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Common Core: 5th Grade Math : Number & Operations in Base Ten

Study concepts, example questions & explanations for Common Core: 5th Grade Math

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All Common Core: 5th Grade Math Resources

7 Diagnostic Tests 225 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #451 : Operations And Properties

What digit is in the tenths place?

45.376 $\displaystyle 45.376$

Possible Answers:

$\displaystyle 3$

$\displaystyle 5$

$\displaystyle 6$

$\displaystyle 4$

$\displaystyle 7$

Correct answer:

$\displaystyle 3$

Explanation:

The tenths place will also be the first digit to the right of the decimal point.

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Example Question #453 : Operations And Properties

What digit is in the thousandths place?

$\displaystyle 4567.321$

Possible Answers:

$\displaystyle 1$

$\displaystyle 7$

$\displaystyle 4$

$\displaystyle 6$

$\displaystyle 5$

Correct answer:

$\displaystyle 1$

Explanation:

The thousandths place will alway be the third digit to the right of the decimal.

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Example Question #461 : Operations And Properties

What digit is in the thousandths place?

$9\textup,834.172$ $\displaystyle 9\textup,834.172$

Possible Answers:

$\displaystyle 9$

$\displaystyle 4$

$\displaystyle 3$

$\displaystyle 8$

$\displaystyle 2$

Correct answer:

$\displaystyle 2$

Explanation:

The thousandths place will always be the third digit to the right of the decimal point.

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Example Question #181 : Number & Operations In Base Ten

What is 9.25 $\displaystyle 9.25$ in expanded form?

Possible Answers:

$9\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{1000}\right)$ $\displaystyle 9\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{1000}\right)$

$9\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{10}\right)$ $\displaystyle 9\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{10}\right)$

$9\times1+2\times\left(\frac{1}{100}\right)+5\times\left(\frac{1}{100}\right)$ $\displaystyle 9\times1+2\times\left(\frac{1}{100}\right)+5\times\left(\frac{1}{100}\right)$

$9\times1+2\times\left(\frac{1}{100}\right)+5\times\left(\frac{1}{1000}\right)$ $\displaystyle 9\times1+2\times\left(\frac{1}{100}\right)+5\times\left(\frac{1}{1000}\right)$

$9\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)$ $\displaystyle 9\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)$

Correct answer:

$9\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)$ $\displaystyle 9\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)$

Explanation:

When we write a number in expanded form, we multiply each digit by its place value.

$\displaystyle 9$ is in the ones place, so we multiply by $\displaystyle 1$.

$9\times1=9$ $\displaystyle 9\times1=9$

$\displaystyle 2$ is in the tenths place, so we multiply by $\frac{1}{10}$ $\displaystyle \frac{1}{10}$.

$2\times\frac{1}{10}=.2$ $\displaystyle 2\times\frac{1}{10}=.2$

$\displaystyle 5$ is in the hundredths place, so we multiply by $\frac{1}{100}$ $\displaystyle \frac{1}{100}$.

$5\times\frac{1}{100}=.05$ $\displaystyle 5\times\frac{1}{100}=.05$

Then we add the products together.

$\frac{\begin{array}[b]{r}9.00\\ +\ .20\\ .05 \end{array}}{ \ \ \space9.25}$ $\displaystyle \frac{\begin{array}[b]{r}9.00\\ +\ .20\\ .05 \end{array}}{ \ \ \space9.25}$

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Example Question #1 : Read And Write Decimals To Thousandths Using Base Ten Numerals, Number Names, And Expanded Form: Ccss.Math.Content.5.Nbt.A.3a

What is 3.92 $\displaystyle 3.92$ in expanded form?

Possible Answers:

$3\times1+9\times\left(\frac{1}{100}\right)+2\times\left(\frac{1}{1000}\right)$ $\displaystyle 3\times1+9\times\left(\frac{1}{100}\right)+2\times\left(\frac{1}{1000}\right)$

$3\times1+9\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{10}\right)$ $\displaystyle 3\times1+9\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{10}\right)$

$3\times1+9\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{1000}\right)$ $\displaystyle 3\times1+9\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{1000}\right)$

$3\times1+9\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)$ $\displaystyle 3\times1+9\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)$

$3\times1+9\times\left(\frac{1}{100}\right)+2\times\left(\frac{1}{100}\right)$ $\displaystyle 3\times1+9\times\left(\frac{1}{100}\right)+2\times\left(\frac{1}{100}\right)$

Correct answer:

$3\times1+9\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)$ $\displaystyle 3\times1+9\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)$

Explanation:

When we write a number in expanded form, we multiply each digit by its place value.

