Examples with solutions for Decimal Fractions' Meaning: Identify Numbers on a Number Line

Exercise #1

Number of ones: 5

Number of tens: 6

Number of hundreds: 4

Determine the correct number according to the above place values:

Video Solution

Step-by-Step Solution

To solve this problem, we need to apply the place value system to construct the number correctly:

  • Step 1: Calculate the contribution of the hundreds place.
    Given: 4 hundreds, which contributes 4×100=400 4 \times 100 = 400 .
  • Step 2: Calculate the contribution of the tens place.
    Given: 6 tens, which contributes 6×10=60 6 \times 10 = 60 .
  • Step 3: Calculate the contribution of the ones place.
    Given: 5 ones, which contributes 5×1=5 5 \times 1 = 5 .
  • Step 4: Sum up all the contributions to find the required number:
    400+60+5=465 400 + 60 + 5 = 465

Therefore, the number formed according to the given place values is 465 465 .

Answer

465

Exercise #2

Number of ones: 9

Number of tens: 3

Number of hundreds: 1

Determine the correct number according to the above place values:

Video Solution

Step-by-Step Solution

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

  • Step 1: Assign each number to the correct place value.
  • Step 2: Construct the number by adding each weighted position.

Now, let's work through each step:
Step 1: We have three digits to place:
- We assign **9** to the ones (units) position.
- We assign **3** to the tens position.
- We assign **1** to the hundreds position.

Step 2: Combine these placements:
- The number is constructed as follows: 100×1+10×3+1×9100 \times 1 + 10 \times 3 + 1 \times 9
- This simplifies to: 100+30+9=139100 + 30 + 9 = 139.

Upon comparing with the provided answer choices, the correct choice is clearly 139\boxed{139}.

Therefore, the solution to the problem is 139139.

Answer

139

Exercise #3

Number of ones: 2

Number of tens: 1

Number of hundreds: 8

Determine the correct number according to the above place values:

Video Solution

Step-by-Step Solution

To determine the number based on place values:

  • Step 1: Calculate hundreds. There are 8 8 hundreds, so 8×100=800 8 \times 100 = 800 .
  • Step 2: Calculate tens. There is 1 1 ten, so 1×10=10 1 \times 10 = 10 .
  • Step 3: Calculate ones. There are 2 2 ones, so 2×1=2 2 \times 1 = 2 .

Now sum the results of these calculations:

  • Total = hundreds + tens + ones =800+10+2=812 = 800 + 10 + 2 = 812 .

Thus, the number formed by the given place values is 812 812 .

Answer

812

Exercise #4

Number of ones: 9

Number of tens: 2

Number of hundreds: 1

Determine the correct number according to the above place values:

Video Solution

Step-by-Step Solution

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

  • Identify the contribution of each place value.
  • Sum these contributions to determine the resulting number.

Now, let's work through each step:

Step 1: Identify the contribution of each place value
We are given the number of ones, tens, and hundreds as follows:

  • Number of ones = 9, so this contributes 9×1=9 9 \times 1 = 9 .
  • Number of tens = 2, so this contributes 2×10=20 2 \times 10 = 20 .
  • Number of hundreds = 1, so this contributes 1×100=100 1 \times 100 = 100 .

Step 2: Sum these contributions to determine the resulting number
The total value is calculated by summing these contributions:
(1×100)+(2×10)+(9×1)=100+20+9=129(1 \times 100) + (2 \times 10) + (9 \times 1) = 100 + 20 + 9 = 129.

Therefore, the number corresponding to the given place values is 129129.

Answer

129

Exercise #5

Number of ones: 6

Number of tens: 3

Number of hundreds: 9

Determine the correct number according to the above place values:

Video Solution

Step-by-Step Solution

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

  • Step 1: Understand place values: Hundreds, Tens, and Ones.
  • Step 2: Assign given numbers to the respective place values.
  • Step 3: Construct the number using the assigned values.

Let's break it down:

Step 1: Recognize the place values:

  • Hundreds place: Any digit here is multiplied by 100.
  • Tens place: Any digit here is multiplied by 10.
  • Ones place: Any digit here is multiplied by 1.

Step 2: Assign the numbers:

  • The number of ones is given as 6. This means the ones place is 6.
  • The number of tens is 3. This means the tens place is 3.
  • The number of hundreds is 9. This means the hundreds place is 9.

Step 3: Construct the number:

Using the place values, compile the number as follows:

  • The hundreds place contributes 9×100=9009 \times 100 = 900.
  • The tens place contributes 3×10=303 \times 10 = 30.
  • The ones place contributes 6×1=66 \times 1 = 6.

Adding these values together gives:

900+30+6=936 900 + 30 + 6 = 936

Thus, the correct number according to the place values provided is 936 936 .

Comparing with the choices provided, the correct choice is Choice 4: 936 936 .

