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SSAT Middle Level Math : Numbers and Operations

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Example Questions

Example Question #37 : Whole And Part

What is 79.25 $\displaystyle 79.25$ in expanded form?

Possible Answers:

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

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

$7\times100+9\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)$ $\displaystyle 7\times100+9\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)$

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

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

Correct answer:

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

Explanation:

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

$\displaystyle 7$ 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 $\frac{1}{100}$ $\displaystyle \frac{1}{100}$.

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

Then we add the products together.

$\frac{\begin{array}[b]{r}70.00\\9.00\\ +\ .20\\ .05 \end{array}}{ \ \ \space79.25}$ $\displaystyle \frac{\begin{array}[b]{r}70.00\\9.00\\ +\ .20\\ .05 \end{array}}{ \ \ \space79.25}$

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Example Question #21 : Read And Write Decimals To Thousandths Using Base Ten Numerals, Number Names, And Expanded Form: Ccss.Math.Content.5.Nbt.A.3a

What is 36.73 $\displaystyle 36.73$ in expanded form?

Possible Answers:

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

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

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

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

$3\times100+6\times1+7\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{10}\right)$ $\displaystyle 3\times100+6\times1+7\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{10}\right)$

Correct answer:

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

Explanation:

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

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

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

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

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

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

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

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

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

Then we add the products together.

$\frac{\begin{array}[b]{r}30.00\\6.00\\ +\ .70\\ .03 \end{array}}{ \ \ \space36.73}$ $\displaystyle \frac{\begin{array}[b]{r}30.00\\6.00\\ +\ .70\\ .03 \end{array}}{ \ \ \space36.73}$

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Example Question #32 : How To Find The Whole From The Part

What is 49.28 $\displaystyle 49.28$ in expanded form?

Possible Answers:

$4\times10+9\times1+2\times\left(\frac{1}{10}\right)+8\times\left(\frac{1}{10}\right)$ $\displaystyle 4\times10+9\times1+2\times\left(\frac{1}{10}\right)+8\times\left(\frac{1}{10}\right)$

$4\times10+9\times1+2\times\left(\frac{1}{10}\right)+8\times\left(\frac{1}{100}\right)$ $\displaystyle 4\times10+9\times1+2\times\left(\frac{1}{10}\right)+8\times\left(\frac{1}{100}\right)$

$4\times10+9\times10+2\times\left(\frac{1}{10}\right)+8\times\left(\frac{1}{100}\right)$ $\displaystyle 4\times10+9\times10+2\times\left(\frac{1}{10}\right)+8\times\left(\frac{1}{100}\right)$

$4\times10+9\times1+2\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{100}\right)$ $\displaystyle 4\times10+9\times1+2\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{100}\right)$

$4\times100+9\times1+2\times\left(\frac{1}{10}\right)+8\times\left(\frac{1}{100}\right)$ $\displaystyle 4\times100+9\times1+2\times\left(\frac{1}{10}\right)+8\times\left(\frac{1}{100}\right)$

Correct answer:

$4\times10+9\times1+2\times\left(\frac{1}{10}\right)+8\times\left(\frac{1}{100}\right)$ $\displaystyle 4\times10+9\times1+2\times\left(\frac{1}{10}\right)+8\times\left(\frac{1}{100}\right)$

Explanation:

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

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

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

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

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

$\displaystyle 8$ is in the hundredths place, so we multiply by $\frac{1}{100}$ $\displaystyle \frac{1}{100}$.

$8\times\frac{1}{100}=.08$ $\displaystyle 8\times\frac{1}{100}=.08$

Then we add the products together.

$\frac{\begin{array}[b]{r}40.00\\9.00\\ +\ .20\\ .08 \end{array}}{ \ \ \space49.28}$ $\displaystyle \frac{\begin{array}[b]{r}40.00\\9.00\\ +\ .20\\ .08 \end{array}}{ \ \ \space49.28}$

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Example Question #211 : Number & Operations In Base Ten

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

Possible Answers:

$5\times100+3\times1+2\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{100}\right)$ $\displaystyle 5\times100+3\times1+2\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{100}\right)$

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

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

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

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

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 #41 : Whole And Part

What is 69.62 $\displaystyle 69.62$ in expanded form?