$\displaystyle 3$ is in the ones place, so we multiply by $\displaystyle 1$.

$3\times1=3$ $\displaystyle 3\times1=3$

$\displaystyle 9$ is in the tenths place, so we multiply by $\frac{1}{10}$ $\displaystyle \frac{1}{10}$.

$9\times\frac{1}{10}=.9$ $\displaystyle 9\times\frac{1}{10}=.9$

$\displaystyle 2$ is in the hundredths place, so we multiply by $\frac{1}{100}$ $\displaystyle \frac{1}{100}$.

$2\times\frac{1}{100}=.02$ $\displaystyle 2\times\frac{1}{100}=.02$

Then we add the products together.

$\frac{\begin{array}[b]{r}3.00\\ +\ .90\\ .02 \end{array}}{ \ \ \space3.92}$ $\displaystyle \frac{\begin{array}[b]{r}3.00\\ +\ .90\\ .02 \end{array}}{ \ \ \space3.92}$

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Example Question #2 : Read And Write Decimals To Thousandths Using Base Ten Numerals, Number Names, And Expanded Form: Ccss.Math.Content.5.Nbt.A.3a

What is 4.89 $\displaystyle 4.89$ in expanded form?

Possible Answers:

$4\times1+8\times\left(\frac{1}{10}\right)+9\times\left(\frac{1}{100}\right)$ $\displaystyle 4\times1+8\times\left(\frac{1}{10}\right)+9\times\left(\frac{1}{100}\right)$

$4\times1+8\times\left(\frac{1}{10}\right)+9\times\left(\frac{1}{10}\right)$ $\displaystyle 4\times1+8\times\left(\frac{1}{10}\right)+9\times\left(\frac{1}{10}\right)$

$4\times1+8\times\left(\frac{1}{100}\right)+9\times\left(\frac{1}{100}\right)$ $\displaystyle 4\times1+8\times\left(\frac{1}{100}\right)+9\times\left(\frac{1}{100}\right)$

$4\times1+8\times\left(\frac{1}{100}\right)+9\times\left(\frac{1}{1000}\right)$ $\displaystyle 4\times1+8\times\left(\frac{1}{100}\right)+9\times\left(\frac{1}{1000}\right)$

$4\times1+8\times\left(\frac{1}{10}\right)+9\times\left(\frac{1}{1000}\right)$ $\displaystyle 4\times1+8\times\left(\frac{1}{10}\right)+9\times\left(\frac{1}{1000}\right)$

Correct answer:

$4\times1+8\times\left(\frac{1}{10}\right)+9\times\left(\frac{1}{100}\right)$ $\displaystyle 4\times1+8\times\left(\frac{1}{10}\right)+9\times\left(\frac{1}{100}\right)$

Explanation:

When we write a number in expanded form, we multiply each digit by its place value.

$\displaystyle 4$ is in the ones place, so we multiply by $\displaystyle 1$.

$4\times1=4$ $\displaystyle 4\times1=4$

$\displaystyle 8$ is in the tenths place, so we multiply by $\frac{1}{10}$ $\displaystyle \frac{1}{10}$.

$8\times\frac{1}{10}=.8$ $\displaystyle 8\times\frac{1}{10}=.8$

$\displaystyle 9$ is in the hundredths place, so we multiply by $\frac{1}{100}$ $\displaystyle \frac{1}{100}$.

$9\times\frac{1}{100}=.09$ $\displaystyle 9\times\frac{1}{100}=.09$

Then we add the products together.

$\frac{\begin{array}[b]{r}4.00\\ +\ .80\\ .09 \end{array}}{ \ \ \space4.89}$ $\displaystyle \frac{\begin{array}[b]{r}4.00\\ +\ .80\\ .09 \end{array}}{ \ \ \space4.89}$

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Example Question #873 : Ssat Middle Level Quantitative (Math)

What is 5.67 $\displaystyle 5.67$ in expanded form?

Possible Answers:

$5\times1+6\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)$ $\displaystyle 5\times1+6\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)$

$5\times1+6\times\left(\frac{1}{100}\right)+7\times\left(\frac{1}{100}\right)$ $\displaystyle 5\times1+6\times\left(\frac{1}{100}\right)+7\times\left(\frac{1}{100}\right)$

$5\times1+6\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{10}\right)$ $\displaystyle 5\times1+6\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{10}\right)$

$5\times1+6\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{1000}\right)$ $\displaystyle 5\times1+6\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{1000}\right)$

$5\times1+6\times\left(\frac{1}{100}\right)+7\times\left(\frac{1}{10}\right)$ $\displaystyle 5\times1+6\times\left(\frac{1}{100}\right)+7\times\left(\frac{1}{10}\right)$

Correct answer:

$5\times1+6\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)$ $\displaystyle 5\times1+6\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)$

Explanation:

When we write a number in expanded form, we multiply each digit by its place value.

