Chapter 12: worked solutions and marking guide
40 review answers and 40 exam answers
Chapter review solutions
How many tenths must be added to 0.3 to make one whole?
One whole is 10 tenths. Subtract 3 from 10 to find the missing parts.
On a number line from 0 to 1 divided into ten equal intervals, what decimal is at the 8th tick after 0?
Each interval is 0.1, so add 8 tenths to 0 to get 0.8.
Write 14/100 as a two-decimal-place number.
14 hundredths are 0.14.
Rename 0.6 as hundredths and write the equivalent decimal to two places.
Every tenth is ten hundredths; multiply the count by ten.
Write 0.14 as a fraction in simplest form.
0.14 = 14/100. Reduce by the common factor 2 to 7/50.
Write 18/25 as a decimal.
Rename 18/25 in tenths or hundredths (or divide numerator by denominator) to get 0.72.
Insert <, > or =: 0.63 ___ 0.91.
Compare 63 hundredths and 91 hundredths; 0.63 is less relative to 0.91.
Round 6.31 to the nearest tenth.
Use the two neighboring nearest tenth benchmarks, identify their midpoint, and round the original number 6.31 directly.
Write 4/10 as a decimal and explain its tenths digit.
4 equal tenths of the same whole are written 0.4.
On a number line from 5 to 6 divided into ten equal intervals, what decimal is at the 2nd tick after 5?
Each interval is 0.1, so add 2 tenths to 5 to get 5.2.
Write 70/100 as a two-decimal-place number.
70 hundredths are 0.70.
How many hundredths are in 2 tenths?
Each tenth consists of 10 hundredths; 2×10=20.
Write 0.09 as a fraction in simplest form.
0.09 = 9/100. Reduce by the common factor 1 to 9/100.
Write 3/4 as a decimal.
Rename 3/4 in tenths or hundredths (or divide numerator by denominator) to get 0.75.
Insert <, > or =: 0.76 ___ 0.41.
Compare 76 hundredths and 41 hundredths; 0.76 is greater relative to 0.41.
Round 1.15 to the nearest tenth.
Use the two neighboring nearest tenth benchmarks, identify their midpoint, and round the original number 1.15 directly.
How many tenths must be added to 0.6 to make one whole?
One whole is 10 tenths. Subtract 6 from 10 to find the missing parts.
On a number line from 3 to 4 divided into ten equal intervals, what decimal is at the 6th tick after 3?
Each interval is 0.1, so add 6 tenths to 3 to get 3.6.
Write 65/100 as a two-decimal-place number.
65 hundredths are 0.65.
Rename 0.8 as hundredths and write the equivalent decimal to two places.
Every tenth is ten hundredths; multiply the count by ten.
Write 0.76 as a fraction in simplest form.
0.76 = 76/100. Reduce by the common factor 4 to 19/25.
Write 1/2 as a decimal.
Rename 1/2 in tenths or hundredths (or divide numerator by denominator) to get 0.5.
Insert <, > or =: 0.49 ___ 0.39.
Compare 49 hundredths and 39 hundredths; 0.49 is greater relative to 0.39.
Round 2.33 to the nearest whole number.
Use the two neighboring nearest whole number benchmarks, identify their midpoint, and round the original number 2.33 directly.
How many tenths must be added to 0.4 to make one whole?
One whole is 10 tenths. Subtract 4 from 10 to find the missing parts.
On a number line from 3 to 4 divided into ten equal intervals, what decimal is at the 1st tick after 3?
Each interval is 0.1, so add 1 tenths to 3 to get 3.1.
Write 23/100 as a two-decimal-place number.
23 hundredths are 0.23.
Rename 0.4 as hundredths and write the equivalent decimal to two places.
Every tenth is ten hundredths; multiply the count by ten.
Write 0.42 as a fraction in simplest form.
0.42 = 42/100. Reduce by the common factor 2 to 21/50.
Write 3/5 as a decimal.
Rename 3/5 in tenths or hundredths (or divide numerator by denominator) to get 0.6.
