Fractions to Decimals

Getting Started

The student does not understand how to represent a fraction in decimal form.

The student does not understand how to write a fraction as a decimal. The student writes each decimal in the form numerator/denominator (e.g., as 8.100).

What is the meaning of the decimal point?

What does the number to the left of the decimal point represent? What does the number to the right of the decimal point represent?

Can you show me the tenths place in the number 0.57? Where is the hundredths place?

What is the value of the six in the number 0.62? What is the value of the two?

Model for the student how to read and write fractions with denominators of 10 and 100 in decimal form. Guide the student to understand that the number of digits to the right of the decimal indicates the number of zeros in the denominator of the fraction. Begin with fractions such as and . Next, introduce fractions requiring placement of zeros in the decimal form such as and . Finally, ask the student to write fractions greater than one in decimal form (e.g., and ).

Instruct the student that the places in decimal notation have the same correspondence as places in whole numbers (e.g., places to the left are ten times greater than the place to their immediate right). Connect the student’s understanding of money (e.g., a dime is ten times the value of a penny, a penny is of a dollar) to the relationship among decimals, place value, and corresponding fractions.

Provide opportunities for the student to use place value mats, blocks, and 10 by 10 grids to represent fractions with denominators of 10 and 100 as decimals.

Consider implementing the MFAS task Decimals to Fractions.

Making Progress

The student makes errors when there is a zero in the tenths or hundredths place.

The student demonstrates some understanding of representing a fraction as a decimal but makes errors when a zero is in the tenths or hundredths place.

The student writes as 0.8.



The student writes as 0.002.

Can you explain how 0.08 and 0.8 are different? What is the value of the digit eight in each of those numbers?

Can you read aloud the number? How many decimal places should be after the zero?

Can you write the fraction as a decimal? How many decimal places will there be?

How would you write three-tenths as a decimal? How would you write three-hundredths?

Instruct the student that the places in decimal notation have the same correspondence as places in whole numbers (e.g., places to the left are ten times greater than the place to their immediate right). Connect the student’s understanding of money (e.g., a dime is ten times the value of a penny, a penny is of a dollar) to the relationship among decimals, place value, and corresponding fractions. Provide additional practice with fractions such as and , and and and .

Consider implementing the MFAS task Hundredths and Tenths.

Got It

The student provides complete and correct responses to all components of the task.

The student correctly uses decimal notation to write each fraction: as 0.08, as 0.4, as 0.20, and as 0.7.



The student writes as 0.2 but is able to explain that 0.2 is equivalent to 0.20 and the decimal notation for  would be 0.20.

Can you write in decimal form? How does it compare to the decimal form of ? How about ?

Is the same as ? How do you know that? Can you represent this visually?

How many times greater is 0.5 than 0.05? (Hint if needed: Think of money.)

Challenge the student to add decimals by expressing them as fractions with like denominators of 10 or 100 (e.g., add 0.6 to 0.14 by writing + = ).

Ask the student to compare decimals to the hundredths place by reasoning about their size (e.g., 0.7 and 0.09 or 0.4 and 0.40).

Partner the student to work with a “Making Progress” student to explain how decimal notation is used to write fractions as decimals with tenths and hundredths.

Challenge the student to write fractions as decimals through the thousandths place.

Consider implementing the MFAS task Using Benchmark Fractions on a Number Line.