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SSAT Middle Level Math : Numbers and Operations

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Example Questions

Example Question #221 : Number & Operations In Base Ten

What is 12.84 $\displaystyle 12.84$ in expanded form?

Possible Answers:

$1\times10+2\times10+8\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{100}\right)$ $\displaystyle 1\times10+2\times10+8\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{100}\right)$

$1\times10+2\times1+8\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{1000}\right)$ $\displaystyle 1\times10+2\times1+8\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{1000}\right)$

$1\times10+2\times10+8\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)$ $\displaystyle 1\times10+2\times10+8\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)$

$1\times10+2\times1+8\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{100}\right)$ $\displaystyle 1\times10+2\times1+8\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{100}\right)$

$1\times10+2\times1+8\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)$ $\displaystyle 1\times10+2\times1+8\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)$

Correct answer:

$1\times10+2\times1+8\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)$ $\displaystyle 1\times10+2\times1+8\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)$

Explanation:

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

$\displaystyle 1$ is in the tens place, so we multiply by $\displaystyle 10$.

$1\times10=10$ $\displaystyle 1\times10=10$

$\displaystyle 2$ is in the ones place, so we multiply by $\displaystyle 1$.

$2\times1=2$ $\displaystyle 2\times1=2$

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

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

$\displaystyle 4$ 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.

$\frac{\begin{array}[b]{r}10.00\\2.00\\ +\ .80\\ .04 \end{array}}{ \ \ \space12.84}$ $\displaystyle \frac{\begin{array}[b]{r}10.00\\2.00\\ +\ .80\\ .04 \end{array}}{ \ \ \space12.84}$

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Example Question #54 : Whole And Part

What is 29.44 $\displaystyle 29.44$ in expanded form?

Possible Answers:

$2\times10+9\times1+4\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)$ $\displaystyle 2\times10+9\times1+4\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)$

$2\times10+9\times10+4\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{1000}\right)$ $\displaystyle 2\times10+9\times10+4\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{1000}\right)$

$2\times10+9\times100+4\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)$ $\displaystyle 2\times10+9\times100+4\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)$

$2\times10+9\times100+4\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)$ $\displaystyle 2\times10+9\times100+4\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)$

$2\times10+9\times1+4\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{1000}\right)$ $\displaystyle 2\times10+9\times1+4\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{1000}\right)$

Correct answer:

$2\times10+9\times1+4\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)$ $\displaystyle 2\times10+9\times1+4\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)$

Explanation:

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

$\displaystyle 2$ is in the tens place, so we multiply by $\displaystyle 10$.

$2\times10=20$ $\displaystyle 2\times10=20$

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

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

$\displaystyle 4$ is in the tenths place, so we multiply by $\frac{1}{10}$ $\displaystyle \frac{1}{10}$.

$4\times\frac{1}{10}=.4$ $\displaystyle 4\times\frac{1}{10}=.4$

$\displaystyle 4$ 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.

$\frac{\begin{array}[b]{r}20.00\\9.00\\ +\ .40\\ .04 \end{array}}{ \ \ \space29.44}$ $\displaystyle \frac{\begin{array}[b]{r}20.00\\9.00\\ +\ .40\\ .04 \end{array}}{ \ \ \space29.44}$

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Example Question #55 : Whole And Part

What is 53.26 $\displaystyle 53.26$ in expanded form?

Possible Answers:

$5\times10+3\times100+2\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{100}\right)$ $\displaystyle 5\times10+3\times100+2\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{100}\right)$

$5\times10+3\times1+2\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{1000}\right)$ $\displaystyle 5\times10+3\times1+2\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{1000}\right)$

$5\times10+3\times100+2\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{1000}\right)$ $\displaystyle 5\times10+3\times100+2\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{1000}\right)$

$5\times10+3\times1+2\times\left(\frac{1}{100}\right)+6\times\left(\frac{1}{1000}\right)$ $\displaystyle 5\times10+3\times1+2\times\left(\frac{1}{100}\right)+6\times\left(\frac{1}{1000}\right)$

$5\times10+3\times1+2\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{100}\right)$ $\displaystyle 5\times10+3\times1+2\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{100}\right)$

Correct answer:

$5\times10+3\times1+2\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{100}\right)$ $\displaystyle 5\times10+3\times1+2\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{100}\right)$

Explanation:

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

$\displaystyle 5$ is in the tens place, so we multiply by $\displaystyle 10$.