Answer

936

Exercise #6

Number of ones: 8

Number of tens: 1

Number of hundreds: 7

Determine the correct number according to the above place values:

Video Solution

Step-by-Step Solution

To solve this problem, we need to construct a number using the digits provided for specific place values.

  • Step 1: Identify the place values: ones, tens, and hundreds.
  • Step 2: Allocate the digits to the correct place values:
    - Ones digit: 88
    - Tens digit: 11
    - Hundreds digit: 77
  • Step 3: Combine these according to place value to form the number.

Thus, we construct the number by starting from the highest place value to the lowest:
Hundreds place: 77
Tens place: 11
Ones place: 88

Hence, the number formed by these place values is 718718.

Therefore, the correct solution is 718718.

Answer

718

Exercise #7

Number of ones: 6

Number of tens: 5

Number of hundreds: 9

Determine the correct number according to the above place values:

Video Solution

Step-by-Step Solution

To solve this problem, we need to apply an understanding of place values in constructing a number. Let's go through the steps:

  • Step 1: Identify the hundreds digit. According to the problem, there are 9 hundreds.
  • Step 2: Identify the tens digit. The problem states there are 5 tens.
  • Step 3: Identify the ones digit. The problem indicates there are 6 ones.
  • Step 4: Assemble the number. The hundreds digit (9) is placed at the leftmost position, followed by the tens digit (5), and finally the ones digit (6) in the rightmost position.

Assembling these digits gives us the number 956, which matches the option identified as correct in the multiple-choice list.

Therefore, the solution to the problem is 956 956 .

Answer

956

Exercise #8

Number of ones: 3

Number of tens: 2

Number of hundreds: 1

Determine the correct number according to the above place values:

Video Solution

Step-by-Step Solution

To solve this problem, we'll use the concept of place value, where each digit in a number has a different value depending on its position.

Given:

  • Number of ones: 33
  • Number of tens: 22
  • Number of hundreds: 11

Step-by-step explanation:

  • Step 1: Start with the hundreds place, which contributes 1×100=1001 \times 100 = 100.
  • Step 2: Next is the tens place, which contributes 2×10=202 \times 10 = 20.
  • Step 3: Finally, the ones place contributes 3×1=33 \times 1 = 3.

Adding these contributions together gives us:

100+20+3=123 100 + 20 + 3 = 123

The number we are looking for, according to the given place values, is 123\textbf{123}.

Therefore, the correct choice is:

Choice 1: 123123

Answer

123

Exercise #9

Number of ones: 1

Number of tens: 4

Number of hundreds: 3

Determine the correct number according to the given place values:

Video Solution

Step-by-Step Solution

To solve this problem, we need to construct a number using the given place values:

  • Step 1: Calculate the hundreds place contribution: 3×100=300 3 \times 100 = 300 .
  • Step 2: Calculate the tens place contribution: 4×10=40 4 \times 10 = 40 .
  • Step 3: Calculate the ones place contribution: 1×1=1 1 \times 1 = 1 .
  • Step 4: Sum these contributions to get the final number: 300+40+1=341 300 + 40 + 1 = 341 .

Therefore, the correct number according to the given place values is 341 341 .

Answer

341

Exercise #10

Number of ones: 6

Number of tens: 3

Number of hundreds: 1

Determine the correct number according to the given place values:

Video Solution

Step-by-Step Solution

To solve this problem, we need to construct a number based on the specified digits for each place value.

  • Step 1: Identify each place value.
    • Hundreds place: 1
    • Tens place: 3
    • Ones place: 6
  • Step 2: Construct the number using these digits.
    • The hundreds digit is 11.
    • The tens digit is 33.
    • The ones digit is 66.
  • Step 3: Combine these digits to form the number 136136.

The number formed by placing 1 in the hundreds place, 3 in the tens place, and 6 in the ones place is 136\textbf{136}.

Therefore, the correct number is 136136.

Answer

136

Exercise #11

Number of ones: 5

Number of tens: 2

Number of hundreds: 8

Determine the correct number according to the given place values:

Video Solution

Step-by-Step Solution

To solve this problem, let's assign the given values to their respective decimal place values and construct the number:

  • Step 1: Assign the values to their decimal places:
    - Hundreds: We have 8 -> This means 8 in the hundreds place -> 8×100=800 8 \times 100 = 800 .
    - Tens: We have 2 -> This means 2 in the tens place -> 2×10=20 2 \times 10 = 20 .
    - Ones: We have 5 -> This is simply 5 -> 5 5 .
  • Step 2: Sum these values to form the number:
    - Total: 800+20+5=825 800 + 20 + 5 = 825 .

Thus, the number composed using the given place values is 825 825 .

