Virginia SOL Math / Grade 5 / Number & Number Sense

5.NS.1

Relate, Compare & Order Fractions and Decimals

What you'll learn

  • Represent and name fractions and decimals through thousandths
  • Compare and order fractions and decimals using benchmarks and place value
  • Relate a fraction to its equivalent decimal form

Words to know

Decimal —
a number with digits to the right of a decimal point
Thousandth —
one of 1,000 equal parts, the third place after the point
Equivalent —
naming the same amount in different forms
Benchmark —
a familiar value such as 0, 1/2, or 1 used to compare
Place value —
the value a digit has because of its position

Why it matters Money, measurement, and data all mix fractions and decimals, so being able to compare and order them keeps our answers accurate.

Worked examples

Model ItI do

Compare 0.7 and 0.68.

Line up the place values: 0.70 and 0.68. The tenths are 7 and 6, and 7 is greater than 6, so 0.7 is greater than 0.68. We write 0.7 > 0.68.

Try It TogetherWe do

Order 3/5, 0.5, and 0.75 from least to greatest.

Rewrite each as a decimal: 3/5 = 0.6, 0.5 stays 0.5, and 0.75 stays 0.75. Comparing 0.5, 0.6, and 0.75 gives the order 0.5, 3/5, 0.75.

Now YouYou do

Write >, <, or = : 0.45 ___ 1/2.

Change 1/2 to a decimal, then compare place values. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Write 3/10 as a decimal.

  2. 2.Write >, <, or = : 0.5 ___ 0.4

  3. 3.Write 0.7 as a fraction with a denominator of 10.

On Level

The core Quick Check from the book.

  1. 1.Write 7/10 as a decimal.

  2. 2.Write >, <, or = : 0.9 ___ 0.89

  3. 3.Order from least to greatest: 0.3, 1/4, 0.35.

  4. 4.Write 0.250 as a fraction in simplest form.

  5. 5.Which is greater: 0.6 or 3/5?

Challenge

Stretch your thinking.

  1. 1.Order from least to greatest: 0.405, 2/5, 0.45.

  2. 2.Write >, <, or = : 0.375 ___ 3/8

  3. 3.Write 0.125 as a fraction in simplest form.