$5\times10=50$ $\displaystyle 5\times10=50$

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

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

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

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

$\displaystyle 6$ 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.

$\frac{\begin{array}[b]{r}50.00\\3.00\\ +\ .20\\ .06 \end{array}}{ \ \ \space53.26}$ $\displaystyle \frac{\begin{array}[b]{r}50.00\\3.00\\ +\ .20\\ .06 \end{array}}{ \ \ \space53.26}$

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Example Question #51 : Whole And Part

What is 79.258 $\displaystyle 79.258$ in expanded form?

$7\times10+9\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$ $\displaystyle 7\times10+9\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

Possible Answers:

$7\times10+9\times1+2\times\left(\frac{1}{100}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$ $\displaystyle 7\times10+9\times1+2\times\left(\frac{1}{100}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

$7\times10+9\times10+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$ $\displaystyle 7\times10+9\times10+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

$7\times10+9\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{1000}\right)+8\times\left(\frac{1}{1000}\right)$ $\displaystyle 7\times10+9\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{1000}\right)+8\times\left(\frac{1}{1000}\right)$

$7\times10+9\times100+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$ $\displaystyle 7\times10+9\times100+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

Correct answer:

Explanation:

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

$\displaystyle 7$ is in the tens place, so we multiply by $\displaystyle 10$.

$7\times10=70$ $\displaystyle 7\times10=70$

$\displaystyle 9$ 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 $\frac{1}{100}$ $\displaystyle \frac{1}{100}$.

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

$\displaystyle 8$ is in the thousandths place, so we will multiply by $\frac{1}{1000}$ $\displaystyle \frac{1}{1000}$.

$8\times\frac{1}{1000}=.008$ $\displaystyle 8\times\frac{1}{1000}=.008$

Then we add the products together.

$\frac{\begin{array}[b]{r}70.000\\9.000\\ +\ .200\\ .050\\.008 \end{array}}{ \ \ \space79.258}$ $\displaystyle \frac{\begin{array}[b]{r}70.000\\9.000\\ +\ .200\\ .050\\.008 \end{array}}{ \ \ \space79.258}$

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Example Question #251 : Numbers And Operations

What is 27.268 $\displaystyle 27.268$ in expanded form?

Possible Answers:

$2\times10+7\times1+2\times\left(\frac{1}{100}\right)+6\times\left(\frac{1}{1000}\right)+8\times\left(\frac{1}{1000}\right)$ $\displaystyle 2\times10+7\times1+2\times\left(\frac{1}{100}\right)+6\times\left(\frac{1}{1000}\right)+8\times\left(\frac{1}{1000}\right)$

$2\times10+7\times100+2\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$ $\displaystyle 2\times10+7\times100+2\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

$2\times1+7\times10+2\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$ $\displaystyle 2\times1+7\times10+2\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

$2\times10+7\times1+2\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{10}\right)+8\times\left(\frac{1}{100}\right)$ $\displaystyle 2\times10+7\times1+2\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{10}\right)+8\times\left(\frac{1}{100}\right)$

$2\times10+7\times1+2\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$ $\displaystyle 2\times10+7\times1+2\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

Correct answer:

Explanation:

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

$\displaystyle 2$ is in the tens place, so we multiply by $\displaystyle 10$.

$2\times10=20$ $\displaystyle 2\times10=20$

$\displaystyle 7$ is in the ones place, so we multiply by $\displaystyle 1$.

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

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

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

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

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

$\displaystyle 8$ is in the thousandths place, so we will multiply by $\frac{1}{1000}$ $\displaystyle \frac{1}{1000}$.