Answer

825

Exercise #12

Number of ones: 6

Number of tens: 6

Number of hundreds: 6

Determine the correct number according to the given place values:

Video Solution

Step-by-Step Solution

To solve the problem of determining the number, we will use the place values provided and construct the number accordingly:

  • Step 1: The number of ones is 6, indicating the digit in the units place is 66.
  • Step 2: The number of tens is 6, indicating the digit in the tens place is 66.
  • Step 3: The number of hundreds is 6, indicating the digit in the hundreds place is 66.

Having established the place values and corresponding digits, the final number is constructed as follows:
- Hundreds place is 66, so it contributes 600600.
- Tens place is 66, so it contributes 6060.
- Ones place is 66, so it contributes 66.

Therefore, by adding these values, we get the number 666666.

Among the choices provided, the option 666 matches our constructed number.

Therefore, the solution to the problem is 666666.

Answer

666

Exercise #13

Number of ones: 1

Number of tens: 3

Number of hundreds: 1

Determine the correct number according to the given place values:

Video Solution

Step-by-Step Solution

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

  • Step 1: Understand and identify the place values.
  • Step 2: Calculate the contribution of each place value.
  • Step 3: Sum the contributions to get the total number.

Now, let's work through each step:
Step 1: We are given the digits: 1 one, 3 tens, and 1 hundred, which means the respective places are:
- Hundreds place: 1
- Tens place: 3
- Ones place: 1

Step 2: Calculate the contributions from each digit:
- For the hundreds place: Multiply 1 (hundreds digit) by 100: 1×100=1001 \times 100 = 100.
- For the tens place: Multiply 3 (tens digit) by 10: 3×10=303 \times 10 = 30.
- For the ones place: Multiply 1 (ones digit) by 1: 1×1=11 \times 1 = 1.

Step 3: Sum the contributions:
Combine all the calculated values: 100+30+1=131100 + 30 + 1 = 131.
Thus, the number formed by these place values is 131.

Therefore, the solution to the problem is 131 131 .

Answer

131

Exercise #14

Number of ones: 3

Number of tens: 7

Number of hundreds: 8

Determine the correct number according to the given place values:

Video Solution

Step-by-Step Solution

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

  • Identify the hundreds, tens, and ones place values from the problem statement.
  • Construct the number by placing each digit in its respective place: hundreds, tens, then ones.

Now, let's work through each step:
Step 1: The problem provides us with the number of ones as 3, the number of tens as 7, and the number of hundreds as 8.
Step 2: In a typical decimal number system, the hundreds digit comes first, followed by the tens digit, and then the ones digit. Hence, the number is constructed as follows:
- Hundreds place: 8
- Tens place: 7
- Ones place: 3
Number=873 \text{Number} = 873

Therefore, the solution to the problem is 873 873 .

Answer

873

Exercise #15

Number of ones: 1

Number of tens: 5

Number of hundreds: 9

Determine the correct number according to the given place values:

Video Solution

Step-by-Step Solution

To solve this problem, we need to construct a number based on given place values. Let's proceed with the solution:

  • Step 1: Identify the digits for each place value.

The problem states:

- The number of ones is 1.
- The number of tens is 5.
- The number of hundreds is 9.

  • Step 2: Use these digits to form the number.

In the decimal system:

  • The ones place contributes 1×1=1 1 \times 1 = 1 .
  • The tens place contributes 5×10=50 5 \times 10 = 50 .
  • The hundreds place contributes 9×100=900 9 \times 100 = 900 .

We add these contributions to get the number:

900+50+1=951 900 + 50 + 1 = 951

Conclusion: Thus, the correct number according to the given place values is 951 951 .

Matching with provided choices:

  • Choice 1: 915 – Incorrect
  • Choice 2: 950 – Incorrect
  • Choice 3: 951 – Correct
  • Choice 4: 955 – Incorrect

Therefore, the answer is choice 3: 951\textbf{951}.

Answer

951

Exercise #16

Number of ones: 2

Number of tens: 3

Number of hundreds: 7

Determine the correct number according to the given place values:

Video Solution

Step-by-Step Solution

To solve this problem, we aim to construct a number using the digits provided for each place value. Here's how we do it:

  • Step 1: Identify the hundreds place digit.

    The number of hundreds is given as 7. Hence, the hundreds place is occupied by 7.

  • Step 2: Identify the tens place digit.

    The number of tens is given as 3. Thus, the tens place is occupied by 3.

  • Step 3: Identify the ones place digit.

    The number of ones is given as 2. So, the ones place is occupied by 2.

  • Step 4: Assemble the digits based on their place values.

    Assembling these digits together, from hundreds to ones, we get the number 732.

Therefore, the answer is 732 732 which corresponds to choice 3 in the given options.

Answer

732

Exercise #17

Number of ones: 1

Number of tens: 2

Number of hundreds: 8

Determine the correct number according to the above place values:

Video Solution

Answer

821