SSAT Middle Level Math : Whole and Part

Study concepts, example questions & explanations for SSAT Middle Level Math

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Example Questions

Example Question #61 : Whole And Part

What is \(\displaystyle 27.268\) in expanded form? 

 

 

Possible Answers:

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

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

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

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

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

Correct answer:

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

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 \(\displaystyle 10\).

\(\displaystyle 2\times10=20\)

 

\(\displaystyle 7\) is in the ones place, so we multiply by \(\displaystyle 1\)

\(\displaystyle 7\times1=7\)

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

\(\displaystyle 2\times\frac{1}{10}=.2\)

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

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

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

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

Then we add the products together. 

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

Example Question #232 : Number & Operations In Base Ten

What is \(\displaystyle 33.128\) in expanded form? 

 

 

Possible Answers:

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

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

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

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

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

Correct answer:

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

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 \(\displaystyle 10\).

\(\displaystyle 3\times10=30\)

 

\(\displaystyle 3\) is in the ones place, so we multiply by \(\displaystyle 1\)

\(\displaystyle 3\times1=3\)

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

\(\displaystyle 1\times\frac{1}{10}=.1\)

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

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

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

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

Then we add the products together. 

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

Example Question #233 : Number & Operations In Base Ten

What is \(\displaystyle 47.236\) in expanded form? 

 

 

Possible Answers:

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

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

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

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

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

Correct answer:

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

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 \(\displaystyle 10\).

\(\displaystyle 4\times10=40\)

 

\(\displaystyle 7\) is in the ones place, so we multiply by \(\displaystyle 1\)

\(\displaystyle 7\times1=7\)

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

\(\displaystyle 2\times\frac{1}{10}=.2\)

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

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

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

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

Then we add the products together. 

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

Example Question #234 : Number & Operations In Base Ten

What is \(\displaystyle 52.354\) in expanded form? 

 

 

Possible Answers:

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

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

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

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

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

Correct answer:

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

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 \(\displaystyle 10\).

\(\displaystyle 5\times10=50\)

 

\(\displaystyle 2\) is in the ones place, so we multiply by \(\displaystyle 1\)

\(\displaystyle 2\times1=2\)

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

\(\displaystyle 3\times\frac{1}{10}=.3\)

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

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

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

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

Then we add the products together. 

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

Example Question #921 : Ssat Middle Level Quantitative (Math)

What is \(\displaystyle 61.742\) in expanded form? 

 

 

Possible Answers:

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

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

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

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

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

Correct answer:

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

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 \(\displaystyle 10\).

\(\displaystyle 6\times10=60\)

 

\(\displaystyle 1\) is in the ones place, so we multiply by \(\displaystyle 1\)

\(\displaystyle 1\times1=1\)

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

\(\displaystyle 7\times\frac{1}{10}=.7\)

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

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

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

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

Then we add the products together. 

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

Example Question #236 : Number & Operations In Base Ten

What is \(\displaystyle 76.278\) in expanded form? 

 

 

Possible Answers:

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

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

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

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

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

Correct answer:

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

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 \(\displaystyle 10\).

\(\displaystyle 7\times10=70\)

 

\(\displaystyle 6\) is in the ones place, so we multiply by \(\displaystyle 1\)

\(\displaystyle 6\times1=6\)

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

\(\displaystyle 2\times\frac{1}{10}=.2\)

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

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

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

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

Then we add the products together. 

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

Example Question #232 : Number & Operations In Base Ten

What is \(\displaystyle 87.376\) in expanded form? 

 

 

Possible Answers:

\(\displaystyle 8\times10+7\times1+3\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{1000}\right)+6\times\left(\frac{1}{1000}\right)\)

\(\displaystyle 8\times1+7\times100+3\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)+6\times\left(\frac{1}{1000}\right)\)

\(\displaystyle 8\times10+7\times100+3\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)+6\times\left(\frac{1}{1000}\right)\)

\(\displaystyle 8\times10+7\times1+3\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{1000}\right)\)

\(\displaystyle 8\times10+7\times1+3\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)+6\times\left(\frac{1}{1000}\right)\)

Correct answer:

\(\displaystyle 8\times10+7\times1+3\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)+6\times\left(\frac{1}{1000}\right)\)

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 \(\displaystyle 10\).

