Tenths and Hundredths

4th Grade MathFractions and Decimals4 pages

About this worksheet

Tenths and hundredths work for 4th grade that ties fractions to decimal notation, covering Common Core 4.NF.5, 4.NF.6 and 4.NF.7. A worked row (4/10 = 40/100 = 0.40) opens a conversion table for 7/10, 2/10, 9/10 and 5/10. Students then add mixed-denominator pairs like 6/10 + 23/100 with a printed tip on converting first, compare six decimal pairs from 0.6 versus 0.58 to 0.32 versus 0.23, and finish with Maya's two ribbons, 0.7 meters against 68/100 meters. Worked answers follow.

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Curriculum objectives covered

4.NF.5

โ€œExpress a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.โ€

The conversion column in Part 1 and all four mixed-denominator sums in Part 2, which use the standard's own 3/10 + 4/100 example as the printed strategy tip.

4.NF.6

โ€œUse decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.โ€

The decimal column in Part 1 and the decimal forms the ribbon problem demands in question 15a.

4.NF.7

โ€œCompare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.โ€

The six comparisons in Part 3 and the 0.7-versus-0.68 ribbon comparison.

What's inside this worksheet

Part 1: Equivalent Fractions and Decimals

A table rewrites 7/10, 2/10, 9/10 and 5/10 as hundredths and as decimals, following the worked example 4/10 = 40/100 = 0.40.

Part 2: Adding Tenths and Hundredths

Four sums pair a tenth with a hundredth: 6/10 + 23/100, 4/100 + 5/10, 8/10 + 15/100 and 30/100 + 7/10. Each has show-work space, and the callout demonstrates 3/10 + 4/100 as 30/100 + 4/100 = 34/100 = 0.34.

Part 3: Comparing Decimals

Six blanks take >, < or =. The pair 0.70 versus 0.7 checks whether students think a trailing zero changes value, and 0.09 versus 0.2 checks place against digit size.

Part 4: Real-World Math Challenge

Maya's blue ribbon is 0.7 meters and her yellow ribbon is 68/100 meters. Students compare them as decimals, then total both lengths in hundredths of a meter.

How teachers use it

Bridge lesson

Use this the week you move from fraction notation to decimals. Part 1's table makes the equivalence visible before any rules get stated.

Misconception hunt

Collect Part 3 and tally the answers to 0.45 versus 0.5. Longer-means-bigger thinking shows up there before anywhere else.

Quick partner task

The ribbon problem works as a two-person finish: one converts, one adds, both check the comparison.

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