equation: $x = \frac{52.3}{0.523}$.
• Step 4: Perform the division to find $x$.

Now, let's work through these steps:

Step 1: We start with $52.3 : x = 0.523$.

Step 2: By converting the division into multiplication, we have $52.3 = 0.523 \times x$.

Step 3: Isolating $x$, we rewrite this as $x = \frac{52.3}{0.523}$.

Step 4: Performing the division yields $x = 100$.

Therefore, the solution to the problem is $x = 100$.

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

• Step 1: Identify the equation $? \times 100 = 511$.
• Step 2: Solve for the unknown by using division.

Now, let's work through the solution:

Step 1: We start with the equation provided: $? \times 100 = 511$.

Step 2: To isolate the unknown, divide both sides of the equation by 100.
$? = \frac{511}{100}$

Performing the division, we have:
$? = 5.11$

Therefore, the solution to the problem is $5.11$.