Grade: Grade 5 Subject: Mathematics Unit: Decimals SAT: Algebra ACT: Math

Converting Decimals and Fractions

Decimals and fractions are two ways to write the same thing - parts of a whole! Learn to switch between them like a pro.

The Connection Between Decimals and Fractions

Two Ways to Show the Same Amount

0.5 and 1/2 represent the exact same amount - half of something! Decimals use place value (tenths, hundredths) while fractions show parts out of a whole number.

Think about money: $0.50 (fifty cents) is the same as 1/2 of a dollar. Both are correct - just different ways of writing it!

Ones . Tenths (1/10) Hundredths (1/100) Thousandths (1/1000)
0 . 5 0 0

0.5 = 5 tenths = 5/10 = 1/2

Key Insight: The place value tells you the denominator! Tenths place = denominator of 10, hundredths place = denominator of 100, and so on.

Converting Decimals to Fractions

1 Read the decimal using place value

Identify the last digit's place: is it tenths? Hundredths? Thousandths?

2 Write the digits as the numerator

The numbers after the decimal become the top of the fraction.

3 Write the place value as the denominator

10 for tenths, 100 for hundredths, 1000 for thousandths.

4 Simplify if possible

Divide top and bottom by their greatest common factor.

Example: 0.7
0.7 →
7 10

7 is in the tenths place

Already simplified!

Example: 0.25
0.25 →
25 100
→
1 4

25 in hundredths place

Divide by 25 to simplify

Example: Convert 0.125 to a fraction
  1. Place value: The 5 is in the thousandths place
  2. Numerator: 125
  3. Denominator: 1000
  4. Simplify: 125/1000 = 25/200 = 5/40 = 1/8
0.125 =
125 1000
=
1 8

Converting Fractions to Decimals

The Division Method

A fraction IS a division problem! The line means "divided by." So 3/4 means 3 ÷ 4.

1 Set up the division

Divide the numerator by the denominator: top ÷ bottom

2 Add a decimal point and zeros

Add .0 or .00 to the numerator so you can continue dividing

3 Divide until it ends or repeats

Some fractions become terminating decimals (they end), others repeat forever

Example: 3/4
3 4
→ 3 ÷ 4 → 0.75

3.00 ÷ 4 = 0.75

Terminating decimal

Example: 1/3
1 3
→ 1 ÷ 3 → 0.333...

1.00 ÷ 3 = 0.333...

Repeating decimal

Shortcut for Common Denominators:
  • If denominator is 10: move decimal 1 place left (7/10 = 0.7)
  • If denominator is 100: move decimal 2 places left (25/100 = 0.25)
  • If denominator is 5: multiply by 2/2 to get tenths (3/5 = 6/10 = 0.6)
  • If denominator is 4: multiply by 25/25 to get hundredths (3/4 = 75/100 = 0.75)

Common Conversions to Memorize

These fraction-decimal pairs come up so often that it's worth memorizing them!

1/2
0.5
50%
1/4
0.25
25%
3/4
0.75
75%
1/5
0.2
20%
2/5
0.4
40%
3/5
0.6
60%
4/5
0.8
80%
1/8
0.125
12.5%
1/10
0.1
10%
1/3
0.333...
33.3%
2/3
0.666...
66.6%
1/6
0.166...
16.6%
SAT/ACT Tip: Knowing these conversions by heart will save you valuable time on standardized tests. When you see 0.75 in a problem, immediately think "3/4" - sometimes the fraction form makes calculations easier!

Conversion Calculator

Practice converting between decimals and fractions!

Convert Decimal to Fraction

Decimal:
Enter a decimal and click "Convert to Fraction"

Convert Fraction to Decimal

Enter a fraction and click "Convert to Decimal"

Practice Problems

Test your conversion skills! Click the correct answer.

Problem 1: Convert 0.4 to a fraction

Problem 2: Convert 3/5 to a decimal

Problem 3: Convert 0.125 to a fraction

Problem 4: Convert 7/8 to a decimal

Problem 5: Which decimal equals 3/8?

Problem 6: Convert 0.8 to a simplified fraction

Problem 7: Which is larger: 0.6 or 5/8?

Problem 8: Convert 0.333... (repeating) to a fraction

Check Your Understanding

To convert a decimal to a fraction, you use the place value as the:

To convert a fraction to a decimal, you:

What makes 1/3 different from 1/4 when converted to decimals?

What We Learned

🔢

Decimal → Fraction

Use place value for denominator, simplify the result

➗

Fraction → Decimal

Divide top by bottom (numerator ÷ denominator)

🔄

Same Value

0.5 = 1/2 = 50% - three ways to show the same amount

📝

Memorize Common Ones

Know your halves, quarters, fifths, and eighths!

Key Takeaway: Converting between decimals and fractions is all about understanding that both represent parts of a whole. Master these conversions and you'll be able to choose whichever form makes a problem easier to solve!

Next Steps

  • Practice the common conversions until you know them by heart
  • Try converting more complex decimals (like 0.375)
  • Learn to recognize when fractions will repeat vs. terminate
  • Use these skills when comparing fractions and decimals!