Insert <, > or =: 0.85 ___ 0.14.
Compare 85 hundredths and 14 hundredths; 0.85 is greater relative to 0.14.
Round 1.60 to the nearest whole number.
Use the two neighboring nearest whole number benchmarks, identify their midpoint, and round the original number 1.60 directly.
Write 3/10 as a decimal and explain its tenths digit. Explain how place value or a model can check your result.
3 equal tenths of the same whole are written 0.3. A correct explanation should name the relevant fractional place values and verify the answer.
On a number line from 4 to 5 divided into ten equal intervals, what decimal is at the 7th tick after 4? Explain how place value or a model can check your result.
Each interval is 0.1, so add 7 tenths to 4 to get 4.7. A correct explanation should name the relevant fractional place values and verify the answer.
Write 88/100 as a two-decimal-place number. Explain how place value or a model can check your result.
88 hundredths are 0.88. A correct explanation should name the relevant fractional place values and verify the answer.
How many hundredths are in 1 tenth? Explain how place value or a model can check your result.
Each tenth consists of 10 hundredths; 1×10=10. A correct explanation should name the relevant fractional place values and verify the answer.
Write 0.22 as a fraction in simplest form. Explain how place value or a model can check your result.
0.22 = 22/100. Reduce by the common factor 2 to 11/50. A correct explanation should name the relevant fractional place values and verify the answer.
Write 3/4 as a decimal. Explain how place value or a model can check your result.
Rename 3/4 in tenths or hundredths (or divide numerator by denominator) to get 0.75. A correct explanation should name the relevant fractional place values and verify the answer.
Order 0.63, 0.77, and 0.17 from least to greatest. Explain how place value or a model can check your result.
Convert all to hundredths and sort the integer counts. A correct explanation should name the relevant fractional place values and verify the answer.
Round 8.93 to the nearest whole number. Explain how place value or a model can check your result.
Use the two neighboring nearest whole number benchmarks, identify their midpoint, and round the original number 8.93 directly. A correct explanation should name the relevant fractional place values and verify the answer.
Practice examination solutions
Write 5/10 as a decimal.
Rename 5/10 in tenths or hundredths (or divide numerator by denominator) to get 0.5.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Write 2 tenths and 1 hundredth as one decimal. Explain how place value or a model can check your result.
2 tenths is 20 hundredths, plus 1 more makes 21 hundredths. A correct explanation should name the relevant fractional place values and verify the answer.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
How many hundredths are in 4 tenths?
Each tenth consists of 10 hundredths; 4×10=40.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
On a number line from 1 to 2 divided into ten equal intervals, what decimal is at the 4th tick after 1?
Each interval is 0.1, so add 4 tenths to 1 to get 1.4.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Write 14/20 as a decimal.
Rename 14/20 in tenths or hundredths (or divide numerator by denominator) to get 0.7.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Write 47/100 as a two-decimal-place number.
47 hundredths are 0.47.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Write 78/100 as a two-decimal-place number.
78 hundredths are 0.78.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Round 9.67 to the nearest tenth.
Use the two neighboring nearest tenth benchmarks, identify their midpoint, and round the original number 9.67 directly.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Write 0.20 as a fraction in simplest form.
0.20 = 20/100. Reduce by the common factor 20 to 1/5.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Write 12/20 as a decimal.
Rename 12/20 in tenths or hundredths (or divide numerator by denominator) to get 0.6.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Explain why the decimal 0.4 is the same quantity as 4 tenths.
A decimal tenths digit counts the same equal parts as numerator 4 over denominator 10.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
Insert <, > or =: 0.67 ___ 0.41.
Compare 67 hundredths and 41 hundredths; 0.67 is greater relative to 0.41.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Write 98/100 as a two-decimal-place number.
98 hundredths are 0.98.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Insert <, > or =: 0.57 ___ 0.25.
Compare 57 hundredths and 25 hundredths; 0.57 is greater relative to 0.25.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Round 4.69 to the nearest whole number.
