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All courses Math Foundations · MF.NS.1 1 of 60

Compare, order, and estimate whole numbers and decimals using place value and magnitude sense.

Compare close decimals

Problem

Compare the decimals 6.407 and 6.47. Write one true comparison statement using both decimals and either < or >.

Your answer

Choose an answer A 6.407 < 6.47 B 6.407 > 6.47 C 6.47 < 6.407 D 6.407 = 6.47

GOZUNTA

More practice for Math Foundations and California Math I–III.

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Hint

Rewrite 6.47 as 6.470 so the decimal places line up, then compare from left to right.

For close decimals, the first place value that is different decides which number is greater.

Solution walkthrough

Line up the decimal places

\[6.407~\text{and}~6.470\]

Writing 6.47 as 6.470 makes the place values line up. A trailing zero does not change the value.

Compare from left to right

\[\text{ones}:~6~=~6,~\text{tenths}:~4~=~4\]

The numbers match in the ones and tenths places, so those places do not decide which decimal is larger.

Use the first place that differs

\[\text{hundredths}:~0~<~7\]

The first difference is in the hundredths place. Since 0 hundredths is less than 7 hundredths, 6.407 is less than 6.470.

Write the true comparison statement

\[6.407~<~6.47\]

This uses the original decimals and the correct inequality symbol.

Another way

Think of them in thousandths: 6.407 is 6 and 407 thousandths, and 6.47 is 6 and 470 thousandths. Since 407 < 470, 6.407 < 6.47.

Common mistake

Looking only at the last digit and saying 7 is bigger than 0, so 6.407 must be bigger. That skips the more important hundredths place, where 0 hundredths is less than 7 hundredths.