SSAT Middle Level Math : Numbers and Operations

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

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Example Questions

Example Question #243 : Number & Operations In Base Ten

What is \(\displaystyle 66.729\) in expanded form? 

 

 

Possible Answers:

\(\displaystyle 6\times1+6\times10+7\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)+9\times\left(\frac{1}{10000}\right)\)

\(\displaystyle 6\times10+6\times1+7\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)+9\times\left(\frac{1}{10000}\right)\)

\(\displaystyle 6\times10+6\times1+7\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)+9\times\left(\frac{1}{1000}\right)\)

\(\displaystyle 6\times10+6\times1+7\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{1000}\right)+9\times\left(\frac{1}{1000}\right)\)

\(\displaystyle 6\times1+6\times10+7\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)+9\times\left(\frac{1}{1000}\right)\)

Correct answer:

\(\displaystyle 6\times10+6\times1+7\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)+9\times\left(\frac{1}{1000}\right)\)

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 \(\displaystyle 10\).

\(\displaystyle 6\times10=60\)

 

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

\(\displaystyle 6\times1=6\)

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

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

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

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

\(\displaystyle 9\) is in the thousandths place, so we will multiply by \(\displaystyle \frac{1}{1000}\).

\(\displaystyle 9\times\frac{1}{1000}=.009\)

Then we add the products together. 

\(\displaystyle \frac{\begin{array}[b]{r}60.000\\6.000\\ +\ .700\\ .020\\.009 \end{array}}{ \ \ \space66.729}\)

Example Question #244 : Number & Operations In Base Ten

What is \(\displaystyle 73.958\) in expanded form? 

 

 

Possible Answers:

\(\displaystyle 7\times10+3\times1+9\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)\)

\(\displaystyle 7\times10+3\times100+9\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)\)

\(\displaystyle 7\times1+3\times10+9\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{10000}\right)\)

\(\displaystyle 7\times1+3\times10+9\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)\)

\(\displaystyle 7\times10+3\times1+9\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{10000}\right)\)

Correct answer:

\(\displaystyle 7\times10+3\times1+9\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)\)

Explanation:

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

\(\displaystyle 7\) 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 \(\displaystyle 1\)

\(\displaystyle 3\times1=3\)

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

\(\displaystyle 9\times\frac{1}{10}=.9\)

\(\displaystyle 5\) 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. 

\(\displaystyle \frac{\begin{array}[b]{r}70.000\\3.000\\ +\ .900\\ .050\\.008 \end{array}}{ \ \ \space73.958}\)

Example Question #245 : Number & Operations In Base Ten

What is \(\displaystyle 84.673\) in expanded form? 

 

 

Possible Answers:

\(\displaystyle 8\times1+4\times10+6\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)+3\times\left(\frac{1}{1000}\right)\)

\(\displaystyle 8\times10+4\times1+6\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)+3\times\left(\frac{1}{1000}\right)\)

\(\displaystyle 8\times10+4\times1+6\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)+3\times\left(\frac{1}{10000}\right)\)

\(\displaystyle 8\times10+4\times1+6\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{1000}\right)+3\times\left(\frac{1}{1000}\right)\)

\(\displaystyle 8\times10+4\times100+6\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)+3\times\left(\frac{1}{1000}\right)\)

Correct answer:

\(\displaystyle 8\times10+4\times1+6\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)+3\times\left(\frac{1}{1000}\right)\)

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 \(\displaystyle 10\).

\(\displaystyle 8\times10=80\)

 

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

\(\displaystyle 4\times1=4\)

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

\(\displaystyle 6\times\frac{1}{10}=.6\)

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

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

\(\displaystyle 3\) is in the thousandths place, so we will multiply by \(\displaystyle \frac{1}{1000}\).

\(\displaystyle 3\times\frac{1}{1000}=.003\)

Then we add the products together. 

\(\displaystyle \frac{\begin{array}[b]{r}80.000\\4.000\\ +\ .600\\ .070\\.003 \end{array}}{ \ \ \space84.673}\)

Example Question #61 : Read And Write Decimals To Thousandths Using Base Ten Numerals, Number Names, And Expanded Form: Ccss.Math.Content.5.Nbt.A.3a

What is \(\displaystyle 94.525\) in expanded form? 

 

 

Possible Answers:

\(\displaystyle 9\times1+4\times10+5\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)+5\times\left(\frac{1}{10000}\right)\)

\(\displaystyle 9\times10+4\times1+5\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)+5\times\left(\frac{1}{1000}\right)\)

\(\displaystyle 9\times10+4\times1+5\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{1000}\right)+5\times\left(\frac{1}{1000}\right)\)

\(\displaystyle 9\times10+4\times10+5\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)+5\times\left(\frac{1}{1000}\right)\)

\(\displaystyle 9\times10+4\times100+5\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)+5\times\left(\frac{1}{1000}\right)\)

Correct answer:

\(\displaystyle 9\times10+4\times1+5\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)+5\times\left(\frac{1}{1000}\right)\)

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 \(\displaystyle 1\)

\(\displaystyle 4\times1=4\)

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

\(\displaystyle 5\times\frac{1}{10}=.5\)

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

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

\(\displaystyle 5\) is in the thousandths place, so we will multiply by \(\displaystyle \frac{1}{1000}\).