Possible Answers:

$6\times10+9\times1+6\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{10}\right)$ $\displaystyle 6\times10+9\times1+6\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{10}\right)$

$6\times10+9\times10+6\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)$ $\displaystyle 6\times10+9\times10+6\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)$

$6\times10+9\times1+6\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)$ $\displaystyle 6\times10+9\times1+6\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)$

$6\times100+9\times10+6\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)$ $\displaystyle 6\times100+9\times10+6\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)$

$6\times10+9\times1+6\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{1000}\right)$ $\displaystyle 6\times10+9\times1+6\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{1000}\right)$

Correct answer:

$6\times10+9\times1+6\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)$ $\displaystyle 6\times10+9\times1+6\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)$

Explanation:

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

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

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

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

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

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

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

$\displaystyle 2$ 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.

$\frac{\begin{array}[b]{r}60.00\\9.00\\ +\ .60\\ .02 \end{array}}{ \ \ \space69.62}$ $\displaystyle \frac{\begin{array}[b]{r}60.00\\9.00\\ +\ .60\\ .02 \end{array}}{ \ \ \space69.62}$

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Example Question #41 : Whole And Part

What is 79.14 $\displaystyle 79.14$ in expanded form?

Possible Answers:

$7\times10+9\times10+1\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)$ $\displaystyle 7\times10+9\times10+1\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)$

$7\times10+9\times1+1\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{1000}\right)$ $\displaystyle 7\times10+9\times1+1\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{1000}\right)$

$7\times10+9\times1+1\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)$ $\displaystyle 7\times10+9\times1+1\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)$

$7\times100+9\times10+1\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)$ $\displaystyle 7\times100+9\times10+1\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)$

$7\times10+9\times1+1\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{100}\right)$ $\displaystyle 7\times10+9\times1+1\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{100}\right)$

Correct answer:

$7\times10+9\times1+1\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)$ $\displaystyle 7\times10+9\times1+1\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)$

Explanation:

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

$\displaystyle 7$ 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 $\displaystyle 1$.

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

$\displaystyle 1$ 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.

$\frac{\begin{array}[b]{r}70.00\\9.00\\ +\ .10\\ .04 \end{array}}{ \ \ \space79.14}$ $\displaystyle \frac{\begin{array}[b]{r}70.00\\9.00\\ +\ .10\\ .04 \end{array}}{ \ \ \space79.14}$

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Example Question #43 : How To Find The Whole From The Part

What is 87.53 $\displaystyle 87.53$ in expanded form?

Possible Answers:

$8\times100+7\times1+5\times\left(\frac{1}{100}\right)+3\times\left(\frac{1}{100}\right)$ $\displaystyle 8\times100+7\times1+5\times\left(\frac{1}{100}\right)+3\times\left(\frac{1}{100}\right)$

$8\times10+7\times1+5\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{10}\right)$ $\displaystyle 8\times10+7\times1+5\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{10}\right)$

$8\times10+7\times1+5\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{100}\right)$ $\displaystyle 8\times10+7\times1+5\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{100}\right)$

$8\times10+7\times10+5\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{100}\right)$ $\displaystyle 8\times10+7\times10+5\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{100}\right)$

$8\times100+7\times1+5\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{1000}\right)$ $\displaystyle 8\times100+7\times1+5\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{1000}\right)$

Correct answer:

$8\times10+7\times1+5\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{100}\right)$ $\displaystyle 8\times10+7\times1+5\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{100}\right)$

Explanation:

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

$\displaystyle 8$ is in the tens place, so we multiply by $\displaystyle 10$.

$8\times10=80$ $\displaystyle 8\times10=80$

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

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

$\displaystyle 5$ is in the tenths place, so we multiply by $\frac{1}{10}$ $\displaystyle \frac{1}{10}$.