$\displaystyle 5$ is in the ones place, so we multiply by $\displaystyle 1$.

$5\times1=5$ $\displaystyle 5\times1=5$

$\displaystyle 6$ is in the tenths place, so we multiply by $\frac{1}{10}$ $\displaystyle \frac{1}{10}$.

$6\times\frac{1}{10}=.6$ $\displaystyle 6\times\frac{1}{10}=.6$

$\displaystyle 7$ is in the hundredths place, so we multiply by $\frac{1}{100}$ $\displaystyle \frac{1}{100}$.

$7\times\frac{1}{100}=.07$ $\displaystyle 7\times\frac{1}{100}=.07$

Then we add the products together.

$\frac{\begin{array}[b]{r}5.00\\ +\ .60\\ .07 \end{array}}{ \ \ \space5.67}$ $\displaystyle \frac{\begin{array}[b]{r}5.00\\ +\ .60\\ .07 \end{array}}{ \ \ \space5.67}$

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Example Question #1 : Read And Write Decimals To Thousandths Using Base Ten Numerals, Number Names, And Expanded Form: Ccss.Math.Content.5.Nbt.A.3a

What is 6.14 $\displaystyle 6.14$ in expanded form?

Possible Answers:

$6\times1+1\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{10}\right)$ $\displaystyle 6\times1+1\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{10}\right)$

$6\times1+1\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{10}\right)$ $\displaystyle 6\times1+1\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{10}\right)$

$6\times1+1\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{100}\right)$ $\displaystyle 6\times1+1\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{100}\right)$

$6\times1+1\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)$ $\displaystyle 6\times1+1\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)$

$6\times1+1\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)$ $\displaystyle 6\times1+1\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)$

Correct answer:

$6\times1+1\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)$ $\displaystyle 6\times1+1\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)$

Explanation:

When we write a number in expanded form, we multiply each digit by its place value.

$\displaystyle 6$ is in the ones place, so we multiply by $\displaystyle 1$.

$6\times1=6$ $\displaystyle 6\times1=6$

$\displaystyle 1$ is in the tenths place, so we multiply by $\frac{1}{10}$ $\displaystyle \frac{1}{10}$.

$1\times\frac{1}{10}=.1$ $\displaystyle 1\times\frac{1}{10}=.1$

$\displaystyle 4$ is in the hundredths place, so we multiply by $\frac{1}{100}$ $\displaystyle \frac{1}{100}$.

$4\times\frac{1}{100}=.04$ $\displaystyle 4\times\frac{1}{100}=.04$

Then we add the products together.

$\frac{\begin{array}[b]{r}6.00\\ +\ .10\\ .04 \end{array}}{ \ \ \space6.14}$ $\displaystyle \frac{\begin{array}[b]{r}6.00\\ +\ .10\\ .04 \end{array}}{ \ \ \space6.14}$

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Example Question #4 : Read And Write Decimals To Thousandths Using Base Ten Numerals, Number Names, And Expanded Form: Ccss.Math.Content.5.Nbt.A.3a

What is 7.81 $\displaystyle 7.81$ in expanded form?

Possible Answers:

$7\times1+8\times\left(\frac{1}{10}\right)+1\times\left(\frac{1}{10}\right)$ $\displaystyle 7\times1+8\times\left(\frac{1}{10}\right)+1\times\left(\frac{1}{10}\right)$

$7\times1+8\times\left(\frac{1}{100}\right)+1\times\left(\frac{1}{100}\right)$ $\displaystyle 7\times1+8\times\left(\frac{1}{100}\right)+1\times\left(\frac{1}{100}\right)$

$7\times1+8\times\left(\frac{1}{10}\right)+1\times\left(\frac{1}{1000}\right)$ $\displaystyle 7\times1+8\times\left(\frac{1}{10}\right)+1\times\left(\frac{1}{1000}\right)$

$7\times1+8\times\left(\frac{1}{100}\right)+1\times\left(\frac{1}{10}\right)$ $\displaystyle 7\times1+8\times\left(\frac{1}{100}\right)+1\times\left(\frac{1}{10}\right)$

$7\times1+8\times\left(\frac{1}{10}\right)+1\times\left(\frac{1}{100}\right)$ $\displaystyle 7\times1+8\times\left(\frac{1}{10}\right)+1\times\left(\frac{1}{100}\right)$

Correct answer:

$7\times1+8\times\left(\frac{1}{10}\right)+1\times\left(\frac{1}{100}\right)$ $\displaystyle 7\times1+8\times\left(\frac{1}{10}\right)+1\times\left(\frac{1}{100}\right)$

Explanation:

When we write a number in expanded form, we multiply each digit by its place value.