Use the two neighboring nearest whole number benchmarks, identify their midpoint, and round the original number 4.69 directly.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Insert <, > or =: 0.51 ___ 0.49.
Compare 51 hundredths and 49 hundredths; 0.51 is greater relative to 0.49.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Insert <, > or =: 0.16 ___ 0.13.
Compare 16 hundredths and 13 hundredths; 0.16 is greater relative to 0.13.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
On a number line from 3 to 4 divided into ten equal intervals, what decimal is at the 3rd tick after 3? Explain how place value or a model can check your result.
Each interval is 0.1, so add 3 tenths to 3 to get 3.3. A correct explanation should name the relevant fractional place values and verify the answer.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
On a number line from 2 to 3 divided into ten equal intervals, what decimal is at the 4th tick after 2?
Each interval is 0.1, so add 4 tenths to 2 to get 2.4.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Write 4 tenths and 3 hundredths as one decimal.
4 tenths is 40 hundredths, plus 3 more makes 43 hundredths.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Write 86/100 as a two-decimal-place number.
86 hundredths are 0.86.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Write 1/10 as a decimal and explain its tenths digit.
1 equal tenths of the same whole are written 0.1.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Write 0.93 as a fraction in simplest form. Explain how place value or a model can check your result.
0.93 = 93/100. Reduce by the common factor 1 to 93/100. A correct explanation should name the relevant fractional place values and verify the answer.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
Round 9.31 to the nearest tenth. Explain how place value or a model can check your result.
Use the two neighboring nearest tenth benchmarks, identify their midpoint, and round the original number 9.31 directly. A correct explanation should name the relevant fractional place values and verify the answer.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
Write 5/20 as a decimal.
Rename 5/20 in tenths or hundredths (or divide numerator by denominator) to get 0.25.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
How many tenths must be added to 0.9 to make one whole?
One whole is 10 tenths. Subtract 9 from 10 to find the missing parts.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Write 22/100 as a two-decimal-place number. Explain how place value or a model can check your result.
22 hundredths are 0.22. A correct explanation should name the relevant fractional place values and verify the answer.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
How many hundredths are in 7 tenths?
Each tenth consists of 10 hundredths; 7×10=70.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Write 0.55 as a fraction in simplest form.
0.55 = 55/100. Reduce by the common factor 5 to 11/20.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
On a number line from 2 to 3 divided into ten equal intervals, what decimal is at the 3rd tick after 2?
Each interval is 0.1, so add 3 tenths to 2 to get 2.3.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Explain why the decimal 0.3 is the same quantity as 3 tenths.
A decimal tenths digit counts the same equal parts as numerator 3 over denominator 10.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
Write 6/25 as a decimal. Explain how place value or a model can check your result.
Rename 6/25 in tenths or hundredths (or divide numerator by denominator) to get 0.24. A correct explanation should name the relevant fractional place values and verify the answer.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
Write 0.51 as a fraction in simplest form.
0.51 = 51/100. Reduce by the common factor 1 to 51/100.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
On a number line from 5 to 6 divided into ten equal intervals, what decimal is at the 5th tick after 5?
Each interval is 0.1, so add 5 tenths to 5 to get 5.5.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Write 0.95 as a fraction in simplest form.
0.95 = 95/100. Reduce by the common factor 5 to 19/20.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Round 6.56 to the nearest tenth.
Use the two neighboring nearest tenth benchmarks, identify their midpoint, and round the original number 6.56 directly.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Round 8.97 to the nearest whole number.
Use the two neighboring nearest whole number benchmarks, identify their midpoint, and round the original number 8.97 directly.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Order 0.98, 0.57, and 0.09 from least to greatest. Explain how place value or a model can check your result.
Convert all to hundredths and sort the integer counts. A correct explanation should name the relevant fractional place values and verify the answer.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
Write 9/10 as a decimal and explain its tenths digit.
9 equal tenths of the same whole are written 0.9.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
How many hundredths are in 1 tenth?
Each tenth consists of 10 hundredths; 1×10=10.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.