$8\times\frac{1}{1000}=.008$ $\displaystyle 8\times\frac{1}{1000}=.008$

Then we add the products together.

$\frac{\begin{array}[b]{r}20.000\\7.000\\ +\ .200\\ .060\\.008 \end{array}}{ \ \ \space27.268}$ $\displaystyle \frac{\begin{array}[b]{r}20.000\\7.000\\ +\ .200\\ .060\\.008 \end{array}}{ \ \ \space27.268}$

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Example Question #232 : Number & Operations In Base Ten

What is 33.128 $\displaystyle 33.128$ in expanded form?

Possible Answers:

$3\times10+3\times1+1\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{1000}\right)+8\times\left(\frac{1}{1000}\right)$ $\displaystyle 3\times10+3\times1+1\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{1000}\right)+8\times\left(\frac{1}{1000}\right)$

$3\times10+3\times10+1\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$ $\displaystyle 3\times10+3\times10+1\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

$3\times10+3\times1+1\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$ $\displaystyle 3\times10+3\times1+1\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

$3\times10+3\times1+1\times\left(\frac{1}{100}\right)+2\times\left(\frac{1}{10}\right)+8\times\left(\frac{1}{1000}\right)$ $\displaystyle 3\times10+3\times1+1\times\left(\frac{1}{100}\right)+2\times\left(\frac{1}{10}\right)+8\times\left(\frac{1}{1000}\right)$

$3\times100+3\times10+1\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$ $\displaystyle 3\times100+3\times10+1\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

Correct answer:

Explanation:

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

$\displaystyle 3$ is in the tens place, so we multiply by $\displaystyle 10$.

$3\times10=30$ $\displaystyle 3\times10=30$

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

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

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

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

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

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

$\displaystyle 8$ is in the thousandths place, so we will multiply by $\frac{1}{1000}$ $\displaystyle \frac{1}{1000}$.

$8\times\frac{1}{1000}=.008$ $\displaystyle 8\times\frac{1}{1000}=.008$

Then we add the products together.

$\frac{\begin{array}[b]{r}30.000\\3.000\\ +\ .100\\ .020\\.008 \end{array}}{ \ \ \space33.128}$ $\displaystyle \frac{\begin{array}[b]{r}30.000\\3.000\\ +\ .100\\ .020\\.008 \end{array}}{ \ \ \space33.128}$

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Example Question #51 : Read And Write Decimals To Thousandths Using Base Ten Numerals, Number Names, And Expanded Form: Ccss.Math.Content.5.Nbt.A.3a

What is 47.236 $\displaystyle 47.236$ in expanded form?

Possible Answers:

$4\times10+7\times1+2\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{100}\right)+6\times\left(\frac{1}{1000}\right)$ $\displaystyle 4\times10+7\times1+2\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{100}\right)+6\times\left(\frac{1}{1000}\right)$

$4\times10+7\times100+2\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{100}\right)+6\times\left(\frac{1}{1000}\right)$ $\displaystyle 4\times10+7\times100+2\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{100}\right)+6\times\left(\frac{1}{1000}\right)$

$4\times10+7\times1+2\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{100}\right)+6\times\left(\frac{1}{10000}\right)$ $\displaystyle 4\times10+7\times1+2\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{100}\right)+6\times\left(\frac{1}{10000}\right)$

$4\times10+7\times100+2\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{100}\right)+6\times\left(\frac{1}{10000}\right)$ $\displaystyle 4\times10+7\times100+2\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{100}\right)+6\times\left(\frac{1}{10000}\right)$

$4\times10+7\times1+2\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{1000}\right)$ $\displaystyle 4\times10+7\times1+2\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{1000}\right)$

Correct answer:

Explanation:

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

$\displaystyle 4$ is in the tens place, so we multiply by $\displaystyle 10$.

$4\times10=40$ $\displaystyle 4\times10=40$

$\displaystyle 7$ is in the ones place, so we multiply by $\displaystyle 1$.