\(\displaystyle 8\times10=80\)

 

\(\displaystyle 7\) is in the ones place, so we multiply by \(\displaystyle 1\)

\(\displaystyle 7\times1=7\)

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

\(\displaystyle 3\times\frac{1}{10}=.3\)

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

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

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

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

Then we add the products together. 

\(\displaystyle \frac{\begin{array}[b]{r}80.000\\7.000\\ +\ .300\\ .070\\.006 \end{array}}{ \ \ \space87.376}\)

Example Question #233 : Number & Operations In Base Ten

What is \(\displaystyle 94.218\) in expanded form? 

 

 

Possible Answers:

\(\displaystyle 9\times10+4\times100+2\times\left(\frac{1}{10}\right)+1\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)\)

\(\displaystyle 9\times10+4\times1+2\times\left(\frac{1}{100}\right)+1\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)\)

\(\displaystyle 9\times10+4\times1+2\times\left(\frac{1}{10}\right)+1\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)\)

\(\displaystyle 9\times10+4\times1+2\times\left(\frac{1}{10}\right)+1\times\left(\frac{1}{1000}\right)+8\times\left(\frac{1}{1000}\right)\)

\(\displaystyle 9\times10+4\times100+2\times\left(\frac{1}{10}\right)+1\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{10000}\right)\)

Correct answer:

\(\displaystyle 9\times10+4\times1+2\times\left(\frac{1}{10}\right)+1\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)\)

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 \(\displaystyle 10\).

\(\displaystyle 9\times10=90\)

 

\(\displaystyle 4\) is in the ones place, so we multiply by \(\displaystyle 1\)

\(\displaystyle 4\times1=4\)

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

\(\displaystyle 2\times\frac{1}{10}=.2\)

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

\(\displaystyle 1\times\frac{1}{100}=.01\)

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

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

Then we add the products together. 

\(\displaystyle \frac{\begin{array}[b]{r}90.000\\4.000\\ +\ .200\\ .010\\.008 \end{array}}{ \ \ \space94.218}\)

Example Question #234 : Number & Operations In Base Ten

What is \(\displaystyle 67.458\) in expanded form? 

 

 

Possible Answers:

\(\displaystyle 6\times1+7\times10+4\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)\)

\(\displaystyle 6\times10+7\times100+4\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)\)

\(\displaystyle 6\times10+7\times100+4\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{10000}\right)\)

\(\displaystyle 6\times10+7\times1+4\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{10000}\right)\)

\(\displaystyle 6\times10+7\times1+4\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)\)

Correct answer:

\(\displaystyle 6\times10+7\times1+4\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)\)

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 \(\displaystyle 10\).

\(\displaystyle 6\times10=60\)

 

\(\displaystyle 7\) is in the ones place, so we multiply by \(\displaystyle 1\)

\(\displaystyle 7\times1=7\)

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

\(\displaystyle 4\times\frac{1}{10}=.4\)

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

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

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

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

Then we add the products together. 

\(\displaystyle \frac{\begin{array}[b]{r}60.000\\7.000\\ +\ .400\\ .050\\.008 \end{array}}{ \ \ \space67.458}\)

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 \(\displaystyle 73.254\) in expanded form? 

 

 

Possible Answers:

\(\displaystyle 7\times1+3\times100+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)\)

\(\displaystyle 7\times10+3\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)\)

\(\displaystyle 7\times10+3\times1+2\times\left(\frac{1}{100}\right)+5\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)\)

\(\displaystyle 7\times10+3\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{1000}\right)+4\times\left(\frac{1}{1000}\right)\)

\(\displaystyle 7\times10+3\times100+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)\)

Correct answer:

\(\displaystyle 7\times10+3\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)\)

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 \(\displaystyle 10\).

\(\displaystyle 7\times10=70\)

 

\(\displaystyle 3\) is in the ones place, so we multiply by \(\displaystyle 1\)

\(\displaystyle 3\times1=3\)

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

\(\displaystyle 2\times\frac{1}{10}=.2\)

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

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

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

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

Then we add the products together. 

\(\displaystyle \frac{\begin{array}[b]{r}70.000\\3.000\\ +\ .200\\ .050\\.004 \end{array}}{ \ \ \space73.254}\)

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