$\displaystyle 9$ is in the ones place, so we multiply by $\displaystyle 1$.

$7\times1=7$ $\displaystyle 7\times1=7$

$\displaystyle 8$ is in the tenths place, so we multiply by $\frac{1}{10}$ $\displaystyle \frac{1}{10}$.

$8\times\frac{1}{10}=.8$ $\displaystyle 8\times\frac{1}{10}=.8$

$\displaystyle 1$ is in the hundredths place, so we multiply by $\frac{1}{100}$ $\displaystyle \frac{1}{100}$.

$1\times\frac{1}{100}=.01$ $\displaystyle 1\times\frac{1}{100}=.01$

Then we add the products together.

$\frac{\begin{array}[b]{r}7.00\\ +\ .80\\ .01 \end{array}}{ \ \ \space7.81}$ $\displaystyle \frac{\begin{array}[b]{r}7.00\\ +\ .80\\ .01 \end{array}}{ \ \ \space7.81}$

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Example Question #21 : How To Find The Whole From The Part

What is 9.16 $\displaystyle 9.16$ in expanded form?

Possible Answers:

$9\times1+1\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{100}\right)$ $\displaystyle 9\times1+1\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{100}\right)$

$9\times1+1\times\left(\frac{1}{100}\right)+6\times\left(\frac{1}{100}\right)$ $\displaystyle 9\times1+1\times\left(\frac{1}{100}\right)+6\times\left(\frac{1}{100}\right)$

$9\times1+1\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{10}\right)$ $\displaystyle 9\times1+1\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{10}\right)$

$9\times1+1\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{1000}\right)$ $\displaystyle 9\times1+1\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{1000}\right)$

$9\times1+1\times\left(\frac{1}{100}\right)+6\times\left(\frac{1}{1000}\right)$ $\displaystyle 9\times1+1\times\left(\frac{1}{100}\right)+6\times\left(\frac{1}{1000}\right)$

Correct answer:

$9\times1+1\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{100}\right)$ $\displaystyle 9\times1+1\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{100}\right)$

Explanation:

When we write a number in expanded form, we multiply each digit by its place value.

$\displaystyle 9$ is in the ones place, so we multiply by $\displaystyle 1$.

$9\times1=9$ $\displaystyle 9\times1=9$

$\displaystyle 1$ is in the tenths place, so we multiply by $\frac{1}{10}$ $\displaystyle \frac{1}{10}$.

$1\times\frac{1}{10}=.1$ $\displaystyle 1\times\frac{1}{10}=.1$

$\displaystyle 6$ is in the hundredths place, so we multiply by $\frac{1}{100}$ $\displaystyle \frac{1}{100}$.

$6\times\frac{1}{100}=.06$ $\displaystyle 6\times\frac{1}{100}=.06$

Then we add the products together.

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All Common Core: 5th Grade Math Resources

7 Diagnostic Tests 225 Practice Tests Question of the Day Flashcards Learn by Concept

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Common Core: 5th Grade Math : Number & Operations in Base Ten

Study concepts, example questions & explanations for Common Core: 5th Grade Math

All Common Core: 5th Grade Math Resources

Example Questions

Example Question #451 : Operations And Properties

Example Question #453 : Operations And Properties

Example Question #461 : Operations And Properties

Example Question #181 : Number & Operations In Base Ten

Example Question #1 : Read And Write Decimals To Thousandths Using Base Ten Numerals, Number Names, And Expanded Form: Ccss.Math.Content.5.Nbt.A.3a

Example Question #2 : Read And Write Decimals To Thousandths Using Base Ten Numerals, Number Names, And Expanded Form: Ccss.Math.Content.5.Nbt.A.3a

Example Question #873 : Ssat Middle Level Quantitative (Math)

Example Question #1 : Read And Write Decimals To Thousandths Using Base Ten Numerals, Number Names, And Expanded Form: Ccss.Math.Content.5.Nbt.A.3a

Example Question #4 : Read And Write Decimals To Thousandths Using Base Ten Numerals, Number Names, And Expanded Form: Ccss.Math.Content.5.Nbt.A.3a

Example Question #21 : How To Find The Whole From The Part

All Common Core: 5th Grade Math Resources

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