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

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

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

$\displaystyle 3$ is in the hundredths place, so we multiply by $\frac{1}{100}$ $\displaystyle \frac{1}{100}$.

$3\times\frac{1}{100}=.03$ $\displaystyle 3\times\frac{1}{100}=.03$

$\displaystyle 6$ is in the thousandths place, so we will multiply by $\frac{1}{1000}$ $\displaystyle \frac{1}{1000}$.

$6\times\frac{1}{1000}=.006$ $\displaystyle 6\times\frac{1}{1000}=.006$

Then we add the products together.

$\frac{\begin{array}[b]{r}40.000\\7.000\\ +\ .200\\ .030\\.006 \end{array}}{ \ \ \space47.236}$ $\displaystyle \frac{\begin{array}[b]{r}40.000\\7.000\\ +\ .200\\ .030\\.006 \end{array}}{ \ \ \space47.236}$

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Example Question #52 : Read And Write Decimals To Thousandths Using Base Ten Numerals, Number Names, And Expanded Form: Ccss.Math.Content.5.Nbt.A.3a

What is 52.354 $\displaystyle 52.354$ in expanded form?

Possible Answers:

$5\times1+2\times10+3\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)$ $\displaystyle 5\times1+2\times10+3\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)$

$5\times10+2\times10+3\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)$ $\displaystyle 5\times10+2\times10+3\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)$

$5\times1+2\times100+3\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)$ $\displaystyle 5\times1+2\times100+3\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)$

$5\times10+2\times1+3\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)$ $\displaystyle 5\times10+2\times1+3\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)$

$5\times10+2\times100+3\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)$ $\displaystyle 5\times10+2\times100+3\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)$

Correct answer:

Explanation:

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

$\displaystyle 5$ is in the tens place, so we multiply by $\displaystyle 10$.

$5\times10=50$ $\displaystyle 5\times10=50$

$\displaystyle 2$ is in the ones place, so we multiply by $\displaystyle 1$.

$2\times1=2$ $\displaystyle 2\times1=2$

$\displaystyle 3$ is in the tenths place, so we multiply by $\frac{1}{10}$ $\displaystyle \frac{1}{10}$.

$3\times\frac{1}{10}=.3$ $\displaystyle 3\times\frac{1}{10}=.3$

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

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

$\displaystyle 4$ is in the thousandths place, so we will multiply by $\frac{1}{1000}$ $\displaystyle \frac{1}{1000}$.

$4\times\frac{1}{1000}=.004$ $\displaystyle 4\times\frac{1}{1000}=.004$

Then we add the products together.

$\frac{\begin{array}[b]{r}50.000\\2.000\\ +\ .300\\ .050\\.004 \end{array}}{ \ \ \space52.354}$ $\displaystyle \frac{\begin{array}[b]{r}50.000\\2.000\\ +\ .300\\ .050\\.004 \end{array}}{ \ \ \space52.354}$

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Example Question #53 : Read And Write Decimals To Thousandths Using Base Ten Numerals, Number Names, And Expanded Form: Ccss.Math.Content.5.Nbt.A.3a

What is 61.742 $\displaystyle 61.742$ in expanded form?

Possible Answers:

$6\times10+1\times1+7\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)+2\times\left(\frac{1}{1000}\right)$ $\displaystyle 6\times10+1\times1+7\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)+2\times\left(\frac{1}{1000}\right)$

$6\times1+1\times100+7\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)+2\times\left(\frac{1}{1000}\right)$ $\displaystyle 6\times1+1\times100+7\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)+2\times\left(\frac{1}{1000}\right)$

$6\times10+1\times1+7\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{1000}\right)+2\times\left(\frac{1}{1000}\right)$ $\displaystyle 6\times10+1\times1+7\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{1000}\right)+2\times\left(\frac{1}{1000}\right)$

$6\times1+1\times10+7\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)+2\times\left(\frac{1}{1000}\right)$ $\displaystyle 6\times1+1\times10+7\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)+2\times\left(\frac{1}{1000}\right)$

$6\times10+1\times1+7\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)+2\times\left(\frac{1}{10000}\right)$ $\displaystyle 6\times10+1\times1+7\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)+2\times\left(\frac{1}{10000}\right)$

Correct answer:

Explanation:

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

$\displaystyle 6$ is in the tens place, so we multiply by $\displaystyle 10$.