$5\times\frac{1}{10}=.5$ $\displaystyle 5\times\frac{1}{10}=.5$

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

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

Then we add the products together.

$\frac{\begin{array}[b]{r}80.00\\7.00\\ +\ .50\\ .03 \end{array}}{ \ \ \space87.53}$ $\displaystyle \frac{\begin{array}[b]{r}80.00\\7.00\\ +\ .50\\ .03 \end{array}}{ \ \ \space87.53}$

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Example Question #44 : How To Find The Whole From The Part

What is 94.25 $\displaystyle 94.25$ in expanded form?

Possible Answers:

$9\times10+4\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{10}\right)$ $\displaystyle 9\times10+4\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{10}\right)$

$9\times100+4\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{1000}\right)$ $\displaystyle 9\times100+4\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{1000}\right)$

$9\times100+4\times10+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{10}\right)$ $\displaystyle 9\times100+4\times10+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{10}\right)$

$9\times100+4\times10+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)$ $\displaystyle 9\times100+4\times10+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)$

$9\times10+4\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)$ $\displaystyle 9\times10+4\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)$

Correct answer:

$9\times10+4\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)$ $\displaystyle 9\times10+4\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)$

Explanation:

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

$\displaystyle 9$ is in the tens place, so we multiply by $\displaystyle 10$.

$9\times10=90$ $\displaystyle 9\times10=90$

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

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

$\displaystyle 2$ 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.

$\frac{\begin{array}[b]{r}90.00\\4.00\\ +\ .20\\ .05 \end{array}}{ \ \ \space94.25}$ $\displaystyle \frac{\begin{array}[b]{r}90.00\\4.00\\ +\ .20\\ .05 \end{array}}{ \ \ \space94.25}$

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Example Question #45 : How To Find The Whole From The Part

What is 23.65 $\displaystyle 23.65$ in expanded form?

Possible Answers:

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

$2\times100+3\times1+6\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)$ $\displaystyle 2\times100+3\times1+6\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)$

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

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

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

Correct answer:

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

Explanation:

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

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

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

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

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

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

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

$\displaystyle 5$ 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.

$\frac{\begin{array}[b]{r}20.00\\3.00\\ +\ .60\\ .05 \end{array}}{ \ \ \space23.65}$ $\displaystyle \frac{\begin{array}[b]{r}20.00\\3.00\\ +\ .60\\ .05 \end{array}}{ \ \ \space23.65}$

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Example Question #46 : How To Find The Whole From The Part

What is 14.57 $\displaystyle 14.57$ in expanded form?

Possible Answers:

$1\times10+4\times10+5\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)$ $\displaystyle 1\times10+4\times10+5\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)$

$1\times100+4\times1+5\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)$ $\displaystyle 1\times100+4\times1+5\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)$

$1\times10+4\times1+5\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{10}\right)$ $\displaystyle 1\times10+4\times1+5\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{10}\right)$

$1\times10+4\times1+5\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)$ $\displaystyle 1\times10+4\times1+5\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)$

$1\times10+4\times10+5\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{1000}\right)$ $\displaystyle 1\times10+4\times10+5\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{1000}\right)$

Correct answer:

$1\times10+4\times1+5\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)$ $\displaystyle 1\times10+4\times1+5\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)$

Explanation:

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

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

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

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

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

$\displaystyle 5$ is in the tenths place, so we multiply by $\frac{1}{10}$ $\displaystyle \frac{1}{10}$.

$5\times\frac{1}{10}=.5$ $\displaystyle 5\times\frac{1}{10}=.5$

$\displaystyle 5$ 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.

$\frac{\begin{array}[b]{r}10.00\\4.00\\ +\ .50\\ .07 \end{array}}{ \ \ \space14.57}$ $\displaystyle \frac{\begin{array}[b]{r}10.00\\4.00\\ +\ .50\\ .07 \end{array}}{ \ \ \space14.57}$

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SSAT Middle Level Math : Numbers and Operations

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