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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
Write <, >, or = to make this statement true: 3/4 ₀.72
Your answer
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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

Use decimals for both numbers

\[3/4~\text{\_\_\_}~0.72\]

The numbers are written in different forms, so it helps to put them on the same scale. Since 0.72 is already a decimal, convert 3/4 to a decimal.

02

Convert 3/4 to a decimal

\[3/4~=~0.75\]

Three fourths means 3 ÷ 4. That equals 0.75.

03

Compare the decimal values

\[0.75~>~0.72\]

0.75 is 75 hundredths, and 0.72 is 72 hundredths. Since 75 hundredths is greater than 72 hundredths, 0.75 is greater.

04

Write the true comparison statement

\[3/4~>~0.72\]

Because 3/4 equals 0.75, the correct symbol is >.

+

Another way

  1. Convert 0.72 to a fraction: 0.72 = 72/100 = 18/25. Then compare 3/4 and 18/25 by using common denominators or cross-products: 3 × 25 = 75 and 18 × 4 = 72, so 3/4 > 18/25.

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Common mistake

A common mistake is comparing the notation instead of the value, like thinking 3/4 must be smaller because 3 is less than 72. You have to compare 3/4 and 0.72 on the same scale first, and 3/4 is 0.75.