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All courses Math Foundations · MF.RN.4 10 of 60
Compare and order rational numbers written as fractions, decimals, and percents.

Compare two rational numbers in different forms

Problem
Compare \(3/4\) and \(0.72\), and write the true comparison statement.
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Hint

Since 0.72 is already a decimal, start by converting 3/4 to a decimal using 3 ÷ 4.

Fractions and decimals can be compared best when they are written on the same scale. Then compare the hundredths.

Solution walkthrough

01

Put both values in decimal form

\[3/4~=~3~/~4\]

The other value is already decimal 0.72, so convert the fraction by dividing its numerator by its denominator.

02

Convert three fourths

\[3~/~4~=~0.75\]

Four goes into 3.00 seventy-five hundredths, so 3/4 equals 0.75.

03

Align place values

\[0.75~\text{versus}~0.72\]

Both decimals have 0 ones and 7 tenths, so compare their hundredths digits.

04

Compare the hundredths

\[5~\text{hundredths}~>~2~\text{hundredths}\]

With equal tenths, 75 hundredths is greater than 72 hundredths.

05

Check by subtraction

\[0.75~-~0.72~=~0.03~>~0\]

The positive difference confirms that 3/4 is greater by three hundredths.

06

Write the true statement

\[3/4~>~0.72\]

Because 3/4 equals 0.75 and 0.75 exceeds 0.72, the true comparison is 3/4 > 0.72.

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Another way

  1. Convert 3/4 to 75% and 0.72 to 72%; 75% is greater.

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Common mistake

Do not compare the digits 3 and 72 directly. First express the fraction and decimal on the same scale.

Solution walkthrough video