Converting Fractions to Decimals for 5th Grade: Division and Number Lines

Converting fractions to decimals helps us compare fractions, use calculators, and work with measurements that are given in decimal form. In Grade 5, students convert fractions to decimals by dividing the numerator by the denominator (since \(\frac{a}{b} = a \div b\)) or by writing an equivalent fraction with a denominator that is a power of 10 (10, 100, 1000), which makes the decimal form obvious.

There are two main methods: (1) Division: \(3 \div 4 = 0.75\), so \(\frac{3}{4} = 0.75\). (2) Equivalent fractions: If we can write the fraction with a denominator of 10, 100, or 1000, we read the decimal directly. For example, \(\frac{1}{5} = \frac{2}{10} = 0.2\). Some fractions produce repeating decimals (e.g., \(\frac{1}{3} = 0.333…\)); in Grade 5 we often round or use a bar notation for repeating decimals.

DETAILED EXPLANATION

Method 1 — Division: \(\frac{a}{b} = a \div b\). Perform long division; place the decimal point in the quotient above the decimal point in the dividend.

Method 2 — Equivalent fractions: Write the fraction with denominator 10, 100, or 1000. Example: \(\frac{3}{4} = \frac{75}{100} = 0.75\).

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Common conversions: \(\frac{1}{2} = 0.5\), \(\frac{1}{4} = 0.25\), \(\frac{3}{4} = 0.75\), \(\frac{1}{5} = 0.2\), \(\frac{1}{10} = 0.1\).

WORKED EXAMPLES WITH STEP BY STEP SOLUTIONS

Example 1

Convert \(\frac{3}{4}\) to a decimal.

Solutions:

Step 1: A fraction represents division: \(\frac{3}{4} = 3 \div 4\).

Step 2: Divide 3 ÷ 4. Set up: 4 ) 3.00

Step 3: 4 does not go into 3, so use 30 (tenths). 4 goes into 30 seven times (4 × 7 = 28). Subtract: 30 − 28 = 2. Bring down 0: 20.

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Step 4: 4 goes into 20 five times (4 × 5 = 20). Subtract: 0.

Step 5: Quotient: 0.75. So \(\frac{3}{4} = 0.75\).

Answer: 0.75

Example 2

Convert \(\frac{1}{5}\) to a decimal.

Solutions:

Step 1: Write an equivalent fraction with denominator 10: \(\frac{1}{5} = \frac{2}{10}\) (multiply numerator and denominator by 2).

Step 2: \(\frac{2}{10}\) means 2 tenths, which is 0.2.

Step 3: So \(\frac{1}{5} = 0.2\).

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Answer: 0.2

Example 3

Maria ran \(\frac{2}{5}\) of a mile. Write this as a decimal.

Solutions:

Step 1: \(\frac{2}{5} = \frac{4}{10}\) (multiply numerator and denominator by 2).

Step 2: \(\frac{4}{10} = 0.4\).

Step 3: Alternatively: 2 ÷ 5 = 0.4.

Answer: 0.4 mile

Example 4

Convert \(\frac{7}{8}\) to a decimal.

Solutions:

Step 1: Divide 7 ÷ 8. 8 ) 7.000. 8 goes into 70 eight times (64), remainder 6. Bring down 0: 60. 8 goes into 60 seven times (56), remainder 4. Bring down 0: 40. 8 goes into 40 five times.

Step 2: Quotient: 0.875.

Answer: 0.875