$6\times10=60$ $\displaystyle 6\times10=60$

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

$1\times1=1$ $\displaystyle 1\times1=1$

$\displaystyle 7$ is in the tenths place, so we multiply by $\frac{1}{10}$ $\displaystyle \frac{1}{10}$.

$7\times\frac{1}{10}=.7$ $\displaystyle 7\times\frac{1}{10}=.7$

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

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

$\displaystyle 2$ is in the thousandths place, so we will multiply by $\frac{1}{1000}$ $\displaystyle \frac{1}{1000}$.

$2\times\frac{1}{1000}=.002$ $\displaystyle 2\times\frac{1}{1000}=.002$

Then we add the products together.

$\frac{\begin{array}[b]{r}60.000\\1.000\\ +\ .700\\ .040\\.002 \end{array}}{ \ \ \space61.742}$ $\displaystyle \frac{\begin{array}[b]{r}60.000\\1.000\\ +\ .700\\ .040\\.002 \end{array}}{ \ \ \space61.742}$

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Example Question #54 : Read And Write Decimals To Thousandths Using Base Ten Numerals, Number Names, And Expanded Form: Ccss.Math.Content.5.Nbt.A.3a

What is 76.278 $\displaystyle 76.278$ in expanded form?

Possible Answers:

$7\times10+6\times1+2\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{1000}\right)+8\times\left(\frac{1}{1000}\right)$ $\displaystyle 7\times10+6\times1+2\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{1000}\right)+8\times\left(\frac{1}{1000}\right)$

$7\times10+6\times1+2\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$ $\displaystyle 7\times10+6\times1+2\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

$7\times1+6\times10+2\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$ $\displaystyle 7\times1+6\times10+2\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

$7\times10+6\times1+2\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{10}\right)+8\times\left(\frac{1}{100}\right)$ $\displaystyle 7\times10+6\times1+2\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{10}\right)+8\times\left(\frac{1}{100}\right)$

$7\times10+6\times100+2\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$ $\displaystyle 7\times10+6\times100+2\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

Correct answer:

Explanation:

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

$\displaystyle 7$ is in the tens place, so we multiply by $\displaystyle 10$.

$7\times10=70$ $\displaystyle 7\times10=70$

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

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

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

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

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

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

$\displaystyle 8$ is in the thousandths place, so we will multiply by $\frac{1}{1000}$ $\displaystyle \frac{1}{1000}$.

$8\times\frac{1}{1000}=.008$ $\displaystyle 8\times\frac{1}{1000}=.008$

Then we add the products together.

$\frac{\begin{array}[b]{r}70.000\\6.000\\ +\ .200\\ .070\\.008 \end{array}}{ \ \ \space76.278}$ $\displaystyle \frac{\begin{array}[b]{r}70.000\\6.000\\ +\ .200\\ .070\\.008 \end{array}}{ \ \ \space76.278}$

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SSAT Middle Level Math : Numbers and Operations

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Example Question #221 : Number & Operations In Base Ten

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Example Question #51 : Read And Write Decimals To Thousandths Using Base Ten Numerals, Number Names, And Expanded Form: Ccss.Math.Content.5.Nbt.A.3a

Example Question #52 : Read And Write Decimals To Thousandths Using Base Ten Numerals, Number Names, And Expanded Form: Ccss.Math.Content.5.Nbt.A.3a

Example Question #53 : Read And Write Decimals To Thousandths Using Base Ten Numerals, Number Names, And Expanded Form: Ccss.Math.Content.5.Nbt.A.3a

Example Question #54 : Read And Write Decimals To Thousandths Using Base Ten Numerals, Number Names, And Expanded Form: Ccss.Math.Content.5.Nbt.A.3a

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