\(\displaystyle 5\times\frac{1}{1000}=.005\)

Then we add the products together. 

\(\displaystyle \frac{\begin{array}[b]{r}90.000\\4.000\\ +\ .500\\ .020\\.005 \end{array}}{ \ \ \space94.525}\)

Example Question #62 : Read And Write Decimals To Thousandths Using Base Ten Numerals, Number Names, And Expanded Form: Ccss.Math.Content.5.Nbt.A.3a

What is \(\displaystyle 28.278\) in expanded form? 

 

 

Possible Answers:

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

\(\displaystyle 2\times10+8\times1+2\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{10000}\right)\)

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

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

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

Correct answer:

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

Explanation:

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

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

\(\displaystyle 2\times10=20\)

 

\(\displaystyle 8\) is in the ones place, so we multiply by \(\displaystyle 1\)

\(\displaystyle 8\times1=8\)

\(\displaystyle 2\) 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. 

\(\displaystyle \frac{\begin{array}[b]{r}20.000\\8.000\\ +\ .200\\ .070\\.008 \end{array}}{ \ \ \space28.278}\)

Example Question #63 : Read And Write Decimals To Thousandths Using Base Ten Numerals, Number Names, And Expanded Form: Ccss.Math.Content.5.Nbt.A.3a

What is \(\displaystyle 49.754\) in expanded form? 

 

 

Possible Answers:

\(\displaystyle 4\times1+9\times10+7\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)\)

\(\displaystyle 4\times10+9\times100+7\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)\)

\(\displaystyle 4\times10+9\times1+7\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{1000}\right)+4\times\left(\frac{1}{1000}\right)\)

\(\displaystyle 4\times10+9\times1+7\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{10000}\right)\)

\(\displaystyle 4\times10+9\times1+7\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)\)

Correct answer:

\(\displaystyle 4\times10+9\times1+7\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)\)

Explanation:

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

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

\(\displaystyle 4\times10=40\)

 

\(\displaystyle 9\) is in the ones place, so we multiply by \(\displaystyle 1\)

\(\displaystyle 9\times1=9\)

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

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

\(\displaystyle 5\) 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. 

\(\displaystyle \frac{\begin{array}[b]{r}40.000\\9.000\\ +\ .700\\ .050\\.004 \end{array}}{ \ \ \space49.754}\)

Example Question #71 : Read And Write Decimals To Thousandths Using Base Ten Numerals, Number Names, And Expanded Form: Ccss.Math.Content.5.Nbt.A.3a

What is \(\displaystyle 76.148\) in expanded form? 

 

 

Possible Answers:

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

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

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

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

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

Correct answer:

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

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 \(\displaystyle 1\)

\(\displaystyle 6\times1=6\)

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

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

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

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

\(\displaystyle 8\) 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. 

\(\displaystyle \frac{\begin{array}[b]{r}70.000\\6.000\\ +\ .100\\ .040\\.008 \end{array}}{ \ \ \space76.148}\)

Example Question #71 : Read And Write Decimals To Thousandths Using Base Ten Numerals, Number Names, And Expanded Form: Ccss.Math.Content.5.Nbt.A.3a

What number is two hundred fifty-three and eighty-six hundredths?

Possible Answers:

\(\displaystyle 253.084\)

\(\displaystyle 253.86\)

\(\displaystyle 25\textup,384\)

\(\displaystyle 253.086\)

\(\displaystyle 25\textup,386\)

Correct answer:

\(\displaystyle 253.86\)

Explanation:

In number form, two hundred fifty-three and eighty-six hundredths is \(\displaystyle 253.86\). The "and" signifies the decimal, and "hundredths" signifies the place value of the last decimal number. 

Example Question #72 : Read And Write Decimals To Thousandths Using Base Ten Numerals, Number Names, And Expanded Form: Ccss.Math.Content.5.Nbt.A.3a

What number is seven hundred forty-two and sixty-six hundredths?

 

Possible Answers:

\(\displaystyle 74\textup,266\)

\(\displaystyle 742.66\)

\(\displaystyle 742.066\)

\(\displaystyle 74.266\)

\(\displaystyle 7.4266\)

Correct answer:

\(\displaystyle 742.66\)

Explanation:

In number form, seven hundred forty-two and sixty-six hundredths is \(\displaystyle 742.66\). The "and" signifies the decimal, and "hundredths" signifies the place value of the last decimal number. 

Example Question #73 : Read And Write Decimals To Thousandths Using Base Ten Numerals, Number Names, And Expanded Form: Ccss.Math.Content.5.Nbt.A.3a

What number is three hundred twenty-four and thirty-seven hundredths?

 

Possible Answers:

\(\displaystyle 3204.37\)

\(\displaystyle 324.37\)

\(\displaystyle 324.037\)

\(\displaystyle 32.437\)

\(\displaystyle 32\textup,437\)

Correct answer:

\(\displaystyle 324.37\)

Explanation:

In number form, three hundred twenty-four and thirty-seven hundredths is \(\displaystyle 324.37\). The "and" signifies the decimal, and "hundredths" signifies the place value of the last decimal number. 

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